# Publications

### 2021

Several nanotubular structures from chalcogenide-based misfit layer compounds (MLC) were reported in recent years. MLCs consist of a stacking of two alternating and dissimilar (2D) atomic layers, e. g. one with rocksalt structure (MX) and the other- TX2 – with hexagonal layer structure. The layers are held together by weak van der Waals forces, i. e. they can be exfoliated with scotch-tape. Furthermore, in analogy to intercalation compounds, partial charge transfer between the layers with dissimilar work function results also in polar forces between the MX and TX2 layers. The mismatch between the alternating (asymmetric) layers and the seaming of the dangling bonds at the edges drives them to form tubular (and also scroll-like) structures. New structural characterization whereby the nanotubes were bisected into lamella via focused ion beam and examined by TEM, are reported.

### 2020

An increasing current through a superconductor can result in a discontinuous increase in the differential resistance at the critical current. This critical current is typically associated either with breaking of Cooper-pairs or with the onset of collective motion of vortices. Here we measure the current-voltage characteristics of superconducting films at low temperatures and high magnetic fields. Using heat-balance considerations we demonstrate that the current-voltage characteristics are well explained by electron overheating enhanced by the thermal decoupling of the electrons from the host phonons. By solving the heat-balance equation we are able to accurately predict the critical currents in a variety of experimental conditions. The heat-balance approach is universal and applies to diverse situations from critical currents to climate change. One disadvantage of the universality of this approach is its insensitivity to the details of the system, which limits our ability to draw conclusions regarding the initial departure from equilibrium.

### 2019

We measured current-voltage characteristics on both sides of the magnetic-field-driven superconductor-insulator transition. On both sides, these show strong nonlinearities leading to a conduction branch that is independent of phonon temperature. We show that a picture of electron overheating can quantitatively explain our data over the entire magnetic field range. We find that electron-phonon coupling strength remains roughly constant throughout the insulating state and across the superconductor-insulator transition, dropping dramatically as the magnetic field approaches zero. Our findings shed light on the origin of the highly debated saturation of resistance at low temperature, which has been interpreted by some as evidence for a new anomalous metallic phase and by others as a result of electrons failing to cool down. At the heart of this treatment lies the assumption that resistance is a function of electron temperature and not the phononic one. The applicability of this framework implies that the conduction mechanism, present in the superconductor and throughout the insulating phase, does not rely on a phonon bath.

Dissipationless charge transport is one of the defining properties of superconductors, but the interplay between dimensionality and disorder in determining the onset of dissipation remains an open theoretical and experimental problem. Here, we present measurements of the dissipation phase diagrams of superconductors in the two-dimensional limit, layer by layer, down to a monolayer in the presence of temperature (T), magnetic field (B) and current (I) in 2H-NbSe2. Our results show that the phase diagram strongly depends on the thickness even in the two-dimensional limit. At four layers we can define a finite region in the I-B phase diagram where dissipationless transport exists at T = 0. At even smaller thicknesses, this region shrinks in area until in a monolayer it approaches a single point defined by T = B = I = 0. In applied field, we show that time-dependent Ginzburg-Landau simulations that describe dissipation by vortex motion qualitatively reproduce our experimental I-B phase diagram. Last, we show that by using non-local transport and time-dependent Ginzburg-Landau calculations that we can engineer charge flow and create phase boundaries between dissipative and dissipationless transport regions in a single sample, demonstrating control over non-equilibrium states of matter.

For more than two decades, there have been reports on an unexpected metallic state separating the established superconducting and insulating phases of thin-film superconductors. To date, no theoretical explanation has been able to fully capture the existence of such a state for the large variety of superconductors exhibiting it. Here, we show that for two very different thin-film superconductors, amorphous indium oxide and a single crystal of 2H-NbSe2, this metallic state can be eliminated by adequately filtering external radiation. Our results show that the appearance of temperature-independent, metallic-like transport at low temperatures is sufficiently described by the extreme sensitivity of these superconducting films to external perturbations. We relate this sensitivity to the theoretical observation that, in two dimensions, superconductivity is only marginally stable.

In most superconductors, the transition to the superconducting state is driven by the binding of electrons into Cooper pairs(1). The condensation of these pairs into a single, phase-coherent, quantum state takes place at the same time as their formation at the transition temperature, T-c. A different scenario occurs in some disordered, amorphous, superconductors: instead of a pairing-driven transition, incoherent Cooper pairs first preform above T-c, causing the opening of a pseudogap, and then, at T-c, condense into the phase-coherent superconducting state(2-11). Such a two-step scenario implies the existence of a new energy scale, Delta(c), driving the collective superconducting transition of the preformed pairs(2-6). Here we unveil this energy scale by means of Andreev spectroscopy(5,12) in super-conducting thin films of amorphous indium oxide. We observe two Andreev conductance peaks at +/-Delta(c) that develop only below T-c and for highly disordered films on the verge of the transition to insulator. Our findings demonstrate that amorphous superconducting films provide prototypical disordered quantum systems to explore the collective superfluid transition of preformed Cooper pairs.

Recent experimental reports suggested the existence of a finite-temperature insulator in the vicinity of the superconductor-insulator transition. The rapid decay of conductivity over a narrow temperature range was theoretically linked to both a finite-temperature transition to a many-body-localized state, and to a charge-Berezinskii-Kosterlitz-Thouless transition. Here we report of low-frequency noise measurements of such insulators to test for many-body localization. We observed a huge enhancement of the low-temperatures noise when exceeding a threshold voltage for nonlinear conductivity and discuss our results in light of the theoretical models.

### 2018

Highly disordered superconductors have a rich phase diagram. At a moderate magnetic field (B) the samples go through the superconductor-insulator quantum phase transition. In the insulating phase, the resistance increases sharply with B up to a magnetoresistance peak beyond which the resistance drops with B. In this paper we follow the temperature (T) evolution of this magnetoresistance peak. We show that as T is reduced, the peak appears at lower B's approaching the critical field of the superconductor-insulator transition. Due to experimental limitations we are unable to determine whether the T = 0 limiting position of the peak matches that of the critical field or is at comparable but slightly higher B. We show that, although the peak appears at different B values, its resistance follows an activated T dependence over a large T range with a prefactor that is very similar to the quantum of resistance for Cooper pairs.

It is observed that many thin superconducting films with not too high disorder level (generally RN/□

### 2017

Thin films of amorphous indium oxide undergo a magnetic field driven superconducting to insulator quantum phase transition. In the insulating phase, the current-voltage characteristics show large current discontinuities due to overheating of electrons. We show that the onset voltage for the discontinuities vanishes as we approach the quantum critical point. As a result, the insulating phase becomes unstable with respect to any applied voltage making it, at least experimentally, immeasurable. We emphasize that unlike previous reports of the absence of linear response near quantum phase transitions, in our system, the departure from equilibrium is discontinuous. Because the conditions for these discontinuities are satisfied in most insulators at low temperatures, and due to the decay of all characteristic energy scales near quantum phase transitions, we believe that this instability is general and should occur in various systems while approaching their quantum critical point. Accounting for this instability is crucial for determining the critical behavior of systems near the transition.

The magnetic field driven superconductor-to-insulator transition in thin films is theoretically understood in terms of the notion of vortex-charge duality symmetry. The manifestation of such symmetry is the exchange of roles of current and voltage between the superconductor and the insulator. While experimental evidence obtained from amorphous indium oxide films supported such duality symmetry, it is shown to be broken, counterintuitively, at low temperatures where the insulating phase exhibits discontinuous current-voltage characteristics. Here, we demonstrate that it is possible to effectively restore duality symmetry by driving the system beyond the discontinuity into its high current, far from equilibrium, state.

### 2016

Highly disordered superconductors, in the magnetic-field-driven insulating state, can show discontinuous current-voltage characteristics. Electron overheating has been shown to give a consistent description of this behavior, but there are other possible explanations, including an electric-field-induced breakdown of the insulating state and a novel “superinsulating” state. We present ac-dc crossed measurements, in which the application of a dc voltage is applied along our sample, while a small ac voltage is applied in the transverse direction. We varied the dc voltage and observed a simultaneous discontinuity in both ac and dc currents. We show that the inferred electron temperature in the transverse measurement matches that in the longitudinal one, strongly supporting electron overheating as the source of observed current-voltage characteristics. Our measurement technique may be applicable as a method of probing electron overheating in various other physical systems, which show discontinuous or nonlinear current-voltage characteristics.

We study magneto-transport properties of several amorphous Indium oxide nanowires of different widths. The wires show superconducting transition at zero magnetic field, but, there exist a finite resistance at the lowest temperature. The R(T) broadening was explained by available phase slip models. At low field, and far below the superconducting critical temperature, the wires with diameter equal to or less than 100 nm, show negative magnetoresistance (nMR). The magnitude of nMR and the crossover field are found to be dependent on both temperature and the cross-sectional area. We find that this intriguing behavior originates from the interplay between two field dependent contributions.

We study the low-temperature magnetotransport properties of several highly disordered amorphous indium oxide (a:InO) samples. Simultaneously fabricated devices comprising a two-dimensional (2D) film and 10-mu m-long wires of different widths were measured to investigate the effect of size as we approach the 1D limit, which is around 4 times the correlation length, and happens to be around 100 nm for a:InO. The film and the wires showed magnetic field (B)-induced superconductor to insulator transition (SIT). In the superconducting side, the resistance increased with decrease in wire width, whereas an opposite trend is observed in the insulating side. We find that this effect can be explained in light of charge-vortex duality picture of the SIT. Resistance of the 2D film follows an activated behavior over the temperature (T), whereas, the wires show a crossover from the high-T-activated to a T-independent behavior. At high-temperature regime the wires' resistance follow the film's until they deviate and became independent of T. We find that the temperature at which this deviation occurs evolves with the magnetic field and the width of the wire, which show the effect of finite size on the transport.

In certain disordered superconductors, upon increasing the magnetic field, superconductivity terminates with a direct transition into an insulating phase. This phase is comprised of localized Cooper pairs and is termed a Cooper-pair insulator. The current-voltage characteristics measured in this insulating phase are highly nonlinear and, at low temperatures, exhibit abrupt current jumps. Increasing the temperature diminishes the jumps until the current-voltage characteristics become continuous. We show that a direct correspondence exists between our system and systems that undergo an equilibrium, second-order, phase transition. We illustrate this correspondence by comparing our results to the van der Waals equation of state for the liquid-gas mixture. We use the similarities to identify a critical point where an out of equilibrium second-order-like phase transition occurs in our system. Approaching the critical point, we find a power-law behavior with critical exponents that characterizes the transition.

### 2015

In superconductors the zero-resistance current-flow is protected from dissipation at finite temperatures (T) by virtue of the short-circuit condition maintained by the electrons that remain in the condensed state. The recently suggested finite-T insulator and the "superinsulating" phase are different because any residual mechanism of conduction will eventually become dominant as the finite-T insulator sets-in. If the residual conduction is small it may be possible to observe the transition to these intriguing states. We show that the conductivity of the high magnetic-field insulator terminating superconductivity in amorphous indium-oxide exhibits an abrupt drop, and seem to approach a zero conductance at T

We conducted a systematic study of the disorder dependence of the termination of superconductivity, at high magnetic fields (B), of amorphous indium oxide films. Our lower disorder films show conventional behavior where superconductivity is terminated with a transition to a metallic state at a well-defined critical field, B-c2. Our higher-disorder samples undergo a B-induced transition into a strongly insulating state, which terminates at higher B's forming an insulating peak. We demonstrate that the B terminating this peak coincides with B-c2 of the lower disorder samples. Additionally, we show that, beyond this field, these samples enter a different insulating state in which the magnetic field dependence of the resistance is weak. These results provide crucial evidence for the importance of Cooper-pairing in the insulating peak regime.

We present results of measurements obtained from a mesoscopic ring of a highly disordered superconductor. Superimposed on a smooth magnetoresistance background we find periodic oscillations with a period that is independent of the strength of the magnetic field. The period of the oscillations is consistent with charge transport by Cooper pairs. The oscillations persist unabated for more than 90 periods, through the transition to the insulating phase, up to our highest field of 12 T.

### 2014

In a "thought experiment," now a classic in physics pedagogy, Feynman visualizes Young's double-slit interference experiment with electrons in magnetic field. He shows that the addition of an Aharonov-Bohm phase is equivalent to shifting the zero-field wave interference pattern by an angle expected from the Lorentz force calculation for classical particles. We have performed this experiment with one slit, instead of two, where ballistic electrons within two-dimensional electron gas diffract through a small orifice formed by a quantum point contact (QPC). As the QPC width is comparable to the electron wavelength, the observed intensity profile is further modulated by the transverse waveguide modes present at the injector QPC. Our experiments open the way to realizing diffraction-based ideas in mesoscopic physics.

### 2013

The superconductor-insulator transition (SIT) is an accessible quantum phase transition(1,2) that is observed in a number of systems and can be driven by various experimental means(3-9). A central outstanding issue regards the physical nature of the insulating phase terminating superconductivity(10). Theoretical advances led to the proposition that this insulator is a new state of matter, termed a superinsulator(11,12), because its properties can be inferred from the superconductor by invoking duality symmetry'. Here we report on the observation of duality symmetry near the magnetic-field-driven SIT in amorphous indium oxide. However, we show that the symmetry is broken by the emergence of the strong insulating state at low temperature.

We present planar tunneling junction spectroscopy measurements on disordered amorphous indium oxide films on both sides of the superconductor-insulator transition. Our measurements directly reveal a superconducting gap in the insulating phase. The measured energy gap has the same energy scale on both sides of the transition. Unlike the case of granular films, the tunneling curves cannot be fitted to the BCS density of state expression, even when introducing a broadening parameter to account for nonthermal broadening sources. The results are consistent with the presence of superconducting islands of which superconducting properties depend on film disorder and on the carrier density of the superconducting material.

### 2012

We present the results of a magnetoresistance study of the disorder-induced superconductor-insulator transition in an amorphous indium-oxide thin film patterned by a nanoscale periodic array of holes. We observed Little-Parks-like oscillations over our entire range of disorder spanning the transition. The period of oscillations was unchanged and corresponded to the superconducting flux quantum in the superconducting as well as in the insulating phases. Our results provide direct evidence for electron pairing in the insulator bordering with superconductivity.

A dripping faucet is an example of an everyday system that exhibits surprisingly rich dynamics ranging from periodic to chaotic. Using a simple capacitive device, we experimentally demonstrate that the dynamics is determined by the degree of synchronization between two temporally disparate processes: the time at which a drop attains a critical mass and an oscillatory process that accompanies the formation of a drop. We present a full experimental phase-space reconstruction of the ensuing dynamics.

We present tunneling spectroscopy measurements that directly reveal the existence of a superconducting gap in the insulating state of homogenously disordered amorphous indium oxide films. Two films on both sides of the disorder induced superconductor to insulator transition show the same energy gap scale. This energy gap persists up to relatively high magnetic fields and is observed across the magnetoresistance peak typical of disordered superconductors. The results provide useful information for understanding the nature of the insulating state in the disorder induced superconductor to insulator transition.

A hundred years after the discovery of superconductivity, one fundamental prediction of the theory, coherent quantum phase slip (CQPS), has not been observed. CQPS is a phenomenon exactly dual(1) to the Josephson effect; whereas the latter is a coherent transfer of charges between superconducting leads(2,3), the former is a coherent transfer of vortices or fluxes across a superconducting wire. In contrast to previously reported observations(4-8) of incoherent phase slip, CQPS has been only a subject of theoretical study(9-12). Its experimental demonstration is made difficult by quasiparticle dissipation due to gapless excitations in nanowires or in vortex cores. This difficulty might be overcome by using certain strongly disordered superconductors near the superconductor-insulator transition. Here we report direct observation of CQPS in a narrow segment of a superconducting loop made of strongly disordered indium oxide; the effect is made manifest through the superposition of quantum states with different numbers of flux quanta(13). As with the Josephson effect, our observation should lead to new applications in superconducting electronics and quantum metrology(1,10,11).

We study the magnetoresistance of an amorphous indium-oxide thin film whose disorder places it in the insulating side immediately after the disorder-tuned superconductor-insulator transition. We examine the magnetic field orientation dependence of the magnetoresistance and find both a pronounced insulating peak as a function of magnetic field and anisotropic behavior at low fields followed by high isotropy at higher fields, which both characterize highly disordered superconductors. Our findings establish a clear link between its low-field insulating phase and superconductivity.

### 2011

Current-voltage characteristics in the insulator bordering superconductivity in disordered thin films exhibit current jumps of several orders of magnitude due to the development of a thermally bistable electronic state at very low temperatures. In this high-resolution study we find that the jumps can be composed of many (up to 100) smaller jumps that appear to be random. This indicates that inhomogeneity develops near the transition to the insulator and that the current breakdown proceed via percolative paths spanning from one electrode to the other.

A significant anisotropy of the magnetic-field driven superconductor-insulator transition is observed in thin films of amorphous indium-oxide. The anisotropy is largest for more disordered films which have a lower transition field. At higher magnetic fields the anisotropy reduces and even changes sign beyond a sample specific and temperature independent magnetic field value. The data are consistent with the existence of more than one mechanism affecting transport at high magnetic fields. (C) 2011 Elsevier Ltd. All rights reserved.

The most profound effect of disorder on electronic systems is the localization of the electrons transforming an otherwise metallic system into an insulator. If the metal is also a superconductor then, at low temperatures, disorder can induce a pronounced transition from a superconducting into an insulating state. An outstanding question is whether the route to insulating behaviour proceeds through the direct localization of Cooper pairs or, alternatively, by a two-step process in which the Cooper pairing is first destroyed followed by the standard localization of single electrons. Here we address this question by studying the local superconducting gap of a highly disordered amorphous superconductor by means of scanning tunnelling spectroscopy. Our measurements reveal that, in the vicinity of the superconductor-insulator transition, the coherence peaks in the one-particle density of states disappear whereas the superconducting gap remains intact, indicating the presence of localized Cooper pairs. Our results provide the first direct evidence that the superconductor-insulator transition in some homogeneously disordered materials is driven by Cooper-pair localization.

### 2010

The effect of the surface treatments on the transport properties of a two-dimensional electron gas was studied at the quantum limit. The surface of the Al(0.36)Ga(0.64)As/GaAs heterostructure was either coated with gold or etched with HCl solution, or etched and then coated by a self-assembled monolayer (SAM) of either phosphonated (ODP-C(18)H(39)PO(3)) or thiolated (ODT-C(18)H(37)S) molecules. The etching process was found to reduce significantly both the mobility and the charge density. This effect was reversed upon sequential adsorption of the phosphonated SAM. We propose fine tuning of the device performance by the flexible chemistry of the assembled molecules, two of them demonstrated here. The results indicate that the surface oxidation does not necessarily play the dominant role in this respect and, in particular, that octadecane phosphonic acid (ODP) can protect the substrate from both oxidation and the formation of a passivating carbon layer. In contrast, octadecanethiol (ODT) is not stable enough and is not effective in eliminating surface states, as a result devices covered with ODT behave like those with etched surfaces.

### 2009

The current-voltage characteristics measured in the insulating state terminating the superconducting phase in disordered superconductors exhibit sharp threshold voltages, where the current abruptly changes by as much as 5 orders of magnitude. We analyze the current-voltage characteristics of an amorphous indium oxide film in the field-tuned insulating state, and show that they are consistent with a bistability of the electron temperature, and with a significant overheating of the electron system above the lattice temperature. An analysis of these current jumps indicates that, in the insulating state, the electrons are thermally decoupled from the phonon bath.

### 2008

We review our recent measurements of the complex AC conductivity of thin InOx films studied as a function of magnetic field through the nominal 2D superconductor-insulator transition. These measurements-the first to probe anything other than the omega = 0 response of these archetypical systems-reveal a significant finite frequency superfluid stiffness well into the insulating regime. Unlike conventional fluctuation superconductivity in which thermal fluctuations can give a superconducting response in regions of parameter space that do not exhibit long range order, these fluctuations are temperature independent as T -> 0 and are exhibited in samples where the resistance is large (greater than 10(6) Omega/square) and strongly diverging. We interpret this as the first direct observation of quantum superconducting fluctuations around an insulating ground state. This system serves as a prototype for other insulating states of matter that derive from superconductors. (C) 2007 Elsevier B.V. All rights reserved.

### 2007

The complex ac conductivity of thin highly disordered InO(x) films was studied as a function of magnetic field through the nominal two-dimensional superconductor-insulator transition. We have resolved a significant finite-frequency superfluid stiffness well into the insulating regime, giving direct evidence for quantum superconducting fluctuations around an insulating ground state and a state of matter with localized Cooper pairs. A phase diagram is established that includes the superconducting state, a transition to a "Bose" insulator, and an eventual crossover to a "Fermi" insulating state at high fields. We speculate on the consequences of these observations, their impact on our understanding of the insulating state, and its relevance as a prototype for other insulating states of matter that derive from superconductors.

We report a comprehensive study of the complex ac conductivity of thin effectively two-dimensional amorphous superconducting InOx films at zero applied field. Below a temperature scale T-c0 where the superconducting order parameter amplitude becomes well defined, there is a temperature where both the generalized superfluid stiffness acquires a frequency dependence and the dc magnetoresistance becomes linear in field. We associate this with a transition of the Kosterlitz-Thouless-Berezinskii (KTB) type. At our measurement frequencies the superfluid stiffness at T-KTB is found to be larger than the universal value. Although this may be understood with a vortex dielectric constant of epsilon(v)approximate to 1.9 within the usual KTB theory, this is a relatively large value and indicates that such a system may be out of the domain of applicability of the low-fugacity (low-vortex-density) KTB treatment. This opens up the possibility that at least some of the discrepancy from a nonuniversal magnitude is intrinsic. Our finite-frequency measurements allow us access to a number of other phenomena concerning the charge dynamics in superconducting thin films, including an enhanced conductivity near the amplitude fluctuation temperature T-c0 and a finite dissipation at low temperature which appears to be a universal aspect of highly disordered superconducting films.

### 2006

We present the results of a systematic study of thin films of amorphous indium-oxide near the superconductor-insulator transition. We show that the film's resistivity follows a simple, well-defined, power law dependence on the perpendicular magnetic field. This dependence holds well into the insulating state. Our results suggest that a single mechanism governs the transport of our films in the superconducting as well as insulating phases.

We designed and performed low-temperature dc transport characterization studies on two-dimensional electron gases confined in lattice-matched In0.53Ga0.47As/In0.52Al0.48As quantum wells grown by molecular beam epitaxy on InP substrates. The nearly constant mobility for samples with the setback distance larger than 50 nm and the similarity between the quantum and transport lifetime suggest that the main scattering mechanism is due to short range scattering, such as alloy scattering, with a scattering rate of 2.2 ps(-1). We also obtain the Fermi level at the In0.53Ga0.47As/In0.52Al0.48As surface to be 0.36 eV above the conduction band, when fitting our experimental densities with a Poisson-Schrodinger model. (c) 2006 American Institute of Physics.

### 2005

We present the results from an experimental study of the magnetotransport of superconducting wires of amorphous indium-oxide having widths in the range 40-120 nm. We find that, below the superconducting transition temperature, the wires exhibit clear, reproducible, oscillations in their resistance as a function of magnetic field. The oscillations are reminiscent of those that underlie the operation of a superconducting quantum interference device.

We present the results of an experimental study of the current-voltage characteristics in a strong magnetic field (B) of disordered, superconducting, thin films of amorphous indium oxide. As the B strength is increased superconductivity degrades, until a critical field (B-c) where the system is forced into an insulating state. We show that the differential conductance measured in the insulating phase vanishes abruptly below a well-defined temperature, resulting in a clear threshold for conduction. Our results indicate that a new collective state emerges in two-dimensional superconductors at high B.

### 2004

We present an experimental study of four-terminal resistance fluctuations of mesoscopic samples in the quantum Hall regime. We show that in the vicinity of integer quantum Hall transitions there exist two kinds of correlations between the longitudinal and Hall resistances of the samples, one on either side of the transition region.

The symmetry properties of the resistance of mesoscopic samples in the quantum Hall regime are investigated. In addition to the reciprocity relation, our samples obey new symmetries, that relate resistances measured with different contact configurations. Different kinds of symmetries are identified, depending on whether the magnetic field value is such that the system is above, or below, a quantum Hall transition. Related symmetries have recently been reported for macroscopic samples in the quantum Hall regime by Ponomarenko [Solid State Commun. 130, 705 (2004)] , and Karmakar (preprint cond-mat/0309694).

We present an approach to study the real-time dynamics of single molecules using capacitance measurements. The method is based on a nonparallel-plate microcapacitor, which has a tapered-gap geometry. A particle moving within such a capacitor induces capacitance changes that depend on its position. Monitoring these changes allows motion to be traced at a resolution which is higher than the smallest fabricated feature of the device. The detection scheme also enables the distinction between particles of different dielectric constants and the exertion of dielectrophoretic forces on the particles. This approach provides a means for studying various aspects of single-particle dynamics at high resolution, in real time, and under conditions compatible with biological systems.

We present the results of an experimental study of superconducting, disordered, thin films of amorphous indium oxide. These films can be driven from the superconducting phase to a reentrant insulating state by the application of a perpendicular magnetic field (B). We find that the high-B insulator exhibits activated transport with a characteristic temperature, T-I. T-I has a maximum value (T-I(p)) that is close to the superconducting transition temperature (T-c) at B=0, suggesting a possible relation between the conduction mechanisms in the superconducting and insulating phases. T-I(p) and T-c display opposite dependences on the disorder strength.

### 2003

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the nu=2 and the nu=1 quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.

We present an experimental study of mesoscopic, two-dimensional electronic systems at high magnetic fields. Our samples, prepared from a low-mobility InGaAs/InAlAs wafer, exhibit reproducible, sample specific, resistance fluctuations. Focusing on the lowest Landau level, we find that, while the diagonal resistivity displays strong fluctuations, the Hall resistivity is free of fluctuations and remains quantized at its nu = 1 value, h/e(2). This is true also in the insulating phase that terminates the quantum Hall series. These results extend the validity of the semicircle law of conductivity in the quantum Hall effect to the mesoscopic regime.

### 2000

A magnetic field applied parallel to the two-dimensional hole system in the GaAs/AlGaAs heterostructure, which is metallic in the absence of an external magnetic field, can drive the system into insulating at a finite field through a well-defined transition. The value of resistivity at the transition is found to depend strongly on density.

Microwave frequency conductivity Re(sigma(xx)) of high quality two-dimensional hole systems (2DHS) in a large perpendicular magnetic field (B) is measured with the carrier density (n(s)) of the 2DHS controlled by a backgate bias. The high-B insulating phase of the 2DHS exhibits a microwave resonance that remains well defined, but shifts to higher peak frequency (f(pk)) as n(s) is reduced. In different regimes, f'(pk) vs n(s) can be fit to f(pk)proportional to n(s)(-1/2) or to f(pk)proportional to n(s)(-3/2). The data clearly indicate that both carrier-carrier interactions and disorder are indispensable in determining the dynamics of the insulator. The n(s) dependence of f(pk) is consistent with a weakly pinned Wigner crystal in which domain size increases with n(s), due to larger carrier-carrier interaction.

### 1999

For many years, it was widely accepted(1) that electrons confined to two dimensions would adopt an insulating ground state at zero temperature and in zero magnetic field. Application of a strong perpendicular magnetic field changes this picture, resulting(2,3) in a transition from the insulating phase to a metallic quantum Hall state. Unexpectedly, an insulator-to-metal transition was recently observed(4) in high-quality two-dimensional systems at zero magnetic field on changing the charge carrier density. The mechanism underlying this transition remains unknown(5-9). Here we investigate the magnetic-field-driven transition in a two-dimensional gallium arsenide system, which also exhibits(10-12) the poorly understood zero-field transition. We find that, on increasing the carrier density, the critical magnetic field needed to produce an insulator-to-metal transition decreases continuously and becomes zero at the carrier density appropriate to the zero-field transition. Our results suggest that both the finite- and zero-magnetic field transitions share a common physical origin.

We present experimental results on the quantized Hall insulator in two dimensions. This insulator, with vanishing conductivities, is characterized by the quantization (within experimental accuracy) of the Hall resistance in units of the quantum unit of resistance, h/e(2). The measurements were performed in a two-dimensional hole system, confined in a Ge/SiGe quantum well, when the magnetic field is increased above the v = 1; quantum Hall state. This quantization leads to a nearly perfect semicircle relation for the diagonal and Hall conductivities. Similar results are obtained with a higher-mobility n-type modulation-doped GaAs/AlGaAs sample, when the magnetic field is increased above the v = 1/3 fractional quantum Hall state.

We report the transport properties of a low disorder two-dimensional hole system (2DHS) in the GaAs/AlGaAs heterostructure, which has an unprecedentedly high peak mobility of 7 x 10(5) cm(2)/V s, with a hole density of 4.8 x 10(9)

The quantized Hall insulator is characterized by vanishing conductivities and a quantized flail resistance. For low mobility samples, the quantized Hall insulator is obtained when the magnetic field is increased well above the nu = 1 quantum Hall state. For higher mobility samples, a similar quantization is observed when the magnetic field is increased above the nu = 1/3 fractional quantum Hall states. This quantization, throughout the quantum Hall liquid-to-insulator transition, leads to a perfect semicircle relation for the diagonal and Hall conductivities. The measurements were performed in Ge/SiGe quantum Wells and in n-type InP/InGaAs and GaAs/AlGaAs heterostructures.

### 1998

The observation of a carrier-density driven metal-insulator transition in n-type GaAs-based heterostructure is reported. Although weaker than in comparable-quality p-type GaAs samples, the main features of the transition are rather similar. [S0163-1829(98)51744-4].

The general theoretical definition of an insulator is a material in which the conductivity vanishes at the absolute zero of temperature. In classical insulators, such as materials with a band gap, vanishing conductivities lead to diverging resistivities. But other insulators can show more complex behaviour, particularly in the presence of a high magnetic field, where different components of the resistivity tensor can display different behaviours: the magnetoresistance diverges as the temperature approaches absolute zero, but the transverse (Hall) resistance remains finite. Such a system is known as a Hall insulator(1). Here we report experimental evidence for a quantized(2) Hall insulator in a two-dimensional electron system-confined in a semiconductor quantum well. The Hall resistance is quantized in the quantum unit of resistance h/e(2),, where h is Planck's constant and e the electronic charge. At low fields, the sample reverts to being a normal Hall insulator.

The low-temperature conductivity of low-density, high-mobility, two-dimensional hole systems in GaAs was studied. We explicitly show that the metal-insulator transition, observed in these systems, is characterized by a well-defined critical density, p(0)(c). We also observe that the low-temperature conductivity of these systems depends linearly on the hole density, over a wide density range. The high-density linear conductivity extrapolates to zero at a density close to the critical density. [S0163-1829(98)50536-X].

We have measured the real part of the diagonal conductivity, Re(sigma(xx)) for a 2D hole system in the low Landau filling, insulating regime. The spectra, Re(sigma(xx)) versus frequency f, show a well-defined, single resonance peak, which is surprisingly sharp. Plots of the resonance peak frequency and integrated intensity versus the applied magnetic field B are in conflict with the model of a 2D harmonic oscillator in B. (C) 1998 Elsevier Science B.V. All rights reserved.

We report on a zero magnetic field transport study of a two-dimensional, variable-density, hole system in GaAs, As the density is varied we observe, for the first time in GaAs-based materials, a crossover from an insulating behavior at low density, to a metalliclike behavior at high density, where the metallic behavior is characterized by a large drop in the resistivity as the temperature is lowered. These results are in agreement with recent experiments on Si-based two-dimensional systems. We show that, in the metallic region, the resistivity is dominated by an exponential temperature dependence with a characteristic temperature which is proportional to the hole density.

A study of the temperature evolution of the recently discovered reflection symmetry of the diagonal resistivity, rho(xx), near quantum Hall-to-insulator transitions, is presented. The data is found to follow a new phenomenological law over a broad range of temperatures, magnetic fields and samples. We note that this law is inconsistent with the scaling description of quantum Hall transitions and indicates the existence of a transport regime distinct from those considered previously. (C) 1998 Published by Elsevier Science Ltd.

### 1997

We present data on finite frequency (0.2 less than or equal to f less than or equal to 8.6 GHz) conductivity, Re(sigma(xx)), of the insulator terminating in a fractional quantum Hall effect series in the high magnetic field (B) limit. As B is increased within the insulator, at temperatures of 50 and 200 mK Re(sigma(xx)) vs f evolves from a decreasing curve into a peak. The height and f of the peak increase with B. Integrals of Re(sigma(xx)) vs f become B-independent at large enough B. The results are discussed within the framework of the Fukuyama-Lee model of the dynamics of a pinned Wigner crystal. (C) 1997 Published by Elsevier Science Ltd.

We have measured microwave conductivity, Re(sigma(xx)), of a high quality two-dimensional hole system (2DHS) in the high magnetic field (B) insulating phase for frequency (f) between 0.2 and 9 GHz. For upsilon

We demonstrate experimentally that the transitions between adjacent integer quantum Hall (QH) states are equivalent to a QH-to-insulator transition occurring in the top Landau level, in the presence of an inert background of the other completely filled Landau levels, each contributing a single unit of quantum conductance, e(2)/h, to the total Hall conductance of the system. The equivalence holds for numerical parameters describing the transition, as well as for the recently discovered reflection symmetry of the resistivity.

We have conducted an experimental study of the linear transport properties of the magnetic-field induced insulating phase which terminates the quantum Hall (QH) series in two dimensional electron systems. We found that a direct and simple relation exists between measurements of the longitudinal resistivity, rho(xx), in this insulating phase and in the neighboring QH phase. In addition, we find that the Hall resistivity, rho(xy), can be quantized in the insulating phase. Our results indicate that a dose relation exists between the conduction mechanism in the insulator and in the QH liquid. (C) 1997 Elsevier Science Ltd.

We report a temperature- and current-scaling study of the quantum Hall liquid-to-insulator transition in an In1-xGaxAs/InP heterostructure. When the magnetic field is at the critical field B-c, rho(xx) = 0.86h/e(2). Furthermore, the transport near B-c scales as \B - B-c\T-kappa with kappa = 0.45 +/- 0.05, and as \B - B-c\I-b with b = 0.23 +/- 0.05. The latter can be due to phonon emission in a dirty piezoelectric medium, or can be the consequence of critical behavior near B-c, within which z = 1.0 +/- 0.1 and nu = 2.1 +/- 0.3 are obtained from our data.

A recent experiment by Shahar et al., on the phase transitions between quantum Hall states and the insulator, found that the current-voltage characteristics in the two phases are related by symmetry. It was suggested in this work that this is evidence for charge-flux duality near quantum Hall transitions. Here we provide details of this analysis. We review some theoretical ideas on charge-flux duality in the composite boson description of the quantum Hall effect, and interpret the data as implying that this duality is asymmetry in the transition region and that the Hall response of the bosons vanishes. We observe that duality for composite bosons is equivalent to a particle-hole symmetry for composite-fermions and show that a Landauer analysis of transport for the latter allows a possible understanding of the reflection symmetry and Wall response beyond the linear regime. We note that the duality interpretation supports the scenario of superuniversality for quantum Hall transitions outlined by Kivelson, Lee, and Zhang. Finally, we discuss how to search for the duality at other transitions in the quantum Hall regime.

We present a magnetotransport study of a disordered two-dimensional hole system in a strained Ce quantum well. As the magnetic field is increased, a clear transition from a low magnetic field insulator to the nu = 1 quantum Hall state at the lowest density range (controlled by a gate), and to the nu = 3 state at higher densities, is observed. We find that these transitions are characterized by a new universality: At the critical point, the diagonal and Hall resistivities are equal, within experimental uncertainty. These results are in conflict with the ''floating'' scenario suggested by Khmel'nitzkii [JETP Lett. 38, 552 (1983)] and Laughlin [Phys. Rev. Lett. 52, 2304 (1984)].

A quantum system can undergo a continuous phase transition at the absolute zero of temperature as some parameter entering its Hamiltonian is varied. These transitions are particularly interesting for, in contrast to their classical finite-temperature counterparts, their dynamic and static critical behaviors are intimately intertwined. Considerable insight is gained by considering the path-integral description of the quantum statistical mechanics of such systems, which takes the form of the classical statistical mechanics of a system in which time appears as an extra dimension. In particular, this allows the deduction of scaling forms for the finite-temperature behavior, which turns out to be described by the theory of finite-size scaling. It also leads naturally to the notion of a temperature-dependent dephasing length that governs the crossover between quantum and classical fluctuations. Using these ideas, a scaling analysis of experiments on Josephson-junction arrays and quantum-Hall-effect systems is presented.

### 1996

A remarkable symmetry has been observed between the diagonal, nonlinear, current-voltage (I-V-xx) characteristics taken in the fractional quantum Hall effect (FQHE) liquid state of the two-dimensional electron system and those taken in the bordering insulating phase. When properly selected, the I-V-xx traces in the FQHE regime are identical, within experimental errors, to V-xx-I traces in the insulator, that is, with the roles of the currents and voltages exchanged. These results can be interpreted as evidence for the existence of charge-flux duality symmetry in the system:

### 1995

### 1994

We present microwave measurements of the diagonal conductivity sigma(xx), in the integer quantum Hall regime. Our frequencies f were between 0.2 and 14 GHz, and the temperature T was greater than or similar to 50 mK. Broadband Re(sigma(x)), was measured by a transmission line method. The widths DELTAB of Re(sigma(xx)) peaks between IQHE minima increase with f roughly as (DELTAB) is-proportional-to f0.41 for f greater than or similar to 1 GHz. At lower f the peak width dependence on f saturates. We interpret the increase in DELTAB with f as due to dynamic scaling. The exponent, together with existing estimates of the localization length exponent nu, yields a dynamic exponent z almost-equal-to 1.

### 1993

We present ac measurements of the diagonal conductivity sigma(xx), in the integer quantum Hall regime for frequency f between 0.2 and 14 GHz and temperature T greater-than-or-equal-to 50 mK. Re(sigma(xx)) was obtained from the measured attenuation of a coplanar transmission line on the sample surface. For f greater than or similar to 1 GHz, sigma(xx) peaks between IQHE minima broaden as f increases, roughly as (DELTAB) is-proportional-to f(gamma), where DELTAB is the peak width. gamma=0.41 +/- 0.04 for spin-split peaks, and for spin-degenerate peaks gamma=0.20 +/- 0.05. We interpret our data in terms of dynamic scaling. Our gamma, when compared with existing estimates of the localization length exponent nu, is consistent with assigning a dynamic exponent z=1.

### 1992

We study the low-temperature transport properties of amorphous indium oxide films as a function of disorder near the metal-insulator transition. Deep in the insulating regime, the conductivity shows simple variable-range hopping that turns into an Arrhenius activation as the transition is approached. With further decrease in static disorder, superconductivity sets in and the transition temperature increases towards a value of almost-equal-to 3.3 K. The transition between a superconducting phase and an insulating one is also accompanied by a sign and anisotropy change in the magnetoresistance of the films. These results are discussed in light of recent theories.