Combining our nano-SQUID on tip with scanning gate measurements in the quantum Hall phase of graphene we were able to measure and identify work and heat dissipation processes separately. The measurements show that the dissipation is governed by crosstalk between counterpropagating pairs of downstream and upstream channels that appear at graphene boundaries because of edge reconstruction. Instead of local Joule heating, however, the dissipation mechanism comprises two distinct and spatially separated processes. The work generating process that we image directly and which involves elastic tunneling of charge carriers between the quantum channels, determines the transport properties but does not generate local heat. The independently visualized heat and entropy generation process, in contrast, occurs nonlocally upon inelastic resonant scattering off single atomic defects at graphene edges (see also our previous work) , while not affecting the transport. Our findings offer a crucial insight into the mechanisms concealing the true topological protection and suggest venues for engineering more robust quantum states for device applications. Below are sequences of scans measured on different graphene devices at 4.2 K.
Video 1
Video 1
A sequence of temperature scans for different backgate voltages Vbg incremented from -8 V to 8 V at 4.2 K, Bz= 1 T, and Vtg= 8 V. A current Idc is driven from the bottom constriction to one of the top contacts and the value of the current is adjusted with Vbg to maintain total power dissipated in the sample of R2p Idc2= 10 nW. The chirality of the system is counterclockwise for negative Landau levels and clockwise for positive Landau levels. In the video, one can observe the evolution of entropy generation processes, visible as sharp rings along the edges, and the evolution of work generation processes, which appear in the form of larger more blurred features. At large filling factors |ν|≥ 10, predominantly downstream "entropy" rings are visible along the bottom edge of the sample to the right (left) of the constriction for negative (positive) ν. In this case the number of downstream channels is significantly larger than of the upstream edge-reconstructed channels. As a result, the channels are better equilibrated and hence there is less backscattering and less work performed along the edges. In this situation most of the work is performed at the constriction and the energetic carriers injected at the constriction flow downstream and lose their excess energy through resonant phonon emission at the atomic defects visible as the "entropy" rings. These rings decay over a distance of ~15 µm from the constriction. At |ν|≲ 10, "work" arcs begin to appear in addition to the "entropy" rings along both downstream and upstream directions and the chirality is gradually lost. This behavior originates from backscattering between counterpropagating nontopological channels resulting in work generation along the channels giving rise to arcs. This work, generated along the entire length of the channels rather than at the constriction, in now the dominant energy source that “feeds” the "entropy" rings, explaining the absence of decay in the ring intensity and the absence of chirality. This dissipation, distributed over the full length of the edges, becomes most prominent in the lowest LL, nLL= 0, where no topological edge channels are present. Yet most of the current still flows along the edges due to the presence of one or more pairs of counterpropagating nontopological edge channels. In this metallic state, as well as in higher LL metallic states, instead of the commonly assumed backscattering between the opposite edges of the sample, most of the backscattering occurs between the counterpropagating channels within the edges. This is the reason that in Video V1, we hardly observe any dissipation in the bulk at any value of Vbg, except very close to charge neutrality point, where the overall dissipation in the sample reaches a maximum revealing barely visible rings along the inner edges of the square holes (ν=-0.14 frame).
Video 2
Video 2
A sequence of scanning gate images of the four-probe resistance Rxx (r) in a zoomed-in region along the top boundary of the same sample as in Video 1. The Rxx (r)=Vxx (r)/Idc is recorded as a function of the tip position r for various back gate voltages Vbg. Here the injected total power is smaller compared to Video 1. The dashed horizontal line denotes the top edge of the sample.
Video 3
Video 3
Video V3 shows an example of the evolution of the simultaneously acquired thermal and scanning gate Rxx (r) images upon varying Vpg. For this high Vtg (6 V) the "entropy rings" and the " work arc-like features" are readily resolved. The rings due to phonon emission at the atomic defects are observed in the thermal images along the entire graphene perimeter, visible in the form of smaller diameter sharp rings. They are powered by the remote work process even when the latter are shifted significantly away from the edges by the plunger gate potential. These rings are invisible in the Rxx (r) images since the dissipation processes do not cause carrier back scattering. The larger "work" arc-like features are clearly visualized in the Rxx (r) images (light blue to red) revealing the work generation through carrier backscattering. Since the work causes nonlocal heating, these features are also observed in the thermal images in a form of halos along their outer contours.
Video 4
Video 4
Remarkably, the tip induced resistance can be extremely large, Rxx (r)≫R0, with Rxx (r)-R0 reaching several kΩ and up to 20 kΩ in the zeroth Landau level. Despite its very large value we find that Rxx (r) is essentially current independent as demonstrated in Video V4. Here the ac current Iac is varied by over more than two orders of magnitude from 10 nA to 1.4 µA with only minor change in Rxx (r). The current independent Rxx (r) implies that the resulting work and the nonlocal heat dissipation increase quadratically with Iac. Indeed, the second harmonic thermal signal in Video V4 is below our sensitivity at low currents and grows quadratically with the current. Note that the sharp thermal rings in the images at elevated currents are district from the "work" arc-like patterns visible both in thermal and Rxx (r) scans.
Video 5
Video 5
Video V5 shows an example of the evolution of Rxx (r) upon varying V_tg at a neutral plunger gate, and very low current of Iac= 10 nA. A negative Vtg causes accumulation of holes under the tip, but this has no observable effect. This is because hole accumulation is already present along the edges and increasing this accumulation in a very small region does not influence (decrease) the backscattering appreciably. As Vtg is increased to small positive values, the induced depletion of the hole accumulation causes compression of the counterpropagating channels resulting in enhanced backscattering and appearance of corresponding features in R_xx (r) which reveal the locations of the most dominant scattering sites. When Vtg becomes sufficiently large (e.g. 1.75 V) to cut off the counterpropagating pairs of channels, the enhanced Rxx (r) becomes visible along the entire edge of the sample where the nontopological channels are present, displaying a highly disordered structure. For Vtg≳ 3 V arc-like features are formed which increase in diameter and become very fine upon further increase of Vtg. In this case an n-doped pocket is formed under the tip. At high Vtg this pocket will contain a number of Landau levels with edge channels strongly compressed against the steep edge potential, apparently causing enhanced backscattering between the channels by the resonant states at the individual atomic defects. The arcs are very fine at the applied low current of 10 nA and become more blurred at higher currents.
This work can be find on arXiv here.