Thermoelectric effect at the quantum Hall-superconductor interface

TL;DR

The paper investigates thermoelectric effects at the interface between a quantum Hall insulator and a superconductor, where heating artifacts can mimic or obscure exotic interfacial states. It reports nonlocal transport measurements in graphene Hall bars bisected by MoRe superconductors and explains the thermoelectric response with a hotspot model in which heat propagates via vortex cores, creating a non-equilibrium electron distribution. The key findings are that the nonlocal voltage $V_T$ is even in the bias $I$ while the nonlocal resistance $R_T$ is odd in $I$, with sign changes controlled by gate voltage and sensitive to vortex configurations; these observations favor thermal transport over simple Andreev reflections. The work underscores the necessity of accounting for thermal effects when probing QH–S interfaces for exotic excitations and provides a framework for interpreting thermoelectric signals in such systems.

Abstract

The interfaces of quantum Hall insulators with superconductors have emerged as a promising platform to realise interesting physics that may be relevant for topologically protected quantum computing. However, these interfaces can host other effects which obscure the detection of the desired excitations. Here we present measurements of the thermoelectric effect at the quantum Hall-superconductor interface. We explain the heat transport by considering the formation of a hotspot at the interface, which results in a non-equilibrium distribution of electrons that can propagate across the superconductor through vortex cores. The observed thermoelectric effect results in a voltage which changes sign on quantum Hall plateaus and responds to the rearrangement of vortices in the wire. These observations highlight the complex interplay of thermal and charge phenomena at the quantum Hall -- superconductor interfaces and should be considered when interpreting transport measurements in similar systems.

Figures (4)

• Figure 1: (a) An optical image of the sample. The 50nm device is on the left and the 250nm is on the right. (b) Device schematic and configuration of the measurements presented in c and d. The orange arrow denotes the direction of travel of electrons when the device is n-doped ($V_G>0$). (c) Measurement of the 'downstream' resistance, $\tilde{R}_{xx}$, as a function of magnetic field and gate voltage in the 50nm device. (d) Transverse conductance, $(\frac{dV_{xy}}{dI})^{-1}$, in the 50nm device as a function of magnetic field and gate voltage.
• Figure 2: (a) Measurement configuration used in Figures 2-4. Orange arrows denote the direction of electron travel. The hotspot is indicated by the red circle. (b) Map of the differential nonlocal resistance ($R_T=\frac{dV_T}{dI}$) measured vs bias $I$ and $V_G$ in the 50 nm device. The resistance signal is strong between the plateaus and clearly changes sign upon changing the sign of either $I$ and $V_G$. (c) Traces from b at constant $I=100$ nA displaying the dependence of the sign of $\frac{dV_T}{dI}$ on $I$ and $V_G$. (d) Schematic energy diagram showing how the non-equilibrium distribution in the metal exchanges electrons with the Landau levels in graphene. The situation is different on-plateau and off-plateau, in which case the level in the bulk should be preferentially filled with electrons (for n-doping).
• Figure 3: (a)$V_T$ measured as a function of $I$ and $V_G$ on the $\nu=4$ plateau at 2 T in the 250 nm device. (b) Vertical cuts of a reveal a prominent 'V' shaped curve of both signs, indicative of thermopower effects. (c) Traces of $V_T$ taken at $I=100$ nA in the $W=50$ nm device. The field is first swept from $B=3$ to 2.9 T and then further to $B=2.7$ T. The $B=3\rightarrow 2.9$ T trace is then repeated. The previously repeatable measured $V_T$ is irrecoverable, indicative of the influence of vortices in the thermal transport.
• Figure 4: (a-b)$V_T$ measured vs bias and gate voltage in the 50 nm device across the $\nu=4$ and $\nu=8$ plateaus respectively. (c) Trace of a-b taken at 100 nA and beginning at the left of each plot. (d-f) Corresponding measurements in the 250 nm device.