Wiedemann-Franz behavior at the Weyl points in compressively strained HgTe

TL;DR

This study probes the gravitational anomaly in a Weyl semimetal realized in compressively strained HgTe by measuring heat transport and testing the Wiedemann-Franz law. Using all-electronic Johnson-Nyquist noise thermometry in a symmetric H-bar device at low lattice temperature, the authors map electron temperatures and extract the thermal conductance κ, confirming a linear dependence of heat flow on temperature differences and accounting for electron-phonon relaxation. They find the Lorenz ratio L = κ / G remains essentially equal to the Sommerfeld value L0 = $(\pi^2/3)(k_B/e)^2 \approx 2.44\times 10^{-8}$ W Ω K^{-2}$ across gate voltages and in-plane magnetic fields, with the Seebeck coefficient following the Mott relation, indicating no detectable gravitational anomaly in this regime. Overall, the work provides a complete set of thermoelectric transport coefficients for a Weyl semimetal and clarifies the conditions under which gravitational anomalies might be observed, while showing conventional heat transport dominates at low temperatures in this system.

Abstract

Weyl semimetals, with their unique electronic band structure, have drawn significant interest for their potential to explore quantum anomalies in condensed matter systems. In this study, we investigate the large positive magneto-thermal conductance associated with the gravitational anomaly -- one of the predicted anomalies -- for a Weyl semimetal based on a compressively strained HgTe layer. We clearly identify the Weyl regime in our device and accurately extract the thermal conductance by performing thermometry measurements at liquid helium temperatures using fully electronic methods. We observe the anticipated increase in thermal conductance, and it perfectly matches the electrical conductance according to the Wiedemann-Franz law. This finding indicates that, despite the unique electronic spectrum of Weyl semimetals, the mechanism governing heat transport in this system is the same as that for electrical transport, with no additional violations of conservation laws.

Figures (9)

• Figure 1: Band structure of compressively strained HgTe. (a) Energy momentum dispersion of HgTe under a compressive strain of 0.28%, calculated using $\boldsymbol{k \cdot p}$ theory, with momentum $k$ along the (100) direction. In order to analyze the surface states, we use a finite-slab geometry, with surfaces perpendicular to the growth direction (001). Bulk bands are shown in orange while surface states are depicted in maroon. The massless $n$-type surface states are located near the Weyl points, with the surface Dirac cone situated deep within the valence band. (b) Magnification of (a) near the Fermi level, showing the two Weyl points on the $k_x$ axis with equal chirality and the four $n$-type surface states (maroon). The surface states are two-fold degenerate on the $k_x$ axis, making up for a total of four surface states, i.e., two at each surface. The inner pair merges into the conduction band for $k\approx 0.05\, \mathrm{nm}^{-1}$. The inset depicts the Fermi surface at the Fermi level for the top (solid) and bottom (dashed) surface states. These surface states at the Fermi level are known as "Fermi arcs". The black dots mark the positions of the Weyl points.
• Figure 2: In-plane magnetoresistance of the island. (a) $R_\mathrm{xx}$ vs $V_\mathrm{g,i}$ at the island at $B=0$. The insets show the optical image of the device and an enlarged view of the island. (b) In-plane magnetoresistance for different positions of the island Fermi level.
• Figure 3: a) The average heater channel ($T_\mathrm{heat}$, black dots, left axis) and detector channel ($T_\mathrm{det}$, orange dots, right axis) temperatures, measured via noise thermometry, as a function of DC heating current, $I_\mathrm{heat}$ for in-plane magnetic field $B=0$. The Fermi level of the island is tuned close to the Weyl point at gate voltage $V_\mathrm{g,i}=-0.29\,\unit{\volt}$. The solid lines are simulations of the heater performance for pure hot electron diffusion (red) and including electron-acoustic phonon relaxation ($q_\mathrm{ph}=\Sigma_\mathrm{ph}(T^3 - T_0^3)$ with coefficient $\Sigma_\mathrm{ph}\approx0.19\,\unit{\watt\meter^{-2}\kelvin^{-3}}$) (light blue). b) The heat flow rate $Q$ through the island as a function of $T_\mathrm{hot}^2 - T_\mathrm{cold}^2$ for different in-plane magnetic fields: $B=0$, $2\,\unit{\tesla}$ and $4\,\unit{\tesla}$. The inset shows a schematic of the thermal transport measurement configuration with the temperature profiles in the channels. Owing to the symmetry of the device, $T_\mathrm{heat}$ is measured via running the current through the detector channel, without a second amplifier. c) Thermal conductance coefficient $\kappa$ of the island as a function of in-plane magnetic field for different positions of Fermi level, ranging from $n$-type regime, through the Weyl point at gate voltage $V_\mathrm{g,i}\approx-0.29\,\unit{\volt}$, and all the way to the $p$-region. d) Data from (c) and Fig.\ref{['fig:resistance']}b, combined yield the Lorenz ratio $L=\kappa / G$ ($G$ is the electrical conductance) in units of $L_0\approx2.44\times10^{-8}\,\unit{\watt\ohm\kelvin^{-2}}$. The error bars are derived from the statistical analysis of noise measurements, representing a 95% confidence level.
• Figure 4: a) The thermopower of the island is measured as a function of the island gate voltage. The Fermi level within the island is adjusted from the $n$-type region ($0.2\,\unit{\volt}$) to the $p$-type region ($-0.5\,\unit{\volt}$), passing through the Weyl point at $\approx-0.29\,\unit{\volt}$. b) The thermopower of the island is investigated as a function of the in-plane magnetic field when the island is near the Weyl point.
• Figure S1: Johnson noise measurement setup .