Nonlocal Transport in Cr-doped (Bi,Sb)2Te3: Absence of Nonchiral Edge States

TL;DR

This work tests whether non-chiral edge states degrade quantized Hall transport in Cr-doped (Bi,Sb)$_2$Te$_3$ by performing symmetry-constrained nonlocal resistance measurements on an 8-terminal Hall bar at $\approx 2\ \mathrm{K}$. Using both Landauer-Buttiker and bulk continuum Ohm's law descriptions, the authors compare fits with and without a non-chiral edge component and apply an $F$-test to assess statistical significance. The continuum Ohm's law model with two parameters describes all configurations well, while incorporating non-chiral edge states yields only marginal improvements and no statistical justification, suggesting negligible non-chiral edge contributions under these conditions. The findings imply limited prospects for high-temperature QAHE in this material and point to designing geometries with lower symmetry to more decisively constrain edge versus bulk transport channels.

Abstract

The quantum anomalous Hall effect shows great promise for realization of the ohm without the need for an external magnetic field. The most mature material platform is magnetically doped topological insulators. In these materials, precise quantization is limited to low temperatures, with the activation energy for dissipative transport typically in the range of 1 K. One potential source of dissipative transport is non-chiral edge states. These states are expected to be present in sufficiently thick samples. In this work, we perform extensive Hall and non-local resistance measurements in a Hall bar geometry at 2 K. By comparing 15 independent transport measurements to different transport models, we find that the system behavior is well-described by a simple continuum Ohm's law model. The addition of non-chiral edge states into the model does not significantly improve the fitting, and we conclude that there is not strong evidence for these states. We discuss the implications of our results for the prospect of high temperature quantized anomalous Hall effect in these materials.

Figures (6)

• Figure 1: (a) Schematic of a 3-dimensional Chern insulator with magnetization along the $z$-direction. Surfaces with normal along $z$ are gapped, while other surfaces remain gapless. (b) Experimental sample with lead index labeling.
• Figure 2: Experimental data of resistance for different measurement configurations. Blue and green curves show upward and downward $B$-field sweeps, respectively, as indicated by the arrows in (b). The red stars in (d), (h), and (i) indicate symmetry-equivalent measurement configurations at $+M$ and $-M$. The blue (green) solid lines correspond to upward (downward) sweeping of the magnetic field. The subplot titles $(i,j;k,\ell)$ indicate the current source/drain lead $i$ and $j$, and leads $k$ and $\ell$ across which voltage is measured. See Fig. \ref{['fig:fig1']}(b) for lead labeling. The $y$-axis is the resistance $R_{ij;k\ell}$ scaled by the von Klitzing constant $R_K$.
• Figure 3: Deviation of the Hall resistance in the center of the device, $\delta R_{xy}$, from the von-Klitzing constant due to non-chiral edge states ($\delta R_{xy}=1-R_{xy}/R_K$). (a) shows the variation of $\delta R_{xy}$ with non-chiral edge scattering parameter $k$, for varying number of leads as shown in the legend. (b) shows the same versus number of leads, for various $k$ values as shown in the legend.
• Figure 4: Results from the continuum Ohm's law model. (a) shows the mesh, where refinement near corners where current crowding occurs is important. In this case, this is around the upper left and lower right corners. (b) shows the electrostatic potential for $\sigma_{xy}/\sigma_{xx}=3.1$, along with arrows depicting the magnitude and direction of current. For this simulation, the source and drain are the left and right vertical edges, and all other edges' boundary condition is a vanishing normal component of current.
• Figure 5: (a) Electrochemical potential versus terminal for both orientations of magnetization for the chiral+non-chiral edge state model. The source and drain are terminals 8 and 1, respectively, and the non-chiral transmission probability is $k=0.3$. (b) depicts the terminal voltages (to lowest order in $k$, normalized by $V_{\rm app}$) and resulting current flow for the $+M$ configuration. The bold red arrows depict chiral states, while the dashed blue arrows depict non-chiral states.