Non-Hermitian topological devices with Chern insulators

TL;DR

The paper demonstrates non-Hermitian topology in quantum anomalous Hall devices formed by interconnecting chiral Chern states in disk and ring geometries, realized without external magnetic fields. It reports an exceptionally well-quantized non-Hermitian invariant w_{PD}, governed by the topological skin effect, which exhibits far stronger quantization and localization than the conventional Chern invariant, and remains robust up to liquid helium temperatures under small magnetic fields. This leads to potential cryogenic sensing applications, including high-impedance and magnetic-field sensors, and opens avenues to engineer other Hamiltonians via local magnetism control. The findings indicate industry-relevant performance and practical usefulness for metrology and topological electronics, with robust behavior across geometries and grounding configurations.

Abstract

Multi-terminal topological devices are a new generation of electronic devices with quantized properties robust against imperfections. In magnetic topological insulators, dissipationless edge states give functional devices in zero magnetic field, of interest for quantum metrology (resistance standard) or topological electronics (Chern networks). Here we show that a new generation of simple quantum circuits (disk, ring) with non-Hermitian topology, based on the interconnection of 1D Chern states in the quantum anomalous Hall regime, can have a much stronger quantization of their invariant than that of the Chern invariant itself, when measured in a non-metrology grade setup - that is, in industry-relevant conditions. Remarkably, the chirality-related topological skin effect is realized without the need of a magnetic field or an electrical gate, with a record degree of localization for a quantum Hall device. This new type of topological quantum devices based on magnets, with an exponential response that can be switched at small magnetic fields (about 200mT), can operate at liquid-Helium temperature with a good quantization and have some potential as cryogenic sensors for applications in high-precision impedance or magnetic field measurements.

Figures (7)

• Figure 1: Disk-shape quantum anomalous Hall device and conductance matrix.(a) 5-site configuration where the grounded arms (grey contacts) are used to disconnect the first and the last site of the chain, thus realizing the open-chain boundary condition. The effective corresponding HN chain is shown schematically below. Active arms are labeled using currents and voltages, $I_j$ and $V_j$. For inactive arms in dashed lines, both contacts are floating. (b) Left, Optical microscopy picture of the QAH disk device, with ten pairs of ohmic contacts; Right, Schematic of the heterostructure realizing the Chern insulator state without the need to apply an electrical gate voltage, as detailed in ref. Okazaki2022. (c) Measured resistance matrix $[R_{i,j}]$ at $B = 0$ T and $T=30$ mK. (d) Calculated conductance matrix $[G_{i,j}]$ constructed by inverting the resistance matrix.
• Figure 2: Topological skin effect in a QAH disk. (a) Exponential localization of the sum of propability densities (SPD), the signature of the non-Hermitian topological skin effect, as measured at $T=30$ mK in zero magnetic field (after saturation of the magnetization in large negative fields) for the 5-site quantum chain; Upper inset: High-field dependence of the device resistances $R_i=V_i/I$, normalized to the von Klitzing constant $R_K$, measured in the current-injection scheme shown in Fig. \ref{['fig1']}a), corresponding to the first raw in Fig. \ref{['fig1']}c) and showing the stability of dissipationless edge states up to 15T; Lower inset: Low-field switching of the resistances measured with the current injected into the central contact $\#3$, showing the chirality switch at the magnetization reversal. (b) Temperature dependence of the SPD measured for the opposite direction of the saturated magnetization (after saturation of the magnetization in large positive fields), as measured under a small +100mT applied field so as to avoid the magnetization reversal at lower fields above 4K. This directly reveals the influence of the reversed chirality on the skin effect as well as its robustness at higher temperatures. (c) Rapid evolution of the skin effect upon magnetization reversal at small fields, after saturation of the magnetization in large negative fields. The skin effect is fully reversed in a narrow 20 mT field range, with a maximum slope $2.10^{-1}$ mT$^{-1}$, and it shows a record degree of localization for a 5-site quantum chain, with an improvement of more than two orders of magnitude with respect to AlGaAs-based devices.
• Figure 3: Quantization of the non-Hermitian topological invariant and of the Hall resistance at various temperatures.(a) Magnetic-field dependence of $1 - \abs{w_{\text{PD}}}$ (left) and of $1 - \abs{R_{xy}/R_{\text{K}}}$ (right), where $R_{\text{K}} = h/e^2$, measured at different temperatures. (b) Temperature dependence of $1 - \abs{w_{\text{PD}}}$ and $1 - \abs{R_{xy}/R_{\text{K}}}$, measured at a fixed magnetic field $B = -1.5$ T. The $w_{\text{PD}}$ is also shown at a lower field $B = -100$ mT and in zero field. Inset: Field dependence of $w_{\text{PD}}$ at 4.2K. A small applied field $\vert B\vert \geq 50$ mT is needed to maintain the magnetization saturated, with a good quantization of $w_{\text{PD}}$ only.
• Figure 4: Comparison of quantum disks and rings Multi-terminal quantum disk (a) and quantum ring (b), and comparison of the temperature dependence of their non-Hermitian topological invariant (c).
• Figure S1: Resistance and conductance matrices measured at $T= 30$ mK (a,b), $T= 1$ K (c,d), $T= 4$ K (e,f), and $T= 30$ K (g,h), from which the $w_{\text{PD}}$ and $R_{\text{xy}}$ parameters are inferred, as shown in Fig. \ref{['fig3']}. $B = -1.5$ T.