Buried Dirac points in quantum spin Hall insulators: Implications for Majorana Kramers pair-based quantum computing

TL;DR

The paper investigates a QSHI-SC heterostructure realized with an InAs/GaSb double quantum well and a Ta superconducting constriction to host Majorana Kramers pairs in a time-reversal invariant setting. Experimentally, it reports a robust three-terminal conductance plateau of $12 e^2/h$ persisting up to $2$ T, with a Ta-induced gap and near-unity Andreev reflection, indicating highly transparent edge-state superconducting pairing. Theory and numerics show the edge Dirac point is buried in the bulk valence band, a scenario that preserves MKP protection under magnetic fields and may yield extended MKP states; a buried Dirac point reduces the tunneling barrier to the QSHI edge, influencing resonant structures and pinning. The work provides concrete device design principles toward MKP-based quantum computing in time-reversal invariant platforms and outlines steps to localize MKPs via narrower constrictions.

Abstract

For heterostructures formed by a quantum spin Hall insulator (QSHI) placed in proximity to a superconductor (SC), no external magnetic field is necessary to drive the system into a phase supporting topological superconductivity with Majorana zero energy states, making them very attractive for the realization of non-Abelian states and fault-tolerant qubits. Despite considerable work investigating QSHI edge states, there is still an open question about their resilience to large magnetic fields and the implication of such resilience for the formation of a quasi-1D topological superconducting state. In this work, we investigate the transport properties of helical edge states in a QSHI-SC junction formed by a InAs/GaSb (15nm/5nm) double quantum well and a superconducting tantalum (Ta) constriction. We observe a robust conductance plateau up to 2 T, signaling resilient edge state transport. Such resilience is consistent with the Dirac point for the edge states being buried in the bulk valence band. Using a modified Landauer-Buttiker analysis, we find that the conductance is consistent with 98% Andreev reflection probability owing to the high transparency of the InAs/GaSb-Ta interface. We further theoretically show that a buried Dirac point does not affect the robustness of the quasi-1D topological superconducting phase, and favors the hybridization of Majorana Kramer pairs and fermionic modes in the QSHI resulting in extended MKP states, highlighting the subtle role of buried Dirac points in probing MKPs.

Figures (20)

• Figure 1: Schematic of TSCs with MZMs (yellow dots) in (a) a gate-defined Lutchyn-Oreg nanowire and (b) planar Josephson junction with applied in-plane magnetic field $B_{\parallel}$, and (c) quantum Hall-superconductor hybrid structure with out-of-plane field $B_{\perp}$. (d) Tetron qubit-based topological quantum computing architecture based on arrays of coupled TSCs. Zero field schemes for TSC: (e) Schematic of approaches relying on intrinsically broken TRS with magnetic adatoms on the surface of a conventional superconductor forming a Shiba chain, or quantum anomalous Hall effects that do not require an external magnetic field. (f) Time-reversal invariant TSC based on a QSHI and SC constriction which hosts two degenerate pairs of Majoranas (Majorana Kramers pairs). (g) Schematic of a Majorana Kramers qubit based on Majorana Kramers pairs than can perform (left) single- and (right) two-qubit gate operations required for universal quantum computing.
• Figure 2: (a) Schematic of Andreev retroreflection and crossed Andreev reflection at a QSHI-SC constriction. (b) Illustration of the material stack. (c) Microscope image of the device with edge states schematically superimposed. Contact 25 is the Ta SC QPC and all other contacts are Ti/Au. Dashed box: Schematic of the superconducting point contact formed by the junction. (d) Longitudinal resistance R$_{xx}$ across normal contacts 3 and 13 vs gate voltage. (e) Three-terminal $dI/dV$ vs voltage bias between contacts 13 and 25 at $B=0$ and $V_g = -0.6,~-1.0$ V
• Figure 3: (a) Three-terminal $dI/dV$ vs $V_{dc}$ under an applied magnetic field $B$. (b) Waterfall plot of $dI/dV$ with increasing $B$. Dashed line follows the evolution of the superconducting gap $\Delta_0$. (c) Gap $\Delta_0$ extracted from the $dI/dV$ traces vs magnetic field.
• Figure 4: (a) Dispersion of BHZ model used in transport simulations. Dashed line indicates the chemical potential used in simulations presented in panels (b,c). (b)$dI/dV$ comparison between experimental measurements (brown) and simulation with various constriction gaps $d$ for $L_y=120a$ and $L_{x,s}=100a$ where $a$ is the tight binding lattice spacing. (c)$dI/dV$ comparison between experimental measurements (brown) and simulation with Anderson disorder (black), $U_A = 60\Delta$ and $d=5a$.
• Figure 5: Dispersion of the Löwdin effective model for InAs/GaSb with a buried Dirac point.