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

This study demonstrates that InAs/GaSb quantum spin Hall insulator-superconductor junctions exhibit robust edge state transport up to 2 T due to buried Dirac points, a feature that theoretically supports the formation of extended Majorana Kramers pairs essential for fault-tolerant quantum computing.

The Gist

Imagine you are trying to build a super-secure, unbreakable digital vault for the future of computing. To do this, scientists are looking for special particles called Majorana Kramers Pairs (MKPs). Think of these particles as "ghost twins" that can store information in a way that is naturally protected from errors and noise.

For a long time, scientists believed they needed to use strong magnets to create these ghost twins. However, strong magnets are like a stormy sea: they are hard to control and can destroy the delicate quantum information you are trying to protect.

This paper presents a new, calmer approach using a special material called a Quantum Spin Hall Insulator (QSHI). Here is a simple breakdown of what the researchers did and found:

1. The "Highway" and the "Bridge"

Imagine the QSHI material as a special highway where electrons can only travel in one direction depending on their spin (like a car that can only drive forward if it's red, and backward if it's blue). These are called helical edge states.

The researchers built a device where this highway meets a "bridge" made of a superconductor (a material that conducts electricity with zero resistance). They wanted to see if the electrons could cross this bridge and turn into the special "ghost twins" (MKPs) without needing a giant magnet to force them.

2. The Mystery of the "Unbreakable" Highway

Usually, if you apply a magnetic field to these highways, the time-reversal symmetry (the rule that keeps the traffic flowing smoothly) breaks, and the road should close down. The traffic should stop.

But here is the surprise: The researchers applied a magnetic field, and the traffic kept flowing. The electrons kept moving along the edge of the material even when the magnetic field was strong enough to break the usual rules. This was unexpected and puzzling.

3. The "Buried Treasure" Explanation

Why didn't the road close? The paper suggests the answer lies in a "buried treasure."

In a standard model, the "crossing point" of the highway (where the traffic rules are defined) is right in the middle of the road. If a magnetic field hits it, the road breaks.

However, in this specific material (a sandwich of Indium Arsenide and Gallium Antimonide), the researchers found that this crossing point is buried deep underground, far below the surface of the road.

• The Analogy: Imagine a bridge that is so sturdy and deep that a storm (the magnetic field) hitting the surface doesn't reach the foundation. Because the "crossing point" is buried deep in the bulk of the material, the magnetic field can't easily disrupt the edge traffic. This explains why the conductance (the flow of electricity) remained strong and stable up to 2 Tesla of magnetic field.

4. The Result: A Robust Path for Quantum Computing

The researchers measured the flow of electricity and found it was almost perfect (98% efficiency). This means the electrons were bouncing off the superconductor bridge and returning perfectly, a process called Andreev reflection.

They then used computer simulations to confirm that:

• Even though the "crossing point" is buried, the special "ghost twins" (MKPs) can still form at the ends of the bridge.
• The fact that the crossing point is buried actually helps protect these twins from being destroyed by magnetic fields.
• The "ghost twins" might be a bit more spread out (extended) rather than sitting in a tight spot, but they remain distinct and protected.

Summary

In short, this paper shows that by using a specific type of material where the critical physics is "buried" deep inside, scientists can create a stable environment for quantum computing particles (MKPs) without needing strong, disruptive magnets. This offers a promising, more stable path toward building the quantum computers of the future.

Technical Summary

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

Problem Statement
Quantum Spin Hall Insulators (QSHIs) host helical edge states protected by time-reversal symmetry (TRS), making them promising candidates for realizing Majorana Kramers pairs (MKPs) in time-reversal invariant topological superconductors (TSCs). These MKPs are theoretically capable of forming robust qubits for universal quantum computing without the need for global magnetic fields, which are often required in other Majorana-based schemes and pose scalability challenges. However, a significant experimental discrepancy exists: QSHI devices, particularly InAs/GaSb double quantum wells, exhibit an unexpected resilience of edge state transport to large magnetic fields (up to 2 T and beyond), despite the expectation that broken TRS should open a gap at the Dirac point of linearly dispersing edge states, thereby suppressing conductance. Furthermore, the realization of high-quality QSHI-superconductor (SC) heterostructures capable of hosting MKPs has been hindered by edge roughness and disorder. Theoretical models often rely on simplified minimal descriptions that may not account for higher-order corrections to the band structure, such as the "burying" of the Dirac point deep within the bulk valence band.

Methodology
The authors present a combined experimental and theoretical investigation:

1. Device Fabrication: A high-quality InAs/GaSb (15 nm/5 nm) double quantum well was grown via molecular beam epitaxy (MBE) to ensure the "inverted-band" regime. A superconducting Tantalum (Ta) constriction was patterned directly onto the mesa to form a superconducting point contact (SPC). The device includes a top gate (Au/Ti) separated by an Al2O3 dielectric to tune the electron density.
2. Experimental Transport: Measurements were performed at 20 mK. The study focused on three-terminal differential conductance ($dI/dV$) across the Ta constriction (contacting the SC and a normal lead) and longitudinal resistance ($R_{xx}$) as a function of gate voltage ($V_g$) and out-of-plane magnetic field ($B$).
3. Numerical Simulations:
   • Transport Modeling: A modified Landauer-Büttiker formalism was used to analyze conductance, accounting for Andreev reflection, crossed Andreev reflection, and backscattering probabilities.
   • Band Structure Modeling: Two Hamiltonians were compared using the Bogoliubov de-Gennes (BdG) formalism within the Kwant package:
     • $H^{(1)}$: A standard Bernevig-Hughes-Zhang (BHZ) model with an exposed Dirac point.
     • $H^{(2)}$: A Löwdin partitioning effective Hamiltonian derived from $k \cdot p$ theory, incorporating higher-order spin-orbit coupling and $k^3$ terms, which results in a Dirac point buried below the bulk valence band.
   • MKP Analysis: The local density of states and eigenenergies of MKPs were calculated for both Hamiltonians under varying Zeeman splittings ($\Delta_Z$) to assess the stability and localization of the pairs.

Key Results

• Robust Edge Transport: The device exhibited a quantized three-terminal conductance plateau of approximately $12(e^2/h)$ at zero field. Crucially, this conductance remained robust up to magnetic fields of 2 T, where the Zeeman splitting ($\sim 0.88$ meV) is nearly half the theoretical bulk gap. This resilience contradicts the standard expectation that broken TRS should gap out the edge states.
• High Andreev Reflection: Analysis using the modified Landauer-Büttiker model indicates that the zero-field conductance is consistent with a 98% probability of Andreev retroreflection, attributed to the high transparency of the InAs/GaSb–Ta interface and the helical nature of the edge states.
• Buried Dirac Point Confirmation: Theoretical simulations using the Löwdin effective model ($H^{(2)}$) successfully reproduced the experimental observation of a Dirac point buried in the bulk valence band. This "burying" explains the resilience to magnetic fields: the Zeeman splitting must be large enough to bridge the energy gap between the buried Dirac point and the bulk valence band edge before it can effectively gap out the edge states.
• Impact on Majorana Kramers Pairs:
  • The study finds that a buried Dirac point does not destroy the topological gap protecting MKPs.
  • However, the buried nature alters the spatial profile of the MKPs. In the absence of a domain wall pinning the MKP (which occurs when the edge dispersion remains gapless in the constriction), the MKPs hybridize with fermionic modes in the QSHI vacuum edge.
  • This results in "extended" MKP states rather than strictly localized defect states.
  • The transition from weakly hybridized MKPs to a spinless p-wave state (single Majorana zero mode) is shifted to larger Zeeman splittings when the Dirac point is buried, suggesting that buried Dirac points may help preserve MKPs under finite magnetic fields.

Significance and Claims
The paper establishes that the unexpected magnetic field resilience in InAs/GaSb QSHI devices is consistent with a buried Dirac point scenario. The authors claim that their device design, featuring high-quality materials and a superconducting constriction, provides a viable path toward realizing MKPs.

The significance of the findings lies in the nuanced role of the buried Dirac point:

1. It explains the experimental anomaly of robust edge transport in high magnetic fields.
2. It suggests that while the topological protection of the MKP phase remains intact, the physical nature of the MKPs changes. They become extended states coupled to the edge, which may complicate the detection of specific resonant signatures (like crossed Andreev reflection) but does not preclude the existence of the pairs.
3. The authors propose that to "pin" these MKPs effectively and observe distinct signatures, the constriction width must be reduced further (to $<100$ nm) to increase the tunneling barrier between the MKP and the bulk edge modes.

The work concludes that buried Dirac points are a critical factor in the design and interpretation of QSHI-SC devices for topological quantum computing, offering a mechanism to preserve MKPs under conditions where standard models predict their suppression.