Gapless Andreev bound states in the quantum spin Hall insulator HgTe

Abstract: In recent years, Majorana physics has attracted considerable attention in both theoretical and experimental studies due to exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a two-dimensional topological insulator that exhibits the quantum spin Hall effect. The ac Josephson effect demonstrates that the supercurrent has a $4\pi$-periodicity with the superconducting phase difference as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, an anomalous SQUID-like response to a perpendicular magnetic field shows that this $4\pi$-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest when the sample is gated towards the quantum spin Hall regime, thus providing evidence for induced topological superconductivity in the quantum spin Hall edge states.

• The paper demonstrates that gapless Andreev bound states emerge in HgTe quantum spin Hall insulators under s-wave superconductivity with clear Shapiro step anomalies.
• The study employs Josephson junctions in HgTe quantum wells, revealing a 4π-periodic supercurrent and SQUID-like interference patterns indicative of edge-bound transport.
• The findings suggest that HgTe-based junctions could become promising platforms for realizing Majorana modes essential for fault-tolerant quantum computing.

Gapless Andreev Bound States in the Quantum Spin Hall Insulator HgTe

This paper investigates the emergence of gapless Andreev bound states in the quantum spin Hall (QSH) insulator HgTe when subjected to proximity-induced superconductivity. Focusing on the interplay between topological insulators and conventional superconductivity, the research aims to explore conditions under which topological superconductivity and Majorana bound states may arise, a phenomenon with significant implications for fault-tolerant quantum computation.

The experimental setup involves HgTe quantum wells, known for supporting QSH states, combined with s-wave superconductors, specifically aluminum contacts. Analyzing Josephson junctions realized within this architecture allows for the manifestation of unconventional supercurrent phenomena, notably the $4\pi$-periodic supercurrent that suggests the presence of gapless Andreev bound states along the edges of the junction.

The authors provide compelling evidence for $4\pi$-periodic supercurrents through distinct experimental signatures, the first being the occurrence of an anomalous sequence in Shapiro steps during the ac Josephson effect. Specifically, under rf excitation, the conventional sequence of integer Shapiro steps evolves such that odd steps are consistently absent, a feature attributed to the presence of $4\pi$-periodic Andreev bound states. Additionally, the response of the critical current to a perpendicular magnetic field transitions from a Fraunhofer to a SQUID-like pattern, further indicating edge-bound current carried by topological modes.

One of the paper's significant achievements is using HgTe quantum wells, the first-known material to host QSH states, to directly observe these phenomena. Although residual bulk modes were detected, possibly due to aluminum diffusion, the observed transport and magnetic interference patterns provide robust evidence supporting the existence of $4\pi$-periodic bound states localized at the sample's edges. This finding is matched by theoretical predictions suggesting that QSH insulators with superconducting contact can emulate spinless $p_x + ip_y$-wave superconductivity, conducive to Majorana states.

The research supports that HgTe-based junctions, devoid of externally applied magnetic fields, might be promising platforms for realizing Majorana qubits. Such platforms are crucial for advancing topological quantum computing architectures, leveraging Majorana states' inherent robustness against decoherence.

Future directions may involve refining the junction fabrication to minimize undesirable bulk contributions and enhance edge-dominant transport to clear the path for potential applications in scalable quantum information systems. Exploring other 2D topological materials under varying experimental parameters could also unveil further insights into the harnessing of topological phases for quantum computing technology. The implications of this research extend beyond physical materials science, reverberating into computational models and quantum algorithm development grounded in the topological properties of condensed matter systems.