Coexisting topological hinges and 1D Rashba states in Bi$_{0.97}$Sb$_{0.03}$ revealed by the Josephson effect

Second-order topological insulating (SOTI) states in three-dimensional materials are helical one-dimensional hinge states. Inducing superconductivity in these states leads to gapless bound states, characterized by the 4$π$-periodic current-phase relation. Here, we provide evidence of the topologically protected hinge states in Dirac semimetal Bi${0.97}$Sb${0.03}$ nanoflakes by an unconventional interference pattern in a magnetic field, and the 4$π$-periodic supercurrent carried by these states via the suppressed first and third Shapiro steps. Tight-binding simulations confirm the presence of multiple hinge modes, supporting our interpretation of Bi${0.97}$Sb${0.03}$ as a prototypical designable SOTI platform. Quantum confinement effect is identified by a quasi-one-dimensional bulk transport, and the confined Rashba states are responsible for the broadened hinge states.

💡 Research Summary

In this work the authors investigate the emergence of second‑order topological insulating (SOTI) hinge states and one‑dimensional Rashba channels in the Dirac semimetal alloy Bi₀.₉₇Sb₀.₀₃ using Josephson junction (JJ) interferometry. Exfoliated flakes (111) oriented with thicknesses of 50–250 nm were contacted with Nb superconducting leads to form two distinct junction geometries on the same flake: an “edge JJ” whose leads span the full width of the flake, thereby including the crystal edges, and a “bulk JJ” whose leads are confined to the central region, leaving the edges uncovered.

Magneto‑interference measurements of the critical current I_c(B) reveal strikingly different patterns. The edge JJ shows a SQUID‑like oscillatory pattern, indicating that the supercurrent is concentrated at the two side edges. By applying the Dynes–Fulton inversion, the spatial current density J_c(x) is reconstructed and displays pronounced peaks at the edges with amplitudes of 130 nA (left) and 80 nA (right). These values exceed the theoretical maximum for a single helical hinge mode (≈30 nA), implying that several parallel hinge channels contribute simultaneously. In contrast, the bulk JJ exhibits a non‑oscillatory, slowly decaying I_c(B) reminiscent of a Fraunhofer‑free response, which the authors attribute to quasi‑one‑dimensional ballistic transport arising from strong quantum confinement in the thin flake.

Temperature dependence I_c(T) and length dependence I_c R_N∝1/L were measured on a series of junctions with lengths from 300 nm to 1 µm. All data are well described by the ballistic Eilenberger formalism with an interface transparency D≈0.999 and a superconducting coherence length ξ_s≈240 nm (derived from T_c≈4 K and v_F≈8×10⁵ m s⁻¹). The fits yield a characteristic single‑mode critical current of ≈52 nA, from which the authors estimate roughly 20 active modes per edge in the 600 nm junction, decreasing to 6–8 modes for longer junctions. The linear scaling of I_c R_N with 1/L confirms the intermediate‑long ballistic regime (L/ξ_s≈2.5).

To probe the topological nature of the edge channels, the authors perform high‑frequency Shapiro step measurements. Under microwave irradiation, the first and third Shapiro steps are strongly suppressed while the second step remains robust, a hallmark of a dominant 4π‑periodic Josephson component associated with Majorana bound states. The suppression persists over a range of temperatures and correlates directly with the presence of the edge‑enhanced supercurrent, providing compelling evidence that the hinge modes host parity‑protected gapless excitations.

Complementary tight‑binding simulations of a realistic Bi₁₋ₓSbₓ crystal with natural step‑edges and terraces reproduce multiple hinge lines along the flake perimeter. The simulations also reveal that strong Rashba spin–orbit coupling, amplified at the edges by the electric‑field gradient, generates one‑dimensional Rashba subbands that overlap with the hinge modes. Experimentally, the extracted edge current width of ≈250 nm is consistent with a Rashba‑induced broadening of the hinge channels.

Overall, the paper establishes Bi₀.₉₇Sb₀.₀₃ as a versatile, air‑stable platform for engineering higher‑order topological superconductivity. It demonstrates (i) the existence of multiple helical hinge modes that dominate the Josephson transport, (ii) their topological protection manifested as a 4π‑periodic supercurrent, and (iii) the coexistence of edge‑localized Rashba states that modify the spatial profile of the supercurrent. These findings open a route toward controllable Majorana devices based on hinge engineering and spin‑orbit tailoring, advancing the prospects for topological quantum computation.