More is different at the edge: helical Luttinger liquid in double quantum spin Hall insulators

Quantum spin Hall insulators (QSHIs) are a cornerstone of time-reversal-symmetric topological phases and play a central role in modern topological band theory. Their hallmark is the presence of helical edge states, where counterpropagating modes are locked to opposite spin orientations and are protected against elastic backscattering by time-reversal symmetry. These edge states provide an excellent platform for exploring frontier phenomena such as topological superconductivity and spintronic responses. While these helical edge states are often introduced within a noninteracting picture, electron–electron interactions are indispensable for the low-energy physics of one-dimensional systems, leading to the helical Luttinger liquid phase. Such a non-Fermi-liquid behavior further enriches the low-energy physics, supporting exotic states such as Majorana-Kramers pairs. In this talk, I will introduce our recent work on helical Luttinger liquid in double quantum spin Hall insulators (DQSHIs). In sharp contrast to QSHIs, DQSHIs support two pairs of helical edge states, enabling gap opening without breaking time-reversal symmetry. This leads to a richer low-energy phase diagram, such as a higher-order topological insulator phase [1] and a novel\ \pi-spin density wave phase. I will show that DQSHIs provides a versatile platform to engineer Majorana-Kramers pairs without relying on the superconducting proximity effect [2], as well as to study the competition between \pi-superconductivity and \pi-spin density wave phases [3].

Reference:

[1] Yi-Chun Hung, Baokai Wang, Chen-Hsuan Hsu, Arun Bansil, and Hsin Lin. Time-reversal soliton pairs in even spin Chern number higher-order topological insulators. Phys. Rev. B 110, 035125 (2024). [2] Yi-Chun Hung, Chen-Hsuan Hsu, and Arun Bansil. Majorana Kramers pairs in synthetic high-spin Chern insulators. Phys. Rev. B 111, 245145 (2025). [3] Yi-Chun Hung, Chen-Hsuan Hsu, and Arun Bansil. Tunable Competing Electronic Orders in Double Quantum Spin Hall Superlattices. Phys. Rev. B 112, 195127 (2025).

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