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Recent observations of the quantum spin Hall effect in transition metal dichalcogenide bilayer systems [1] provide a new material platform for helical liquids on their edges [2]. These correlated one-dimensional channels with spin–momentum locking enable topological superconductivity through the proximity effect [3-5]. In this talk, I discuss interaction-, phonon-,
and disorder-driven topological phase transitions in helical liquids, focusing on a proximitized double helical liquid composed of two parallel helical channels with both local and nonlocal superconducting pairings. In the first part, I show that Coulomb interactions and electron–phonon coupling can renormalize the effective pairing strength and thereby drive transitions between topological and trivial superconducting phases [6]. Within a nonperturbative framework, we demonstrate that phonon-induced renormalization can substantially modify the superconducting gap and suppress topological zero modes. These results highlight that interactions and phonons, which are ubiquitous in real materials, can serve as important tuning knobs for topological phase transitions in helical systems. In the second part, we incorporate experimentally relevant imperfections, including pairing asymmetry, Coulomb-interaction imbalance, and random spin-flip backscattering arising from magnetic disorder or from coexisting charge disorder and magnetic fields [7]. Using bosonization and renormalization-group analysis, we determine how interactions, superconducting pairing, and disorder compete to shape the transport and topological properties. We derive an analytic expression for the number of zero modes in terms of renormalized couplings, revealing a topological Z invariant in contrast to the Z2 invariant in the clean limit. Spin-flip backscattering lifts the degeneracy of the zero-mode conditions and drives a
symmetry-class transition from DIII to BDI, enabling a phase hosting a single Majorana zero mode per corner. Our findings demonstrate that disorder and channel asymmetry can induce or revive Majorana zero modes and generate cascades of topological transitions tunable through interaction strength.
These results establish imperfect helical liquids as a realistic and versatile platform for electrically tunable topological superconductivity.
References:
[1] K. Kang et al., Nature 628, 522 (2024); K. Kang et al., Nano Lett. 24, 14901 (2024).
[2] C.-H. Hsu et al., J. Phys. Mater. 9, 011001 (2026); invited Perspective.
[3] C.-H. Hsu et al., Semicond. Sci. Technol. 36, 123003 (2021); topical review.
[4] J. Klinovaja et al., Phys. Rev. B 90, 155447 (2014).
[5] C.-H. Hsu et al., Phys. Rev. Lett. 121, 196801 (2018).
[6] C.-H. Hsu, Nanoscale Horiz. 9, 1725 (2024); highlighted on the journal cover.
[7] A. Ohorodnyk and C.-H. Hsu, arXiv:2512.10335 (2025).