2020/12/31 by Yang-Zhi Chou, Rahul Nandkishore, Rahul M. Nandkishore
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Fermion #Gapless playback #Geometry #MAJORANA #Mathematics #Physics #Quantum many-body systems #Quantum mechanics #Spins #Superconductivity #Symmetry (geometry) #Symmetry breaking #T-symmetry #Topological Materials and Phenomena #Topology (electrical circuits) #Zero-point energy #cond-mat.dis-nn #cond-mat.mes-hall #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.103.075120
published as Phys. Rev. B 103, 075120 (2021) · 8 pages, 2 figures, published version
arxiv created 2021/02/09 · openalex publication_date 2021/02/09 · arxiv updated 2021/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We demonstrate that the one-dimensional helical Majorana edges of two-dimensional time-reversal symmetric topological superconductors (class DIII) can become gapless and insulating by a combination of random edge velocity and interaction. Such a gapless insulating edge breaks time-reversal symmetry inhomogeneously, and the local symmetry broken regions can be regarded as static mass potentials or dynamical Ising spins. In both limits, we find that such gapless insulating Majorana edges are generically exponentially localized and trap Majorana zero modes. Interestingly, for a statistically time-reversal symmetric edge (symmetry is broken locally, but the symmetry breaking order parameter is zero on average), the low-energy theory can be mapped to a Dyson model at zero energy, manifesting a diverging density of states and exhibiting marginal localization (i.e., a diverging localization length). Although the ballistic edge state transport is absent, the localized Majorana zero modes reflect the nontrivial topology in the bulk. Experimental signatures are also discussed.