Surface-dependent Majorana vortex phases in topological crystalline insulators

Abstract

The topological crystalline insulator SnTe exhibits two types of surface Dirac cones: one located at non-time-reversal-invariant momenta on the (001) and (110) surfaces, and the other at time-reversal-invariant momenta on the (111) surface. Motivated by the recent experimental evidence of Majorana vortex end modes (MVEMs) and their hybridization on the (001) surface [Nature 633, 71 (2024)], we present a comprehensive investigation of Majorana vortex phases in SnTe, including topological classification, surface-state Hamiltonians analysis, and lattice model calculations. By utilizing rotational and magnetic mirror symmetries, we present two equivalent methods to reveal the topology of Majorana phases on different surfaces. We find that the MVEMs on the (001) and (110) surfaces are protected by both magnetic group and rotational symmetries. In contrast, the MVEMs on the (111) surface are protected by magnetic group or particle-hole symmetry. Due to the different properties of Dirac fermions in the $\bar{\Gamma }$ and $\bar{M}$ valleys on the (111) surfaces, including Fermi velocities and energy levels, we find that abundant vortex phase transitions can occur for the [111]-direction vortex. As the chemical potential increases, the number of robust MVEMs can change from $0\to 1\to 2$. These vortex transitions are characterized by both $Z$ winding number and $Z_2$ pfaffian topological invariants.

15 pages, 5 figures

References in corpus (60)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Non-Abelian Anyons and Topological Quantum Computation
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Helical liquids and Majorana bound states in quantum wires
• Classification of topological quantum matter with symmetries
• Topological Crystalline Insulators
• A generic new platform for topological quantum computation using semiconductor heterostructures
• Higher-Order Topological Insulators
• Topological Crystalline Insulators in the SnTe Material Class
• Experimental realization of a topological crystalline insulator in SnTe
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• Majorana Fermion Induced Resonant Andreev Reflection
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Evidence for Majorana bound state in an iron-based superconductor
• A topological crystalline insulator (TCI) phase via topological phase transition and crystalline mirror symmetry
• Topological classification of crystalline insulators through band structure combinatorics
• Topology of crystalline insulators and superconductors
• Spin-filtered Edge States with an Electrically Tunable Gap in a Two-Dimensional Topological Crystalline Insulator
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Observation of Dirac node formation and mass acquisition in a topological crystalline insulator
• Topological invariants for spin-orbit coupled superconductor nanowires
• Topological superconductivity on the surface of Fe-based superconductors
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Surface States of Topological Crystalline Insulators in IV-VI Semiconductors
• Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators
• Topological Mirror Superconductivity
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Topological non-symmorphic crystalline insulators
• Topological Crystalline Insulators and Dirac Octets in Anti-perovskites
• Rotation Anomaly and Topological Crystalline Insulators
• Symmetry-Protected Majorana Fermions in Topological Crystalline Superconductors: Theory and Application to Sr2RuO4
• Topological Classification of Crystalline Insulators with Point Group Symmetry
• Crystal Field Effect Induced Topological Crystalline Insulators In Monolayer IV-VI Semiconductors
• Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators
• Experimental observation of Dirac-like surface states and topological phase transition in Pb${}_{1-x}$Sn${}_x$Te(111) films
• Two types of Dirac-cone surface states on (111) surface of topological crystalline insulator SnTe
• Lattice symmetry assisted second order topological superconductors and Majorana patterns
• New class of topological superconductors protected by magnetic group symmetries
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• Real-space recipes for general topological crystalline states
• Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals
• Topological semimetals in the SnTe material class: Nodal lines and Weyl points
• Electrically Tunable Quantum Spin Hall State in Topological Crystalline Insulator Thin films
• Demonstrating Lattice-Symmetry-Protection in Topological Crystalline Superconductors
• Topological Superconductivity from Unconventional Band Degeneracy with Conventional Pairing
• Double Majorana vortex zero modes in superconducting topological crystalline insulators with surface rotation anomaly
• Topological Superconducting Vortex From Trivial Electronic Bands
• Valley-Polarized quantum Hall phase in a strain-controlled Dirac system
• Topological classification of intrinsic 3D superconductors using anomalous surface construction
• Majorana zero modes in twisted transition metal dichalcogenides homobilayers
• Direct observation of a photoinduced topological phase transition in Bi-doped (Pb,Sn)Se
• Controllable Majorana vortex states in iron-based superconducting nanowires
• Majorana multipole response with magnetic point group symmetry

Cited by in corpus (4)

• Double Majorana Vortex Flat Bands in the Topological Dirac Superconductor
• Altermagnetism Induced Bogoliubov Fermi Surfaces Form Topological Superconductivity
• Unveiling In-Gap States and Majorana Zero Modes in Superconductor-Topological Insulator Bilayer model
• Majorana vortex phases in time-reversal invariant higher-order topological insulators and topologically trivial insulators