Interplay between intrinsic and emergent topological protection on interacting helical modes

Abstract

The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent ${\mathbb{Z}}_2$ topological protection, and hence a zero-temperature conductance of $G=e^2/h$. We show that when interactions are added to the model, the ground state exhibits two different phases as function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the non-interacting topological phase is spontaneously broken. In this phase, there is zero conductance $G=0$ at zero-temperature. The other phase displays enhanced topological properties, with the neutral sector described by a massive version of ${\mathbb{Z}}_3$ parafermions. In this phase, the system at low energies displays an emergent ${\mathbb{Z}}_3$ symmetry, which is not present in the lattice model, and has a topologically protected zero-temperature conductance of $G=3e^2/h$. This state is an example of a dynamically enhanced symmetry protected topological state.

arXiv commentExtended discussion on disorder, one figure and references added

References in corpus (51)

• Topological Insulators
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ 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
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantum Spin Hall Effect
• Periodic table for topological insulators and superconductors
• Bosonization and Strongly Correlated Systems
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Nonlocal edge state transport in the quantum spin Hall state
• Topological phases of fermions in one dimension
• The Quantum Spin Hall Effect: Theory and Experiment
• The effects of interactions on the topological classification of free fermion systems
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Impurity scattering and transport of fractional Quantum Hall edge state
• Helical edge resistance introduced by charge puddles
• Time-Reversal Invariant Parafermions in Interacting Rashba Nanowires
• Three-dimensional disordered conductors in a strong magnetic field: surface states and quantum Hall plateaus
• Chiral Surface States in the Bulk Quantum Hall Effect
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Resistance of helical edges formed in a semiconductor heterostructure
• Fractional Helical Liquids and Non-Abelian Anyons in Quantum Wires
• Criticality in self-dual sine-Gordon models
• Parafermions in Interacting Nanowire Bundle
• Trionic phase of ultracold fermions in an optical lattice: A variational study
• Spontaneous breakdown of topological protection in two dimensions
• Polaronic atom-trimer continuity in three-component Fermi gases
• Population imbalance and pairing in the BCS-BEC crossover of three-component ultracold fermions
• Emergent topological properties in interacting one-dimensional systems with spin-orbit coupling
• From one-dimensional charge conserving superconductors to the gapless Haldane phase
• Critical entropies and magnetic-phase-diagram analysis of ultracold three-component fermionic mixtures in optical lattices
• Exotic Quantum Criticality in One-Dimensional Coupled Dipolar Bosons Tubes
• Interaction induced topological protection in one-dimensional conductors
• Spinful fermionic ladders at incommensurate filling: Phase diagram, local perturbations, and ionic potentials
• Exact diagonalization study of the trionic crossover and the trion liquid in the attractive three-component Hubbard model
• Trion and Dimer Formation of Three-Color Fermions
• An integrable model with parafermion zero energy modes
• Stability of the Superfluid State in Three-Component Fermionic Optical Lattice Systems
• Phase diagram of two interacting helical states
• Interaction Protected Topological Insulators with Time Reversal Symmetry
• Transmission through a potential barrier in Luttinger liquids with a topological spin gap
• Stability of a topological insulator: interactions, disorder and parity of Kramers doublets
• Trionic and quartetting phases in one-dimensional multicomponent ultracold fermions
• Bound-States Dynamics in One-Dimensional Multi-Species Fermionic Systems

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• Helical Liquids in Semiconductors
• Composite helical edges from Abelian fractional topological insulators
• Time-Reversal Soliton Pairs In Even Spin-Chern-Number Higher-Order Topological Insulators
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators