Gapped boundary phases of topological insulators via weak coupling

@article{Seiberg2016GappedBP,
  title={Gapped boundary phases of topological insulators via weak coupling},
  author={Nathan Seiberg and Edward Witten},
  journal={Progress of Theoretical and Experimental Physics},
  year={2016},
  volume={2016}
}
  • N. Seiberg, E. Witten
  • Published 12 February 2016
  • Physics
  • Progress of Theoretical and Experimental Physics
The standard boundary state of a topological insulator in 3 + 1 dimensions has gapless charged fermions. We present model systems that reproduce this standard gapless boundary state in one phase, but also have gapped phases with topological order. Our models are weakly coupled and all the dynamics is explicit. We rederive some known boundary states of topological insulators and construct new ones. Consistency with the standard spin/charge relation of condensed matter physics places a nontrivial… 

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References

SHOWING 1-10 OF 87 REFERENCES

Fermion Path Integrals And Topological Phases

Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here, we

Topological stability of Majorana zero-modes in superconductor-topological insulator systems

We derive an index theorem for zero-energy Majorana fermion modes in a superconductor–topological insulator system in both two and three dimensions, which is valid for models with chiral symmetry as

Superconducting proximity effect and majorana fermions at the surface of a topological insulator.

TLDR
It is shown that linear junctions between superconductors mediated by the topological insulator form a nonchiral one-dimensional wire for Majorana fermions, and that circuits formed from these junctions provide a method for creating, manipulating, and fusing Majorana bound states.

Topological insulators and superconductors

Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the

Topological phases and the quantum spin Hall effect in three dimensions

We show the existence of topological phases of Bloch insulators with time-reversal symmetry in three dimensions. These phases are characterized by topological ${Z}_{2}$ invariants whose stability is

Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect

We discuss physical properties of `integer' topological phases of bosons in D=3+1 dimensions, protected by internal symmetries like time reversal and/or charge conservation. These phases invoke

Interacting fermionic topological insulators/superconductors in three dimensions

Symmetry protected topological (SPT) phases are a minimal generalization of the concept of topological insulators to interacting systems. In this paper, we describe the classification and properties

Dual Dirac Liquid on the Surface of the Electron Topological Insulator

We discuss a non-fermi liquid gapless metallic surface state of the topological band insulator. It has an odd number of gapless Dirac fermions coupled to a non-compact U(1) gauge field. This can be

Bosonic topological insulator in three dimensions and the statistical Witten effect

It is well-known that one signature of the three-dimensional electron topological insulator is the Witten effect: if the system is coupled to a compact electromagnetic gauge field, a monopole in the

Gapped symmetry preserving surface state for the electron topological insulator

It is well known that the 3D electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often
...