Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model

@article{Fidkowski2013NonAbelianTO,
  title={Non-Abelian Topological Order on the Surface of a 3D Topological Superconductor from an Exactly Solved Model},
  author={Lukasz M. Fidkowski and Xie Chen and Ashvin Vishwanath},
  journal={arXiv: Strongly Correlated Electrons},
  year={2013}
}
Three dimensional topological superconductors (TScs) protected by time reversal (T) symmetry are characterized by gapless Majorana cones on their surface. Free fermion phases with this symmetry (class DIII) are indexed by an integer n, of which n=1 is realized by the B-phase of superfluid Helium-3. Previously it was believed that the surface must be gapless unless time reversal symmetry is broken. Here we argue that a fully symmetric and gapped surface is possible in the presence of strong… 

Figures and Tables from this paper

A time-reversal invariant topological phase at the surface of a 3D topological insulator
A 3D fermionic topological insulator has a gapless Dirac surface state protected by time-reversal symmetry and charge conservation symmetry. The surface state can be gapped by introducing
Realizing topological surface states in a lower-dimensional flat band
The anomalous surface states of symmetry protected topological (SPT) phases are usually thought to be only possible in conjunction with the higher dimensional topological bulk. However, it has
Unhinging the Surfaces of Higher-Order Topological Insulators and Superconductors.
We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting
Anomalous Crystal Symmetry Fractionalization on the Surface of Topological Crystalline Insulators.
TLDR
It is shown that for a mirror-symmetry-protected topological crystalline insulator with mirror Chern number n=4, its surface can be gapped out by an anomalous Z_{2} topological order, where all anyons carry mirror-Symmetry fractionalization M^{2}=-1.
Higher-order topological superconductors from Weyl semimetals
We propose that doped Weyl semimetals with {time-reversal and certain crystalline symmetries} are natural candidates to realize higher-order topological superconductors, which exhibit a fully gapped
Anomalous Symmetry Protected Topological States in Interacting Fermion Systems.
TLDR
The essential idea that there exists a new class of the so-called anomalous SPT (ASPT) states which are only well defined on the boundary of a trivial fermionic bulk system is demonstrated and the layer structure and systematical construction of ASPT states in interacting fermion systems in 2D with a total symmetry G_{f}=G_{b}×Z_{2}^{f}.
Coupled-wire description of surface ADE topological order
Symmetry-protected and symmetry-enriched topological (SPT/SET) phases in three dimensions are quantum systems that support non-trivial two-dimensional surface states. These surface states develop
Fractional Quantum Hall Effect in Weyl Semimetals.
TLDR
The situation when the interactions are not weak is considered and it is found that it is possible to open a gap in a magnetic Weyl semimetal while preserving its nontrivial electronic structure topology along with the translational and the charge conservation symmetries.
Anomalous Symmetry Fractionalization and Surface Topological Order
In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological
Theory of oblique topological insulators
A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary
...
...

References

SHOWING 1-10 OF 42 REFERENCES
Exactly Soluble Model of a 3 D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
We construct an exactly soluble Hamiltonian on the D=3 cubic lattice, whose ground state is a topological phase of bosons protected by time reversal symmetry, i.e a symmetry protected topological
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
Periodic table for topological insulators and superconductors
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a
Classification of topological insulators and superconductors in three spatial dimensions
We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial
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
Interacting one-dimensional fermionic symmetry-protected topological phases.
TLDR
This work shows that one-dimensional fermionic superconducting phases with Z(n) discrete S(z) spin rotation and time-reversal symmetries are classified by Z4 when n is even and Z2 when n are odd; all these strongly interacting topological phases can be realized by noninteracting fermions.
Three-Dimensional Topological Insulators
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states (SSs) as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of
Symmetry-Protected Topological Orders in Interacting Bosonic Systems
TLDR
Just as group theory allows us to construct 230 crystal structures in three-dimensional space, group cohomology theory is used to systematically construct different interacting bosonic SPT phases in any dimension and with any symmetry, leading to the discovery of bosonic topological insulators and superconductors.
Three-dimensional topological lattice models with surface anyons
We study a class of three dimensional exactly solvable models of topological matter first put forward by Walker and Wang [arXiv:1104.2632v2]. While these are not models of interacting fermions, they
Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
The effect of interactions on topological insulators and superconductors remains, to a large extent, an open problem. Here, we describe a framework for classifying phases of one-dimensional
...
...