A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator

Chetan Nayak; Parsa Bonderson; Xiao-Liang Qi

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A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator

Parsa Bonderson, Chetan Nayak, Xiao-Liang Qi

Strongly Correlated Electrons · Submitted 13 Jun 2013

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The authors' main claim In this paper, we construct a minimal gapped topological phase that preserves both time-reversal and charge conservation symmetries and supports Ising-type non-Abelian anyons.

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arXiv ID1306.3230 (version 2)

Pith IDHRIGPIWI, Pith's permanent record of this paper and its review

CitationChetan Nayak, Parsa Bonderson, Xiao-Liang Qi. "A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator." arXiv:1306.3230 (2013). https://pith.science/paper/HRIGPIWI

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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 ferromagnetism to break time-reversal symmetry, introducing superconductivity to break charge conservation, or entering a topological phase. In this paper, we construct a minimal gapped topological phase that preserves both time-reversal and charge conservation symmetries and supports Ising-type non-Abelian anyons. This phase can be understood heuristically as emerging from a surface s-wave superconducting state via the condensation of eight-vortex composites. The topological phase inherits vortices supporting Majorana zero modes from the surface superconducting state. However, since it is time-reversal invariant, the surface topological phase is a distinct phase from the Ising topological phase, which can be viewed as a quantum-disordered spin-polarized p_x + i p_y superconductor. We discuss the anyon model of this topological phase and the manner in which time-reversal symmetry is realized in it. We also study the interfaces between the topological state and other surface gapped phases.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	A 3D fermionic topological insulator has a gapless Dirac surface state protected by time-reversal symmetry and charge conservation symmetry.	background 1.00	0.06	0.03	asserted 1.00
s1	The surface state can be gapped by introducing ferromagnetism to break time-reversal symmetry, introducing superconductivity to break charge conservation, or entering a topological phase.	background 1.00	0.08	0.03	asserted 0.90
s2	In this paper, we construct a minimal gapped topological phase that preserves both time-reversal and charge conservation symmetries and supports Ising-type non-Abelian anyons.	contribution 0.99	0.95	0.82	asserted 1.00
s3	This phase can be understood heuristically as emerging from a surface s-wave superconducting state via the condensation of eight-vortex composites.	interpretation 0.98	0.66	0.08	hedged possibility 0.61
s4	The topological phase inherits vortices supporting Majorana zero modes from the surface superconducting state.	interpretation 0.64	0.62	0.08	asserted 1.00
s5	However, since it is time-reversal invariant, the surface topological phase is a distinct phase from the Ising topological phase, which can be viewed as a quantum-disordered spin-polarized p_x + i p_y superconductor.	interpretation 0.81	0.54	0.14	asserted 0.98
s6	We discuss the anyon model of this topological phase and the manner in which time-reversal symmetry is realized in it.	contribution 1.00	0.88	0.05	asserted 0.63
s7	We also study the interfaces between the topological state and other surface gapped phases.	contribution 1.00	0.90	0.03	asserted 0.90

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.71.

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Original abstract

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 ferromagnetism to break time-reversal symmetry, introducing superconductivity to break charge conservation, or entering a topological phase. In this paper, we construct a minimal gapped topological phase that preserves both time-reversal and charge conservation symmetries and supports Ising-type non-Abelian anyons. This phase can be understood heuristically as emerging from a surface s-wave superconducting state via the condensation of eight-vortex composites. The topological phase inherits vortices supporting Majorana zero modes from the surface superconducting state. However, since it is time-reversal invariant, the surface topological phase is a distinct phase from the Ising topological phase, which can be viewed as a quantum-disordered spin-polarized p_x + i p_y superconductor. We discuss the anyon model of this topological phase and the manner in which time-reversal symmetry is realized in it. We also study the interfaces between the topological state and other surface gapped phases.

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References

Forward citations

Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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How the literature uses it

31 arXiv papers cite this in 51 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 33 sentences without a confident label

Uses its data or values 1 paper

The $S$ matrix of the T-Pfaffian topological order can be found in Ref. [ref] .

Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries · Examples · 0.96

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We find that the gauged T-Pfaffian$_±$ state, discussed in Refs. [ref] and [ref] , has $𝒵(ℝℙ^4) = ±1$ and $𝒵(ℂℙ^2) = 1$, agreeing with the analysis of Ref. [ref] .

Reflection and time reversal symmetry enriched topological phases of matter: path integrals, non-orientable manifolds, and anomalies · Examples · 0.88
Qi [ref] which obtains the same STO as in Ref. [ref] .

Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator · Discussion · 0.86

Cites it as background 9 papers

In the past few years, special attention has been paid to 3D SPT systems with a gapped, symmetric, and topologically ordered surface state [ref] , i.e., the surface is a symmetric-enriched topological (SET) state [ref] .

Anomaly indicators and bulk-boundary correspondences for 3D interacting topological crystalline phases with mirror and continuous symmetries · Introduction · 0.83
In the case where $T ∈G$ corresponds to a time-reversal symmetry, i.e. $T^2 = 0$, $q(T) = 1$, and $p(T) = 0$, Refs. [ref] and [ref] defined the local projective phase $η_a(T, T)$ associated with topological charge $a$, which characterizes the symmetry fractionalization class.

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The model $(U(1)_-8×Ising)/_2$ is known as T-Pfaffian [ref] .

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Following Refs. [ref] , we assign projective representations of $T^2$ locally to each quasiparticle type $a$, which amounts to ascribing a local $𝒯^2$ value of $η_a$ to type $a$ quasiparticles [Typically, one may assume $η_a = ±1$, but we can derive our results without making this assumption.].

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Following Refs. [ref] , we assign projective representations of $T^2$ locally to each quasiparticle type $a$, which amounts to ascribing a local $𝒯^2$ value of $η_a$ to type $a$ quasiparticles [Typically, one may assume $η_a = ±1$, but we can derive our results without making this assumption.].

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Wang et al. [ref] constructing another time-reversal invariant and charge-conserving topological phase, described by the anyon model $.

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Cites as background 7 papers

A TI is an example of a more general class called symmetry-protected topological (SPT) phases [ref] , which cannot be adiabatically transformed into the vacuum state so long as a symmetry group $G$ is preserved.

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A TI is an example of a more general class called symmetry-protected topological (SPT) phases [ref] , which cannot be adiabatically transformed into the vacuum state so long as a symmetry group $G$ is preserved.

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A TI is an example of a more general class called symmetry-protected topological (SPT) phases [ref] , which cannot be adiabatically transformed into the vacuum state so long as a symmetry group $G$ is preserved.

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