A topological superconductor is characterized by having a pairing gap in the bulk and gapless self-hermitian Majorana modes at its boundary. In one dimension, these are zero-energy modes bound to the ...ends, while in two dimensions these are chiral gapless modes traveling along the edge. Majorana modes have attracted a lot of interest due to their exotic properties, which include non-abelian exchange statistics. Progress in realizing topological superconductivity has been made by combining spin–orbit coupling, conventional superconductivity, and magnetism. The existence of protected Majorana modes, however, does not inherently require the breaking of time-reversal symmetry by magnetic fields. Indeed, pairs of Majorana modes can reside at the boundary of a time-reversal-invariant topological superconductor (TRITOPS). It is the time-reversal symmetry which then protects this so-called Majorana Kramers’ pair from gapping out. This is analogous to the case of the two-dimensional topological insulator, with its pair of helical gapless boundary modes, protected by time-reversal symmetry. Realizing the TRITOPS phase will be a major step in the study of topological phases of matter. In this paper we describe the physical properties of the TRITOPS phase, and review recent proposals for engineering and detecting them in condensed matter systems, in one and two spatial dimensions. We mostly focus on extrinsic superconductors, where superconductivity is introduced through the proximity effect. We emphasize the role of interplay between attractive and repulsive electron–electron interaction as an underlying mechanism. When discussing the detection of the TRITOPS phase, we focus on the physical imprint of Majorana Kramers’ pairs, and review proposals of transport measurement which can reveal their existence.
Generalized global symmetries Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan ...
The journal of high energy physics,
02/2015, Letnik:
2015, Številka:
2
Journal Article
Recenzirano
Odprti dostop
A
bstract
A
q
-form global symmetry is a global symmetry for which the charged operators are of space-time dimension
q
; e.g. Wilson lines, surface defects, etc., and the charged excitations have
q
...spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries (
q
= 0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a sub-group). They can also have ’t Hooft anomalies, which prevent us from gauging them, but lead to ’t Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.
A
bstract
It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with
...ℤ
2
symmetry, where
ℤ
2
is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension
D
≤ 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.
Topological states of non-Hermitian systems Martinez Alvarez, V. M.; Barrios Vargas, J. E.; Berdakin, M. ...
The European physical journal. ST, Special topics,
12/2018, Letnik:
227, Številka:
12
Journal Article
Recenzirano
Odprti dostop
Recently, the search for topological states of matter has turned to non-Hermitian systems, which exhibit a rich variety of unique properties without Hermitian counterparts. Lattices modeled through ...non-Hermitian Hamiltonians appear in the context of photonic systems, where one needs to account for gain and loss, circuits of resonators, and also when modeling the lifetime due to interactions in condensed matter systems. Here we provide a brief overview of this rapidly growing subject, the search for topological states and a bulk-boundary correspondence in non-Hermitian systems.
A
bstract
We discuss bosonization and Fermionic Short-Range-Entangled (FSRE) phases of matter in one, two, and three spatial dimensions, emphasizing the physical meaning of the cohomological ...parameters which label such phases and the connection with higher-form symmetries. We propose a classification scheme for fermionic SPT phases in three spatial dimensions with an arbitrary finite point symmetry
G
. It generalizes the supercohomology of Gu and Wen. We argue that the most general such phase can be obtained from a bosonic “shadow” by condensing both fermionic particles and strings.
A
bstract
It is known that the ’t Hooft anomalies of invertible global symmetries can be characterized by an invertible TQFT in one higher dimension. The analogous statement remains to be understood ...for non-invertible symmetries. In this note we discuss how the linking invariants in a non-invertible TQFT known as the Symmetry TFT (SymTFT) can be used as a diagnostic for ’t Hooft anomalies of non-invertible symmetries. When the non-invertible symmetry is non-intrinsically non-invertible, and hence the SymTFT is a Dijkgraaf-Witten model, the linking invariants can be computed explicitly. We illustrate this proposal through the examples of the abelian Higgs model in 2d, as well as adjoint QCD and
N
= 4 super Yang-Mills in 4d. We also comment on how the ’t Hooft anomalies of non-invertible symmetries impose new constraints on the dynamics.
A
bstract
We investigate a higher-group structure of massless axion electrodynamics in (3 + 1) dimensions. By using the background gauging method, we show that the higher-form symmetries necessarily ...have a global semistrict 3-group (2-crossed module) structure, and exhibit ’t Hooft anomalies of the 3-group. In particular, we find a cubic mixed ’t Hooft anomaly between 0-form and 1-form symmetries, which is specific to the higher-group structure.
A
bstract
We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the 4d U(1) gauge theory with electric and magnetic matters, and it enjoys the SL(2
...,
ℤ) self-duality at low-energies. SL(2
,
ℤ) self-duality does not realize in a naive way, but we notice that the
ST
p
duality transformation becomes the legitimate duality operation by performing the gauging of ℤ
N
1-form symmetry with including the level-
p
discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a
K
3 surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.
A
bstract
We discuss the classification of SPT phases in condensed matter systems. We review Kitaev’s argument that SPT phases are classified by a generalized cohomology theory, valued in the ...spectrum of gapped physical systems
20
,
23
. We propose a concrete description of that spectrum and of the corresponding cohomology theory. We compare our proposal to pre-existing constructions in the literature.
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