Related papers: Topological superfluid 3He-B in magnetic field and…
We here demonstrate that the superfluid 3He-B under a magnetic field in a particular direction stays topological due to a discrete symmetry, that is, in a symmetry protected topological order. Due to the symmetry protected topological…
Owing to the richness of symmetry and well-established knowledge on the bulk superfluidity, the superfluid $^3$He has offered a prototypical system to study intertwining of topology and symmetry. This article reviews recent progress in…
Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, topology allows us to determine generic features of their fermionic spectrum, which…
We consider topological invariant describing the vacuum states of superfluid 3He-B, which belongs to the special class of time-reversal invariant topological insulators and superfluids. Discrete symmetries important for classification of…
Magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ were anticipated to exhibit magnetic energy gaps while recent spectroscopic studies did not observe them. Thus, magnetism on the surface is under debate. In this work, we…
We theoretically investigate the role of surface Andreev bound states (SABSs) on the phase diagram and spin susceptibilities of superfluid 3He confined to a restricted geometry. We first explicitly derive the dispersion of the SABS in 3He-B…
The theoretical study of topological superfluids and superconductors has so far been carried out largely as a translation of the theory of noninteracting topological insulators into the superfluid language, whereby one replaces electrons by…
The $p$-wave superfluid $^3$He is a textbook example of topological superfluids. Among its multiple superfluid phases, the B phase ($^3$He-B) is known as a topological state protected by time-reversal symmetry. One of the important…
The B-phase of superfluid $^3$He is a 3D time-reversal invariant (TRI) topological superfluid with an isotropic energy gap separating the ground-state and bulk continuum states. We report calculations of surface spectrum, spin- and mass…
It is shown that superfluids in two and three dimensions which have time reversal invariant ground states have phases which are distinguished by a topological invariant. Further, it is shown that the B-phase of $^3$ He is a superfluid in…
The B phase of superfluid $^\textrm 3$He ($^\textrm 3$He-B) is topologically nontrivial and the surface Andreev bound states formed on a surface are conceived as Majorana fermions. In a magnetic field, the surface Andreev bound states…
In this article, we give a comprehensive review of recent progress in research on symmetry-protected topological superfluids and topological crystalline superconductors, and their physical consequences such as helical and chiral Majorana…
Superfluid 3He-B belongs to the important special class of time-reversal invariant topological superfluids. It has Majorana fermions as edge states on the surface of bulk 3He-B. On the rough wall these fermion zero modes have finite density…
An electron moving in a magnetically ordered background feels an effective magnetic field that can be both stronger and more rapidly varying than typical externally applied fields. One consequence is that insulating magnetic materials in…
Topological insulators(1-8) are a novel form of matter which features metallic surface states with quasirelativistic dispersion similar to graphene(9). Unlike graphene, the locking of spin and momentum and the protection by time-reversal…
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,…
We provide topological classification of possible phases with the symmetry of the planar phase of superfluid $^3$He. Compared to the B-phase (class DIII in classification of Altland and Zirnbauer), it has an additional symmetry, which…
We discuss topological properties of the ground state of spatially homogeneous ensemble of fermions. There are several classes of topologically different fermionic vacua; in each case the momentum space topology of the vacuum determines the…
Three-dimensional topological insulators (3D-TIs) possess a specific topological order of electronic bands, resulting in gapless surface states via bulk-edge correspondence. Exotic phenomena have been realized in ferromagnetic TIs, such as…
Antiferromagnetic topological insulators harbor topological in-gap surface states protected by an anti-unitary $S$ symmetry, which is broken by the inevitable presence of domain walls. Whether an antiferromagnetic topological insulator with…