Related papers: Topological superfluid $^3$He-B: fermion zero mode…
Topological phases like topological insulators or superconductors are fascinating quantum states of matter, featuring novel properties such as emergent chiral edge states or Majorana fermions with non-Abelian braiding statistics. The recent…
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving Dirac fermions that behave as massless relativistic particles. These Dirac fermions are responsible for achieving a…
We study the vortex zero-energy bound states in presence of pairing among the low-energy Dirac fermions on the surface of a topological insulator. The pairing symmetries considered include the $s$-wave, $p$-wave, and, in particular, the…
We discuss the dispersionless spectrum with zero energy in the linear topological defects - vortices. The flat band emerges inside the vortex living in the bulk medium containing topologically stable Fermi points in momentum space. The…
Supersymmetry has been studied at a linear level between normal modes of metamaterials described by rigidity matrices and non-interacting quantum Hamiltonians. The connection between classical and quantum was made through the matrices…
We describe how color superfluidity is modified in the presence of color-flip and color-orbit fields in the context of ultra-cold atoms, and discuss connections between this problem and that of color superconductivity in quantum…
We consider quantized vortices in two-component Bose-Einstein condensates and three-component Fermi gases with attractive interactions. In these systems, the vortex core can be either empty (normal in the fermion case) or filled with…
Currently, there is much interest in discovering analytically tractable (3+1)-dimensional models that describe interacting fermions with emerging topological properties. Towards that end we present a three-dimensional tight-binding model of…
In the past few years materials with protected gapless surface (edge) states have risen to the central stage of condensed matter physics. Almost all discussions centered around topological insulators and superconductors, which possess full…
Topological semimetals are gapless states of matter which have robust surface states and interesting electromagnetic responses. In this paper, we consider the electromagnetic response of gapless phases in $3+1$-dimensions with line nodes.…
In this letter we demonstrate that the fermionic zero modes on a superconducting domain wall can be associated to an one dimensional $N=6$ supersymmetry that contains non-trivial topological charges. In addition, the system also possesses…
Flat bands, emergent in strongly correlated electron systems, stand at the frontier of condensed matter physics, providing fertile ground for unconventional quantum phases. Recent observations of dispersionless bands at the Fermi level in…
We map the topological properties of a one dimensional superlattice to the optical properties of an electronic system. We find that the nonlinear-optical response is optimized for electrons that live in the transitional morphology between…
We consider the quasi-one dimensional system realized by an array of weakly coupled parallel one-dimensional "tubes" in a two-dimensional lattice which permits free motion of atoms in an axial direction in the presence of a Zeeman field,…
Topological semimetals with different types of band crossings provide a rich platform to realize novel fermionic excitations, known as topological fermions. In particular, some fermionic excitations can be direct analogues of elementary…
Topological band structures in electronic systems like topological insulators and semimetals give rise to highly unusual physical properties. Analogous topological effects have also been discussed in bosonic systems, but the novel phenomena…
Optical lattices play a versatile role in advancing our understanding of correlated quantum matter. The recent implementation of orbital degrees of freedom in chequerboard and hexagonal optical lattices opens up a new thrust towards…
Topological invariants for the 4D gapped system are discussed with application to the quantum vacua of relativistic quantum fields. Expression $\tilde{\cal N}_3$ for the 4D systems with mass gap defined in \cite{Volovik2010} is considered.…
Recently, topological quantum states of non-Hermitian systems, exhibiting rich new exotic states, have attracted great attention in condensed-matter physics. As for the demonstration, most of non-Hermitian topological phenomena previously…
We present a simple scheme for implementing a one-dimensional (1D) magnetic-flux lattice of ultracold fermionic spin-$1/2$ atoms. The resulting tight-binding model supports gapped and gapless topological phases, and chiral currents for…