Related papers: Berry-Chern monopoles and spectral flows
We show that the non-Abelian Berry phase emerges naturally in the s-wave and spin quintet pairing channel of spin-3/2 fermions. The topological structure of this pairing condensate is characterized by the second Chern number. This…
We give a mathematical analysis of the periodic band inversion phenomenon observed by Tan--Devakul for an electron in a two-dimensional periodic potential coupled to a circularly polarized photon cavity mode. In the strong-coupling limit,…
Topological properties of quantum system is directly associated with the wave function. Based on the decomposition theory of gauge potential, a new comprehension of topological quantum mechanics is discussed. One shows that a topological…
Employing the Foldy-Wouthuysen transformation it is demonstrated straightforwardly that the first and second Chern numbers are equal to the coefficients of the 2+1 and 4+1 dimensional Chern-Simons actions which are generated by the massive…
In this work, we study the connection between two subjects: the space of conformal boundary conditions in boundary conformal field theories (BCFTs) and the space of gapped systems characterized by higher Berry phases. We explore this…
We investigate the effect of the Berry phase on quadrupoles that occur for example in the low-energy description of spin models. Specifically we study here the one-dimensional bilinear-biquadratic spin-one model. An open question for many…
This chapter describes topological (Dirac and Weyl) semimetals from the viewpoint of their observable electromagnetic response. We argue that this response may be represented by topological terms with unquantized (non-integer) coefficients…
In topological phase transitions involving a change in topological invariants such as the Chern number and the $\mathbb{Z}_2$ topological invariant, the gap closes, and the electric polarization becomes undefined at the transition. In this…
Recently discovered Weyl semimetals (WSM) have found special place in topological condensed matter studies for they represent first example of massless Weyl fermions found in condensed matter systems. A WSM shows gapless bulk energy spectra…
We consider fermionic states bound on domain walls in a Weyl superfluid $^3$He-A and on interfaces between $^3$He-A and a fully gapped topological superfluid $^3$He-B. We demonstrate that in both cases fermionic spectrum contains Fermi arcs…
We study the topological characterization of the energy gaps in general two-dimensional quasiperiodic systems consisting of multiple periodicities, represented by twisted two-dimensional materials. We show that every single gap is uniquely…
In recent years there has been a great interest in topological photonics and protected edge states. Here, we present a first principles method to compute topological invariants of three-dimensional gapless phases. Our approach allows to…
Topology and chirality of fermionic quasiparticles have enabled exciting discoveries, including quantum anomalous Hall liquids and topological superconductivity. Recently, topological and chiral phonons emerge as new and fast-evolving…
The Chern number is a crucial topological invariant for distinguishing the phases of Chern insulators. Here we find that for Chern insulators with inversion symmetry, the Chern number alone is insufficient to fully characterize their…
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…
We study the constraints of supersymmetry on the non-Abelian holonomy given by U=P exp(i\int A), the path-ordered exponential of a connection A. For theories with four supercharges, we show that A satisfies the tt* equations if it is a…
Chiral superconductors are one of the predominant quantum electronic states of matter where topology, symmetry, and Fermiology intertwine. This is pushed to a new limit by further invoking the coupling between spin and charge degrees of…
The present paper explores how the spectral sequence introduced in a previous work (and obtained by taking moduli spaces of any dimension into account in the Floer construction), interacts with the presence of bubbling. As consequences are…
We analyse second order (in Riemann curvature) geometric flows (un-normalised) on locally homogeneous three manifolds and look for specific features through the solutions (analytic whereever possible, otherwise numerical) of the evolution…
This paper discusses a connection between two important classes of materials, namely quasicrystals and topological insulators as exemplified by the Quantum Hall problem. It has been remarked that the quasicrystal ``inherits" topological…