Related papers: Topological zero modes at nonzero chemical potenti…
We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potentials. Although the existence of the non-Hermiticity, the Majorana zero mode is still robust against the disorder perturbation. The analytic…
One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the construction of multiple zero modes has been sucessfully carried out only very recently.…
We study the properties of low-lying Dirac modes in quenched compact QED at $\beta =1.01$, employing $12^3\times N_t$ ($N_t =4,6,8,10,12$) lattices and the overlap formalism for the fermion action. We pay attention to the spatial…
We have derived algebraic, analytic expressions for the chemical potential without any restriction on temperature for all types of doped, or extrinsic, gapped Dirac cone materials including gapped graphene, silicene, germanene and…
We study SU(2) Lattice Gauge Theory with dynamical fermions at non-zero chemical potential $\mu$. The symmetries special to SU(2) for staggered fermions on the lattice are discussed explicitly and their relevance to spectroscopy and…
Majorana zero mode is an exotic quasi-particle excitation with non-Abelian statistics in topological superconductor systems, and can serve as the cornerstone for topological quantum computation, a new type of fault-tolerant quantum…
Topological phenomena in gauge theories have long been recognized as the driving force for chiral symmetry breaking and confinement. These phenomena can be conveniently investigated in the semi-classical picture, in which the topological…
We compute low-lying eigenmodes of the gauge covariant Laplace operator on the lattice at finite temperature. For classical configurations we show how the lowest mode localizes the monopole constituents inside calorons and that it hops upon…
Physics of topological materials have attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological…
Color superconductivity in high density QCD exhibits the color-flavor locked (CFL) phase. To explore zero modes in the CFL phase in the presence of a non-Abelian vortex with an SU(2) symmetry in the vortex core, we apply the index theorem…
We introduce topological non-trivial colorful regions around intersection points of two perpendicular vortex pairs and investigate their influence on topological charge density and eigenmodes of the Dirac operator. With increasing distance…
We study characteristic features of the eigenvalues of the Wilson-Dirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role of eigenvectors…
Fermionic zero modes associated with doubly periodic SU(2) instantons of unit charge are considered. In cases where the action density exhibits two `instanton cores' the zero mode peaks on one of four line-segments joining the two…
The exploration of topological superconductivity and Majorana zero modes has become a rapidly developing field. Many types of proposals to realize topological superconductors have been presented, and significant advances have been recently…
We study spectra, localization properties and local chirality of eigenvectors of the lattice Dirac operator. We analyze ensembles of quenched SU(3) configurations on both sides of the QCD phase transition. Our Dirac operator is a systematic…
The purpose of this study is to investigate the relations between instantons, monopoles, and Chiral symmetry breaking. The monopoles are important topological configurations existing in QCD which are believed to produce colour confinement.…
We show that the local gauge-invariance of the quantum geometric tensor (QGT) defined in the Block-momentum space of a generic $N$-level (sublattice degrees of freedom) band insulator implies the existence of zero modes of non-abelian Dirac…
We systematically compare filtering methods used to extract topological excitations (like instantons, calorons, monopoles and vortices) from lattice gauge configurations, namely APE-smearing and spectral decompositions based on lattice…
We study the localization properties of the eigenmodes of the staggered Dirac operator in finite-temperature $\mathbb{Z}_2$ pure gauge theory on the lattice in 2+1 dimensions. We find that the low modes turn from delocalized to localized as…
In continuum QCD, nontrivial gauge topologies give rise to zero eigenvalues of the massless Dirac operator. In lattice QCD with Wilson fermions, these zero modes appear as exactly real eigenvalues of the Wilson-Dirac operator and hence as…