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We explicitly calculate the Green functions describing quantum changes of topology in Friedman-Lemaitre-Robertson-Walker Universes whose spacelike sections are compact but endowed with distinct topologies. The calculations are performed…
Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…
Motivated by recent advances in digital quantum emulation using noisy intermediate-scale quantum (NISQ) devices and an increased interest in topological Green's function zeros in condensed matter systems, we here study Green's function…
One of the defining properties of the conventional three-dimensional ("$\mathbb{Z}_2$-", or "spin-orbit"-) topological insulator is its characteristic magnetoelectric effect, as described by axion electrodynamics. In this paper, we discuss…
We formulate a continuum model to study the low-energy electronic structure of heterostructures formed by graphene on a strong three-dimensional topological insulator (TI) for the case of both commensurate and incommensurate stacking. The…
We employ quantum Monte Carlo techniques to calculate the $Z_2$ topological invariant in a two-dimensional model of interacting electrons that exhibits a quantum spin Hall topological insulator phase. In particular, we consider the parity…
It is known that, under short-range interactions many topological superconductors (TSC) and topological insulators (TI) are trivialized, which means the boundary state of the system can be trivially gapped out by interaction without leading…
We theoretically address the impact of a random distribution of non-magnetic impurities on the surface states formed at the interface between a trivial and a topological insulator. The interaction of electrons with the impurities is…
Topological invariants in terms of the Green's function in momentum and real space determine properties of smooth textures within topological media. In space dimension D=1 the topological invariant N_3 in terms of the Green's function…
The outstanding transport properties expected at the edge of two-dimensional time-reversal invariant topological insulators have proven to be challenging to realize experimentally, and have so far only been demonstrated in very short…
We study the effect of interactions on the time reversal invariant topological insulators in four and three spatial dimensions. Their topological indices are expressed by the interacting Green's functions. Under the local self-energy…
We use a lattice Green function approach to study the stationary modes of a linear/nonlinear (Kerr) impurity embedded in a periodic one-dimensional lattice where we replace the standard discrete Laplacian by a fractional one. The energies…
We study the dynamics of a non-magnetic impurity interacting with the surface states of a 3D and 2D topological insulator. Employing the linked cluster technique we develop a formalism for obtaining the Greens function of the mobile…
The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently the generalization of this expression has been proposed for the non - uniform magnetic field. \rev{The…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the…
Charge transport in topological insulators is primarily characterised by so-called topologically projected helical edge states, where charge carriers are correlated in spin and momentum. In principle, dissipation-less current can be carried…
It has been understood that short range interactions can reduce the classification of topological superconductors in all dimensions. In this paper we demonstrate by explicit calculations that when the topological phase transition between…
We found that non-magnetic defects in two-dimensional topological insulators induce bound states of two kinds for each spin orientation: electron- and hole-like states. Depending on the sign of the defect potential these states can be also…
The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require…
We investigate topological invariants in strongly interacting many-body systems within holographic mean-field theory (H-MFT) framework. Analytic expressions for retarded Green's functions are obtained for all possible fermionic bilinear…