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Topology, like symmetry, is a fundamental concept in understanding general properties of physical systems. In condensed matter, nontrivial topology may manifest itself as singular features in the energy spectrum or the quantization of…
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…
The detection of topological phases of matter becomes a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or…
Conductivity of Integer Quantum Hall Effect (IQHE) may be expressed as the topological invariant composed of the two - point Green function. Such a topological invariant is known both for the case of homogeneous systems with intrinsic…
We introduce a real-space slave rotor theory of the physics of topological Mott insulators, using the Kane-Mele-Hubbard model as an example, and use it to show that a topological gap in the Green function zeros corresponds to a gap in the…
The topological invariant responsible for the stability of Fermi point/Fermi surface in homogeneous systems is expressed through the one particle Green function, which depends on momentum. It is given by an integral over the 3D hypersurface…
We study topological defects as inhomogeneous (localized) condensates of particles in Quantum Field Theory. In the framework of the Closed-Time-Path formalism, we consider explicitly a $(1+1)$ dimensional $\la \psi^4$ model and construct…
Owing to the presence of exceptional points (EPs), non-Hermitian (NH) systems can display intriguing topological phenomena without Hermitian analogs. However, experimental characterizations of exceptional topological invariants have been…
This thesis uses Path Integrals and Green's Functions to study Gravity, Quantum Field Theory and Statistical Mechanics, particularly with respect to: finite temperature quantum systems of different spin in gravitational fields; finite…
We introduce three new analytical and semi-analytical tools that allow one to determine the topological character of impurity Shiba chains. The analytical methods are based on calculating the effective Green's function of an infinite…
Currently, the superconducting diode effect (SDE) is actively discussed due to large application potential in superconducting electronics. In particular, the superconducting hybrid structures based on three-dimensional (3D) topological…
We bring forward a Green function approach for the prediction of Floquet topological phases in driven superconductor-semiconductor hybrids. Although it is common to treat the superconducting component as a mere Cooper-pair reservoir, it was…
We present a generalization of free fermionic topological insulators that are composed of topological subsystems of differing dimensionality. We specifically focus on topological subsystems of nonzero co-dimension are embedded within a…
We study the quantization of the excess charge on $N$ localized (ultra-screened) impurities in $d$-dimensional crystalline insulating systems. Solving Dyson's equation, we demonstrate that such charges are topological, by expressing them as…
Higher dimensions provide fertile ground for diverse topological phases and their associated localization phenomena, thanks to the rich geometric features of boundaries and defects. In this paper, we investigate non-Hermitian lattices with…
Topological Insulators are the best thermoelectric materials involving a sophisticated physics beyond their solid state and electronic structure. We show that exists a topological contribution to the thermoelectric effect that arise between…
The study of the propagation of electrons with a varying spinor orientability is performed using the coordinate transformation method. Topological Insulators are characterized by an odd number of changes of the orientability in the…
It is shown that the Hamiltonian for a quantum magnetic impurity on the surface of a topological insulator can be mapped to the conventional pseudo-gap Anderson impurity model, albeit with the combinations of continuum states which…
The standard boundary state of a topological insulator in 3+1 dimensions has gapless charged fermions. We present model systems that reproduce this standard gapless boundary state in one phase, but also have gapped phases with topological…
Band structures of topological insulators are characterized by non-local topological invariants. Consequently, proposals for the experimental detection using local probes are rare. A recent paper [Slager et al., Phys. Rev. B 92, 085126…