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Two closely related topological phenomena are studied at finite density and temperature. These are chiral anomaly and Chern--Simons term. It occurs that the chiral anomaly doesn't depend on density and temperature. Chern-Simons term…
As a topological insulator, the quantum Hall (QH) effect is indexed by the Chern and spin-Chern numbers $\mathcal{C}$ and $\mathcal{C}_{\text{spin}}$. We have only $\mathcal{C}_{\text{spin}}=0$ or $\pm \frac{1}{2}$ in conventional QH…
We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of…
Quantum metrology is deeply connected to quantum geometry, through the fundamental notion of quantum Fisher information. Inspired by advances in topological matter, it was recently suggested that the Berry curvature and Chern numbers of…
We study the polaritonic bandstructure of two-dimensional atomic lattices coupled to a single excitation of a surface plasmon polariton mode. We show the possibility of realizing topological gaps with different Chern numbers by having…
We consider topological insulators and superconductors with discrete symmetries and clarify the relevant index theory behind the periodic table proposed by Kitaev. An effective Hamiltonian determines the analytical index, which can be…
We theoretically and numerically investigate Chern vector insulators and topological surface states in a three-dimensional lattice, based on phase-delayed temporal-periodic interactions within the tight-binding model. These Floquet…
We study the response of a class of topological systems to electromagnetic and gravitational sources, including torsion and curvature. By using the technology of anomaly polynomials, we derive the parity-odd response of a massive Dirac…
Topological phases in two-dimensional quantum lattice models are often studied on cylinders for revealing different topological properties and making the problem numerically tractable. This makes a proper understanding of…
Bulk-edge correspondence is one of the most distinct properties of topological insulators. In particular, the 1D winding number $\n$ has a one-to-one correspondence to the number of edge states in a chain of topological insulators with…
Topological phases of matter can be classified by using Clifford algebras through Bott periodicity. We consider effective topological field theories of quantum Hall systems and topological insulators that are Chern-Simons and BF field…
In 2D semiconductors and insulators, the Chern number of the valence band Bloch state is an important quantity that has been linked to various material properties, such as the topological order. We elaborate that the opacity of 2D materials…
We obtain the band structure of a particle moving in a magnetic spin texture, classified by its chirality and structure factor, in the presence of spin-orbit coupling. This rich interplay leads to a variety of novel topological phases…
Topology has appeared in different physical contexts. The most prominent application is topologically protected edge transport in condensed matter physics. The Chern number, the topological invariant of gapped Bloch Hamiltonians, is an…
Chern insulators are band insulators which exhibit a gap in the bulk and gapless excitations in the edge. Detection of Chern insulators is a serious challenge in cold atoms since the Hall transport measurements are technically unrealistic…
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of…
We consider interacting fermions in a magnetic field on a two-dimensional lattice with the periodic boundary conditions. In order to measure the Hall current, we apply an electric potential with a compact support. Then, due to the Lorentz…
We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct…
Topological quantum phases of matter have been a topic of intense interest in contemporary condensed matter physics. Extensive efforts are devoted to investigate various exotic properties of topological matters including topological…
Topological insulators are a novel state of matter that share a common feature: their spectral bands are associated with a nonlocal integer-valued index, commonly manifesting through quantized bulk phenomena and robust boundary effects. In…