Related papers: Topo-fermiology
The use of topological invariants to describe geometric phases of quantum matter has become an essential tool in modern solid state physics. The first instance of this paradigmatic trend can be traced to the study of the quantum Hall…
In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…
The Berry connection plays a central role in our description of the geometric phase and topological phenomena. In condensed matter, it describes the parallel transport of Bloch states and acts as an effective "electromagnetic" vector…
We show that sharply defined topological quantum phase transitions are not limited to states of matter with gapped electronic spectra. Such transitions may also occur between two gapless metallic states both with extended Fermi surfaces.…
A series of strong anomalies in the thermoelectric power is observed in the heavy fermion compound YbRh$_2$Si$_2$ under the effect of magnetic field varying in the range from 9.5~T to 13~T. We identify these features with a sequence of…
The interplay of crystal symmetry, magnetism, band topology and electronic correlation can be the origin of quantum phase transitions in condensed matter. Particularly, square-lattice materials have been serving as a versatile platform to…
Motivated by the recent progress in engineering artificial non-Abelian gauge fields for ultracold fermions in optical lattices, we investigate the time-reversal-invariant Hofstadter-Hubbard model. We include an additional staggered lattice…
The Klein bottle Benalcazar-Bernevig-Hughes (BBH) insulator phase plays a pivotal role in understanding higher-order topological phases. The insulator phase is characterized by a unique feature: a nonsymmorphic glide symmetry that exists…
We review our recent works on the quantum transport, mainly in topological semimetals and also in topological insulators, organized according to the strength of the magnetic field. At weak magnetic fields, we explain the negative…
We consider the semiclassical quantization condition for the energy of an electron in a magnetic field in the case when the electron orbit lies on a Fermi-surface pocket surrounding the Weyl point of a topological semimetal and analyze the…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
The emergence of the Pomeranchuk instability (PI) in a Helical Fermi liquid (HFL) residing on the surface of a three-dimensional topological insulator (3D TI) is addressed at the mean-field level. An expression for the PI condition is…
The Fermi surface properties of a nontrivial system YSi is investigated by de Haas-van Alphen (dHvA) oscillation measurements combined with the first-principle calculations. Three main frequencies ($\alpha$, $\beta$, $\gamma$) are probed up…
Topology is now securely established as a means to explore and classify electronic states in crystalline solids. This review provides a gentle but firm introduction to topological electronic band structure suitable for new researchers in…
This article reviews recent theoretical and experimental work on transport due to the surface states of three-dimensional topological insulators. The theoretical focus is on longitudinal transport in the presence of an electric field,…
Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here, we describe in detail what this picture means…
We consider electrons on a two-leg triangular ladder at half-filling and in an orbital magnetic field. In a two-band regime in the absence of the field, the electronic system remains conducting for weak interactions since there is no…
We have derived a new set of semiclassical equations for electrons in magnetic Bloch bands. The velocity and energy of magnetic Bloch electrons are found to be modified by the Berry phase and magnetization. This semiclassical approach is…
Using quantum Monte Carlo simulations, we map out the phase diagram of Hamiltonians interpolating between trivial and non-trivial bosonic symmetry-protected topological phases, protected by $\mathbb{Z}_2$ and $\mathbb{Z}_2^3$ symmetries, in…
A Berry phase of odd multiples of $\pi$ inferred from quantum oscillations (QOs) has often been treated as evidence for nontrivial reciprocal space topology. However, disentangling the Berry phase values from the Zeeman effect and the…