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The quantum geometry of Bloch wavefunctions underpins a wealth of emergent phenomena in quantum materials. Its imaginary part, the Berry curvature, has long been recognized as a key source for hallmark effects such as quantum Hall and…
Bloch wave functions of electrons have properties called quantum geometry, which has recently attracted much attention as the origin of intriguing physical phenomena. In this paper, we introduce the notion of the quantum-geometric pair…
For decades, ``geometry" in band theory has largely meant Berry phase and Berry curvature-quantities that reshape semiclassical dynamics and underpin modern topological matter. Yet the full geometric content of a Bloch band is richer and…
Quantized transport is a prominent feature in topological physics, with canonical examples being the quantum Hall effect and adiabatic Thouless pump, which are based on the Chern number, a topological invariant of 2D systems. Going beyond…
Conduction of electrons in matter is ultimately described by quantum mechanics. Yet at low frequency or long time scales, low temperature quantum transport is perfectly described by this very simple idea: electrons are emitted by the…
Using the Landauer formulation of transport theory, we predict that dielectric quantum wires should exhibit quantized thermal conductance at low temperatures in a ballistic phonon regime. The quantum of thermal conductance is universal,…
The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the…
Quantum geometry, encoded in the Berry curvature and quantum metric, has unified diverse anomalous transport phenomena in solids, yet a microscopic quantum-geometric theory of entropy transport for Bloch electrons is still lacking. We…
The equivalence between thermal field theory and the Boltzmann transport equation is investigated at higher orders in the context of quantum electrodynamics. We compare the contributions obtained from the collisionless transport equation…
Quantum geometry of Bloch wavefunctions has gained considerable interest with the discovery of moir\'e materials that exhibit bands flattened by quantum interference. The quantum metric, the symmetric part of the quantum geometric tensor,…
Novel intrinsic two-dimensional materials have attracted many researchers' attention. The unusual transport and optical properties of these materials originate mainly from triangular lattices (TLs). Therefore, the application of energy…
The thermal power ($PF=S^2G_e$) depends on the Seebeck coefficient ($S$) and electron conductance ($G_e$). The enhancement of $G_e$ will unavoidably suppress $S$ because they are closely related. As a consequence, the optimization of $PF$…
Quantum geometry, a quantum mechanical quantity comprised of Berry curvature and quantum metric, describes the geometric structure of the electronic bands in solids. The correlation between nontrivial quantum geometry and quantum materials…
Although quasiparticles in flat bands have zero group velocity, they can display an anomalous velocity due to the quantum geometry. We address the thermal and thermoelectric transport in flat bands in the clean limit with a small amount of…
We present a geometric optics theory for the transport of quantum particles (or classical waves) in a chiral and dissipative periodic crystal subject to slowly varying perturbations in space and time. Taking account of some properties of…
This paper posits the existence of, and finds a candidate for, a variable change that allows quantum mechanics to be interpreted as quantum geometry. The Bohr model of the Hydrogen atom is thought of in terms of an indeterministic electron…
Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in…
We apply the semi-classical quantum Boltzmann formalism for the computation of transport properties to multilayer graphene. We compute the electrical conductivity as well as the thermal conductivity and thermopower for Bernal-stacked…
We discuss in general how to geometrically visualize a qudit system, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian…
Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the…