Related papers: Quantum geometry in the dynamics of band-projected…
Starting from the density-matrix equation of motion, we derive a semiclassical kinetic equation for a general two-band electronic Hamiltonian, systematically including quantum-mechanical corrections up to second order in space-time…
Berry curvature-related topological phenomena have been a central topic in condensed matter physics. Yet, until recently other quantum geometric quantities such as the metric and connection received only little attention due to the…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
Recent studies have revealed that the quantum geometry of electronic bands determines the electromagnetic properties of non-interacting insulators and semimetals. However, the role of quantum geometry in the optical responses of interacting…
The eigenvalues of a parameter-dependent Hamiltonian matrix form a band structure in parameter space. In such $N$-band systems, the quantum geometric tensor (QGT), consisting of the Berry curvature and quantum metric tensors, is usually…
The nonlinear optical behavior of quantum systems plays a crucial role in various photonic applications. This study introduces a novel framework for understanding these nonlinear effects by incorporating gauge-covariant formulations based…
We review recent developments in the research of nonlinear and nonequilibrium phenomena in solids focusing on their geometrical aspects. We start with introducing the basic concepts of geometrical phases of Bloch electrons and Floquet…
Electronic properties of quantum materials solids are often well understood via the low energy dispersion of Bloch bands, motivating single band approximations in many metals and semiconductors. However, a closer look reveals length and…
We have studied particle motion in generalized forms of noncommutative phase space, that simulate monopole and other forms of Berry curvature, that can be identified as effective internal magnetic fields, in coordinate and momentum space.…
We develop a unified theory for the nonadiabatic wave-packet dynamics of Bloch electrons subject to slowly varying spatial and temporal perturbations. Extending the conventional wave-packet ansatz to include interband contributions, we…
We explore how the quantum geometric properties of the Bloch wave function, characterized by the Hilbert-Schmidt quantum distance, impact magnetic phases in solid-state systems. To this end, we investigate the spin susceptibility within the…
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…
We propose a solution to the problem of Bloch electrons in a homogeneous magnetic field by including the quantum fluctuations of the photon field. A generalized quantum electrodynamical (QED) Bloch theory from first principles is presented.…
Quantum geometric formulations of linear and nonlinear responses can be constructed from a single building block in the form of a gauge-invariant interband transition operator. Here, we identify a second building block for quantum geometry:…
In this article we show that if the electrons in a quantum Hall sample are subjected to a constant electric field in the plane of the material, comparable in magnitude to the background magnetic field on the system of electrons, a…
Geometry and topology are fundamental to modern condensed matter physics, but their precise connection in quantum systems remains incompletely understood. Here, we develop an analytical scheme for calculating the curvature of the quantum…
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 topology of a single-particle band structure plays a fundamental role in understanding a multitude of physical phenomena. Motivated by the connection between quantum walks and such topological band structures, we demonstrate that a…
Within the wave-packet semiclassical approach, the Bloch electron energy is derived to second order in the magnetic field and classified into gauge-invariant terms with clear physical meaning, yielding a fresh understanding of the complex…
We present a unified theory for wave-packet dynamics of electrons in crystals subject to perturbations varying slowly in space and time. We derive the wave-packet energy up to the first order gradient correction and obtain all kinds of…