Related papers: Quantum geometry in the dynamics of band-projected…
In the first part of this Dissertation, we study non-perturbative aspects of quantum electrodynamics on Riemannian manifolds by using heat kernel asymptotic expansion techniques. Here, we established the existence of a new non-perturbative…
Recent discoveries in semi-metallic multi-gap systems featuring band singularities have galvanized enormous interest in particular due to the emergence of non-Abelian braiding properties of band nodes. This previously uncharted set of…
y formally diagonalizing with accuracy $\hbar$ the Hamiltonian of electrons in a crystal subject to electromagnetic perturbations, we resolve the debate on the Hamiltonian nature of semiclassical equations of motion with Berry-phase…
Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry.…
Exploiting novel aspects of the quantum geometry of charged particles in a magnetic field via gauge-invariant variables, we provide tangible connections between the response of quantum Hall fluids to non-uniform electric fields and the…
Excitons are neutral objects, that, naively, should have no response to a uniform, electric field. Could the Berry curvature of the underlying electronic bands alter this conclusion? In this work, we show that Berry curvature can indeed…
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…
Understanding the relationship between quantum geometry and topological invariants is a central problem in the study of topological states. In this work, we establish the relationship between the quantum metric and the Euler curvature in…
There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key…
In solid state physics, electronic properties of crystalline materials are often inferred from the spectrum of periodic Schr\"odinger operators. As a consequence of Bloch's theorem, the numerical computation of electronic quantities of…
The emerging possibilities to steer and control electronic motion on subcycle time scales with strong electric fields enable studying the nonperturbative optical response and Bloch bands' topological properties, originated from Berry's…
We investigate the low energy continuum limit theory for electrons in a graphene sheet under strain. We use the quantum field theory in curved spaces to analyze the effect of the system deformations into an effective gauge field. We study…
Magnetic field emerging from the geometric curvature of quantum structure of electrons in a crystal bends electronic trajectory causing anomalous linear and nonlinear electrical Hall effects that have been observed in low symmetry crystals…
Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation.…
Starting from a general $N$-band Hamiltonian with weak spatial and temporal variations, we derive a low energy effective theory for transport within one or several overlapping bands. To this end, we use the Wigner representation that allows…
The semiclassical approximation for electron wave-packets in crystals leads to equations which can be derived from a Lagrangian or, under suitable regularity conditions, in a Hamiltonian framework. In the plane, these issues are studied %in…
The optical properties of solids are governed not only by their energy band dispersions but also by the quantum geometry of Bloch states. While the role of energy bands in determining the perceived optical appearance of materials, such as…
We present a comprehensive study of the velocity operator, $\hat{\boldsymbol{v}}=\frac{i}{\hbar} [\hat{H},\hat{\boldsymbol{r}}]$, when used in crystalline solids calculations. The velocity operator is key to the evaluation of a number of…
Contrary to the conventional view point of quantization that breaks the gauge symmetry, a gauge invariant formulation of quantum electrodynamics is proposed. Instead of fixing the gauge, some frame is chosen to yield the locally invariant…
Based on the Keldysh formalism, we derive an effective Boltzmann equation for a quasi-particle associated with a particular Fermi surface in an interacting Fermi liquid. This provides a many-body derivation of Berry curvatures in electron…