Related papers: Berry phase, semiclassical quantization and Landau…
We study the energy spectrum and the quantized Hall conductance of electrons in a two-dimensional periodic potential with perpendicular magnetic field WITHOUT neglecting the coupling of the Landau bands. Remarkably, even for weak Landau…
Geometric phases are well known in classical electromagnetism and quantum mechanics since the early works of Pantcharatnam and Berry. Their origin relies on the geometric nature of state spaces and has been studied in many different systems…
An effective Hamiltonian approach is used to study the effect of Landau-level mixing on the energy spectrum of electrons in a smooth but random magnetic field B(r) with a finite uniform component B_0. It is found that, as opposed to…
Properly regularized second-order degenerate perturbation theory is applied to compute the contribution of higher Landau levels to the low-energy spectrum of interacting electrons in a disk-shaped quantum dot. At ``filling factor'' near…
We consider an electron in two dimensions submitted to a magnetic field and to the potential of impurities. We show that when the electron is confined to a half-space by a planar wall described by a smooth increasing potential, the total…
We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed…
Berry phases have long been known to significantly alter the properties of periodic systems, resulting in anomalous terms in the semiclassical equations of motion describing wave-packet dynamics. In non-Hermitian systems, generalizations of…
We generalize the fractional quantum Hall hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Applying this to the nu = 5/2 Moore-Read state, we construct new explicit trial wavefunctions to…
We show that the geometric phase of the gyro-motion of a classical charged particle in a uniform time-dependent magnetic field described by Newton's equation can be derived from a coherent Berry phase for the coherent states of the…
We develop a theory of magnetic breakdown (MB) near high-order saddle points in the dispersions of two-dimensional materials, where two or more semiclassical cyclotron orbits approach each other. MB occurs due to quantum tunneling between…
Manipulating valley-dependent Berry phase effects provides remarkable opportunities for both fundamental research and practical applications. Here, by referring to effective model analysis, we propose a general scheme for realizing…
We study the Landau quantization of the electronic spectrum for graphene bilayers that are rotationally faulted to produce periodic superlattices. Commensurate twisted bilayers exist in two families distinguished by their sublattice…
The properties that quantify photonic topological insulators (PTIs), Berry phase, Berry connection, and Chern number, are typically obtained by making analogies between classical Maxwell's equations and the quantum mechanical…
We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moir\'e superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures,…
Broken symmetry and tilting effects are ubiquitous in Weyl semimetals (WSMs). Therefore, it is crucial to understand their impacts on the materials' electronic and optical properties. Here, using a realistic four-band model for WSMs that…
We investigate the competition between electron-solid and quantum-liquid phases in graphene, which arise in partially filled Landau levels. The differences in the wave function describing the electrons in the presence of a perpendicular…
Semiclassical methods are extremely valuable in the study of transport and thermodynamical properties of ballistic microstructures. By expressing the conductance in terms of classical trajectories, we demonstrate that quantum interference…
Using semi-classical formalism and asymptotic proliferation law of periodic orbits, we obtain an analytical expressions for the two-level cluster function, spectral form factor, level spacing distribution and the number variance for…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
Berry phase was originally defined for systems whose states are separated by finite energy gaps. One might naively expect that a system without a gap cannot have a Berry phase. Despite this we ask whether a Berry phase can be observed in a…