Related papers: Relation between winding numbers and energy disper…
We identify a mapping between two-dimensional (2D) electron transport in a minimally twisted graphene bilayer and a 1D quantum walk, where one spatial dimension plays the role of time. In this mapping a magnetic field B perpendicular to the…
We describe some semiclassical spectral properties of Harper-like operators, i.e. of one-dimensional quantum Hamiltonians periodic in both momentum and position. The spectral region corresponding to the separatrices of the classical…
Topological quantum state described by the global invariant has been extensively studied in theory and experiment. In this letter, we investigate the relationship between \emph{Zitterbewegung} and the topology of systems that reflect the…
Flux-energy and angle-energy diagrams for an exact three-dimensional Hamiltonian of the Bloch electron in a uniform magnetic field are analyzed. The dependence of the structure of the diagrams on the direction of the field, the geometry of…
We investigate the dynamics of Bloch electrons using a density operator method and connect this approach with previous theories based on wave packets. We study non-interacting systems with negligible disorder and strong spin-orbit…
We rigorously yet concisely prove the bulk-edge correspondence for general $d$-dimensional ($d$D) topological insulators in complex Altland-Zirnbauer classes, which states that the bulk topological number equals to the edge-mode index.…
We consider the Hall conductivity of two-dimensional non-interacting Bloch electrons when the magnetic flux per unit cell is a rational number $p/q$ where $p$ and $q$ are mutually coprime. We present a counter-example for the naive…
The velocity-vorticity correlation integral (Chkhetiani invariant) is an invariant of a viscous Karman-Howarth equation. In the tree-dimensional space this invariant can naturally determine a turbulent diffusivity (viscosity). It is shown,…
We study the relation between the global topology of the Hofstadter butterfly of a multiband insulator and the topological invariants of the underlying Hamiltonian. The global topology of the butterfly, i.e., the displacement of the energy…
For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of…
We study the phenomenon of wave packet revivals of Bloch electrons and explore how to control them by a magnetic field for quantum information transfer. It is showed that the single electron system can be modulated into a linear dispersion…
The geometric characteristics of Bloch wave functions play a crucial role in electronic transport properties. We show that the thermoelectric performance of materials is governed by the geometric structure of Bloch wave functions within the…
The study of band topology in photonic crystals was primarily focused on near-field effects, including edge states and high order corner states. However, this work investigated the polarization distribution of radiated fields for photonic…
We study the turbulent velocity dispersion spectra of the coexistent HCN and HCO+ molecular species as a function of length scale in the M17 star-forming molecular cloud. We show that the observed downward shift of the ion's spectrum…
The characteristics of topologically protected wave propagation is typically predicted via the band structure of the primitive unit cell, using Berry curvature to predict localized interface or boundary states (as well as their degree of…
The study of topology of energy bands in solid has always been interesting and fruitful. Historically, Thouless et al proposed the TKNN number or Chern number of the energy bands to explain the quantization of Hall conductance in the…
A Lie-algebraic approach successfully used to describe one-dimensional Bloch oscillations in a tight-binding approximation is extended to two dimensions. This extension has the same algebraic structure as the one-dimensional case while the…
The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and…
We investigate further the relationship between the entanglement spectrum of a composite many-body system and the energy spectrum of a subsystem making use of concepts of canonical thermodynamics. In many important cases the entanglement…
We investigate Bloch oscillations of wave packets in monolayer phosphorene with broken inversion symmetry. We find that the real space trajectories, Berry and group velocities of Bloch electron undergo Bloch oscillations in the system. The…