Related papers: Hofstadter butterfly and integer quantum Hall effe…
We address the energy spectrum of honeycomb lattice with various defects or impurities under a perpendicular magnetic field. We use a tight-binding Hamiltonian including interactions with the nearest neighbors and investigate its energy…
We calculate the energy spectrum of an electron moving in a two-dimensional lattice which is defined by an electric potential and an applied perpendicular magnetic field modulated by a periodic surface magnetization. The spatial direction…
Motivated by recent experimental breakthroughs in realizing hyperbolic lattices in superconducting waveguides and electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. By utilizing large hyperbolic lattices…
We theoretically investigate the orbital effects of an in-plane magnetic field on the spectrum of a quantum dot embedded in a two-dimensional electron gas (2DEG). We derive an effective two-dimensional Hamiltonian where these effects enter…
We investigated the behavior of fractional quantum Hall (FQH) states in a two-dimensional electron system with layer thickness and an in-plane magnetic field. Our comparisons across various filling factors within the first Landau level…
The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms, calls for systematic studies of orbital effects of the magnetic field…
Integral Apollonian packing, the packing of circles with integer curvatures, where every circle is tangent to three other mutually tangent circles, is shown to encode the fractal structure of the energy spectrum of two-dimensional Bloch…
Since the discovery of the Fractional Quantum Hall Effect in 1982 there has been considerable theoretical discussion on the possibility of fractional quantization of conductance in the absence of Landau levels formed by a quantizing…
Physical systems with non-trivial topological order find direct applications in metrology[1] and promise future applications in quantum computing[2,3]. The quantum Hall effect derives from transverse conductance, quantized to unprecedented…
A Kubo inspired formalism is proposed to compute the longitudinal and transverse dynamical conductivities of an electron in a plane (or a gas of electrons at zero temperature) coupled to the potential vector of an external local magnetic…
We analyze a square lattice graph in a magnetic field assuming that the vertex coupling is of a particular type violating the time reversal invariance. Calculating the spectrum numerically for rational values of the flux per plaquette we…
The low-field quantum Hall effect is investigated on a two-dimensional electron system in an AlGaAs/GaAs heterostructure. Magneto-oscillations following the semiclassical Shubnikov-de Haas formula are observed even when the emergence of the…
The quantum kicked particle in a magnetic field is studied in a weak-chaos regime under realistic conditions, i.e., for {\em general} values of the conserved coordinate $x_{{\rm c}}$ of the cyclotron orbit center. The system exhibits…
Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram,…
Quasicrystal is now open to search for novel topological phenomena enhanced by its peculiar structure characterized by an irrational number and high-dimensional primitive vectors. Here we extend the concept of a topological insulator with…
The Landau Hamiltonian governing the behavior of a quantum particle in dimension 2 in a constant magnetic field is perturbed by a compactly supported magnetic field and a similar electric field. We describe how the spectral subspaces change…
We investigate the electronic properties in the Bloch electron on a square lattice with vacancies in the uniform magnetic field. We show that a single vacancy site introduced to the system creates a defect energy level in every single…
The spectrum of charged particles in translation-invariant systems in a magnetic field is characterized by the Landau levels, which play a fundamental role in the thermodynamic and transport properties of solids. The topological nature and…
We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the…
The problem of Bloch electrons in two dimensions subject to magnetic and intense electric fields is investigated, the quantum Hall conductance is calculated beyond the linear response approximation. Magnetic translations, electric evolution…