Related papers: Quantization of Hall Conductance For Interacting E…
We discuss the construction of a ground state wavefunction on a finite ring given the ground state on a long chain. In the presence of local symmetries, we can obtain the ground state with arbitrary flux inserted through the ring. A key…
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and…
The characterization and the experimental measurement of the Berry curvature in solids have become an increasingly relevant task in condensed matter physics. We present the theoretical prediction of a gate tunable anomalous Hall effect…
Electron motion in crystals is governed by the coupling between crystal momentum and internal degrees of freedom such as spin implicit in the band structure. The description of this coupling in terms of a momentum-dependent effective field…
In recent years, there is an increasing interest in transport phenomena that are fundamentally linked to the presence of multiple bands. In this thesis, we develop, discuss, and apply a theory of the electrical conductivity that includes…
We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons…
We show how to numerically calculate several quantities that characterize topological order starting from a microscopic fractional quantum Hall (FQH) Hamiltonian. To find the set of degenerate ground states, we employ the infinite density…
We use Dirac quantization of flux to study fractional charges and axion angles \theta in interacting topological insulators with gapless surface modes protected by time-reversal symmetry. In interacting topological insulators, there are two…
We find an analytical expression for the conductance of a single electron transistor in the regime when temperature, level spacing, and charging energy of a grain are all of the same order. We consider the model of equidistant energy levels…
Interference of fractionally charged quasi-particles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are…
Topological defects are ubiquitous from solid state physics to cosmology, where they drive phase transitions by proliferating as domain walls, monopoles or vortices. As quantum excitations, they often display fractional charge and anyonic…
Transport measurements indicate strong oscillations in the Hall-,$R_{xy}$, and the diagonal-, $R_{xx}$, resistances and exhibit Hall plateaus at the lowest temperatures, in three-dimensional Highly Oriented Pyrolytic Graphite (HOPG). At the…
We examined the magneto-transport behavior of electrons confined at the conducting LaAlO3/SrTiO3 interface in the low sheet carrier density regime. We observed well resolved Shubnikov-de Haas quantum oscillations in the longitudinal…
The thermodynamic potential of an ideal nonrelativistic gas of two-dimensional electrons in crossed uniform magnetic and electric fields is constructed. For low temperatures and very weak electric fields, it is shown that the Hall…
We have investigated the Hall resistance $R_H$ near the plateau-insulator transition of a two-dimensional electron gas in the quantum critical regime. High-field magnetotransport data taken on a low-mobility InGaAs/InP heterostructure with…
We develop a method to characterize topological phase transitions for strongly correlated Hamiltonians defined on two-dimensional lattices based on the many-body Berry curvature. Our goal is to identify a class of quantum critical points…
The paper introduces a semi-analytical method for calculating the Hall conductivity in the single-band approximations. The method goes beyond the linear response theory and, thus, imposes no limitation on the electric fields magnitude. It…
It is well known that the quantum Hall conductivity in the presence of constant magnetic field is expressed through the topological TKNN invariant. The same invariant is responsible for the intrinsic anomalous quantum Hall effect (AQHE),…
We develop a simple model of surface states for topological insulators, developing matching relations for states on surfaces of different orientations. The model allows one to write simple Dirac Hamiltonians for each surface, and to…
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…