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We investigate the emergence of both quantum anomalous Hall and disorder-induced Anderson Chern insulating phases in two dimensional hexagonal lattices, with antiferromagnetically ordered 3Q state and in the absence of spin-orbit coupling.…
Strongly interacting electrons in a topologically non trivial band may form exotic phases of matter. An especially intriguing example of which is the fractional quantum anomalous Hall phase, recently discovered in twisted transition metal…
We present a microscopic theory of the chiral one-dimensional electron gas system localized on the sidewalls of magnetically-doped Bi$_2$Se$_3$-family topological insulator nanoribbons in the quantum anomalous Hall effect (QAHE) regime. Our…
The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the…
We study the ground state energy of integrable $1+1$ quantum field theories with boundaries (the genuine Casimir effect). In the scalar case, this is done by introducing a new, ``R-channel TBA'', where the boundary is represented by a…
We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate…
We consider the edge and bulk conductances for 2D quantum Hall systems in which the Fermi energy falls in a band where bulk states are localized. We show that the resulting quantities are equal, when appropriately defined. An appropriate…
We study quantum spin Hall insulators with local Coulomb interactions in the presence of boundaries using dynamical mean field theory. We investigate the different influence of the Coulomb interaction on the bulk and the edge states.…
We discuss the role of boundary conditions in determining the physical content of the solutions of the Schrodinger equation. We study the standing-wave, the ``in,'' the ``out,'' and the purely outgoing boundary conditions. As well, we…
A finite photonic lattice with two bands and a random gap is considered. Using a two-dimensional Dirac equation, the effect of a random sign of the Dirac mass is studied numerically. The edge state at the sample boundary has a strong…
We study the quantum theory of two-dimensional electrons in a magnetic field and an electric field generated by a homogeneous background. The dynamics separates into a microscopic and macroscopic mode. The latter is a circular Hall current…
We study purely magnetic Schr\"odinger operators in two-dimensions $(x,y)$ with magnetic fields $b(x)$ that depend only on the $x$-coordinate. The magnetic field $b(x)$ is assumed to be bounded, there are constants $0 < b_- < b_+ < \infty$…
We address the problem of magnetic-field-induced corner states in quantum spin Hall insulators (QSHIs) beyond the particle-hole-symmetric limit. Starting from a realistic low-energy model for zinc-blende semiconductor quantum wells (QWs),…
We have investigated the formation of spin textures at the edges of quantum Hall systems for several ferromagnetic filling factors. The textures are driven by the same physics that leads to ``skyrmions'' in the bulk. For hard confinement…
Nonrelativistic bound states are studied using an effective field theory. Large logarithms in the effective theory can be summed using the velocity renormalization group. For QED, one can determine the structure of the leading and…
We address the experimentally relevant situation, where a non-equilibrium state is created at the edge of a quantum Hall system by injecting charge current into a chiral edge state with the help of a quantum point contact, quantum dots, or…
We study pairing effects in the edge states of paired fractional quantum Hall states by using persistent edge currents as a probe. We give the grand partition functions for edge excitations of paired states (Pfaffian, Haldane-Rezayi, 331)…
The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrodinger's equation with generalized…
The effects of randomness are investigated in the fractional quantum Hall systems. Based on the Chern-Simons Ginzburg-Landou theory and considering relevant quasi-particle tunneling, the edge state network model for the hierarchical state…
Boundary conditions play a crucial role in the path-integral approach to quantum gravity and quantum cosmology, as well as in the current attempts to understand the one-loop semiclassical properties of quantum field theories. Within this…