Abstract: The interplay between a magnetic field and the Coulomb potential from a charged vacancy on the electron states in graphene is investigated within the tight-binding model. The Coulomb potential removes locally Landau level degeneracy, while the vacancy introduces a satellite level next to the normal Landau level. These satellite levels are found throughout the positive-energy region, but in the negative-energy region, they turn into atomic collapse resonances. Crossings between Landau levels with different angular quantum number m are found. Unlike the point impurity system in which an anticrossing occurs between Landau levels of the same m, in this work anticrossing is found between the normal Landau level and the vacancy-induced level. The atomic collapse resonance hybridizes with the Landau levels. The charge at which the lowest Landau level m = -1, N = 1 crosses E = 0 increases with enhancing magnetic field. A Landau level scaling anomaly occurs when the charge is larger than the critical charge beta 0.6 and this critical charge is independent of the magnetic field.

Abstract: Transport measurements are readily used to probe different phases in disordered topological insulators (TIs), where determining topological invariants explicitly is challenging. On that note, universal conductance fluctuations (UCF) theory asserts the conductance G for an ensemble has a Gaussian distribution, and that standard deviation 8G depends solely on the symmetries and dimensions of the system. Using a real-space tight -binding Hamiltonian on a system with Anderson disorder, we explore conductance fluctuations in a thin Bi2Se3 film and demonstrate the agreement of their behavior with UCF hypotheses. We further show that magnetic field applied out-of-plane breaks the time -reversal symmetry and transforms the system's Wigner-Dyson class from root symplectic to unitary, increasing 8G by 2. Finally, we reveal that while Bi2Se3 is a strong TI, weak TI and metallic phases can be stabilized in presence of strain and disorder, and detected by monitoring the conductance fluctuations.

Abstract: Magnetization reversal is a well-studied problem with obvious applicability in computer hard drives. One can accomplish a magnetization reversal in at least one of two ways: application of a magnetic field or through a spin current. The latter is more amenable to a fully quantum-mechanical analysis. We formulate and solve the problem whereby a spin current interacts with a ferromagnetic Heisenberg spin chain, to eventually reverse the magnetization of the chain. Spin flips are accomplished through both elastic and inelastic scattering. A consequence of the inelastic-scattering channel, when it is no longer energetically possible, is the occurrence of a nonequilibrium bound state, which is an emergent property of the coupled local plus itinerant spin system. For certain definite parameter values the itinerant spin lingers near the local spins for some time, before eventually leaking out as an outwardly diffusing state. This phenomenon results in spin-flip dynamics and filtering properties for this type of system.

Abstract: Correlated, or extended, impurities play an important role in the transport properties of dirty metals. Here, we examine, in the framework of a tight-binding lattice, the transmission of a single electron through an array of correlated impurities. In particular we show that particles transmit through an impurity array in identical fashion, regardless of the direction of traversal. The demonstration of this fact is straightforward in the continuum limit, but requires a detailed proof for the discrete lattice. We also briefly demonstrate and discuss the time evolution of these scattering states, to delineate regions (in time and space) where the aforementioned symmetry is violated.