Haidekker Galambos Tamás

We consider a hybrid quantum Hall-superconductor system, where a superconducting finger with oblique profile is wedged into a two-dimensional electron gas in the presence of a perpendicular magnetic field, as considered by Lee et al., Nat. Phys. 13, 693 (2017). The electron gas is in the quantum Hall regime at filling factor ν=1. Due to the Meissner effect, the perpendicular magnetic field close to the quantum Hall-superconductor boundary is distorted and gives rise to an in-plane component of the magnetic field. This component enables nonlocal crossed Andreev reflection between the spin-polarized chiral edge states running on opposite sides of the superconducting finger, thus opening a gap in the spectrum of the edge states without the need of spin-orbit interaction or nontrivial magnetic textures. We compute numerically the transport properties of this setup and show that a negative resistance exists as a consequence of nonlocal Andreev processes. We also obtain numerically the zero-energy local density of states, which systematically shows peaks stable to disorder. The latter result is compatible with the emergence of Majorana bound states.

We study superconducting quantum interference in a Josephson junction linked via edge states in two-dimensional (2D) insulators. We consider two scenarios in which the 2D insulator is either a topological or a trivial insulator supporting one-dimensional (1D) helical or nonhelical edge states, respectively. In equilibrium, we find that the qualitative dependence of critical supercurrent on the flux through the junction is insensitive to the helical nature of the mediating states and can, therefore, not be used to verify the topological features of the underlying insulator. However, upon applying a finite voltage bias smaller than the superconducting gap to a relatively long junction, the finite-frequency interference pattern in the non-equilibrium transport current is qualitatively different for helical edge states as compared to nonhelical ones.

We explore the correlated electron states in harmonically confined few-electron quantum dots in an external magnetic field by the path-integral Monte Carlo method for a wide range of the field and the Coulomb interaction strength. Using the phase structure of a preceding unrestricted Hartree-Fock calculation for phase fixing, we find a rich variety of correlated states, often completely different from the prediction of mean-field theory. These are finite temperature results, but sometimes the correlations saturate with decreasing temperature, providing insight into the ground-state properties.

We elaborate on the methodology to simulate bulk systems in the absence of time-reversal symmetry by the phase-fixed path-integral Monte Carlo method under (possibly twisted) periodic boundary conditions. Such systems include two-dimensional electrons in the quantum Hall regime and rotating ultracold Bose and Fermi gases; time-reversal symmetry is broken by an external magnetic field and the Coriolis force, respectively. We provide closed-form expressions in terms of Jacobi elliptic functions for the thermal density matrix (or the Euclidean propagator) of a single particle on a flat torus under very general conditions. We then modify the multislice sampling method in order to sample paths by the magnitude of the complex-valued thermal density matrix. Finally, we demonstrate that these inventions let us study the vortex melting process of a two-dimensional Yukawa gas in terms of the de Boer interaction strength parameter, temperature, and rotation (Coriolis force). The bosonic case is relevant to ultracold Fermi-Fermi mixtures of widely different masses under rotation.