Diagnosing topological phase transitions in 1D superconductors using Berry singularity markers.

In this work I demonstrate how to characterize topological phase transitions in BDI symmetry class superconductors (SCs) in 1D, using the recently introduced approach of Berry singularity markers (BSMs). In particular, I apply the BSM method to the celebrated Kitaev chain model, as well as to a variant of it, which contains both nearest and next nearest neighbor equal spin pairings. Depending on the situation, I identify pairs of external fields which can detect the topological charges of the Berry singularities which are responsible for the various topological phase transitions. These pairs of fields consist of either a flux knob which controls the supercurrent flow through the SC, or, strain, combined with a field which can tune the chemical potential of the system. Employing the present BSM approach appears to be within experimental reach for topological nanowire hybrids.

Synthetic Weyl Points and Chiral Anomaly in Majorana Devices with Nonstandard Andreev-Bound-State Spectra.

We demonstrate how to design various nonstandard types of Andreev-bound-state (ABS) dispersions, via a composite construction relying on Majorana bound states (MBSs). Here, the MBSs appear at the interface of a Josephson junction consisting of two topological superconductors (TSCs). Each TSC harbors multiple MBSs per edge by virtue of a chiral or unitary symmetry. We find that, while the ABS dispersions are 2π periodic, they still contain multiple crossings which are protected by the conservation of fermion parity. A single junction with four interface MBSs and all MBS couplings fully controllable, or networks of such coupled junctions with partial coupling tunability, open the door for topological band structures with Weyl points or nodes in synthetic dimensions, which in turn allow for fermion-parity (FP) pumping with a cycle set by the ABS-dispersion details. In fact, in the case of nodes, the FP pumping is a manifestation of chiral anomaly in 2D synthetic spacetime. The possible experimental demonstration of ABS engineering in these devices further promises to unveil new paths for the detection of MBSs and higher-dimensional chiral anomaly.

Circular-polarization-sensitive metamaterial based on triple-quantum-dot molecules.

We propose a new type of chiral metamaterial based on an ensemble of artificial molecules formed by three identical quantum dots in a triangular arrangement. A static magnetic field oriented perpendicular to the plane breaks mirror symmetry, rendering the molecules sensitive to the circular polarization of light. By varying the orientation and magnitude of the magnetic field one can control the polarization and frequency of the emission spectrum. We identify a threshold frequency Ω, above which we find strong birefringence. In addition, Kerr rotation and circular-polarized lasing action can be implemented. We investigate the single-molecule lasing properties for different energy-level arrangements and demonstrate the possibility of circular-polarization conversion. Finally, we analyze the effect of weak stray electric fields or deviations from the equilateral triangular geometry.