Fano resonances in tilted Weyl semimetals in an oscillating quantum well.

Considering the low-energy model of tilted Weyl semimetal, we study the electronic transmission through a periodically driven quantum well, oriented in the transverse direction with respect to the tilt. We adopt the formalism of Floquet scattering theory and investigate the emergence of Fano resonances as an outcome of matching between the Floquet sidebands and quasi-bound states. The Fano resonance energy changes linearly with the tilt strength suggesting the fact that tilt-mediated part of quasi-bound states energies depends on the above factor.

Anomalous Hall transport in tilted multi-Weyl semimetals.

We study the effect of a perpendicular magnetic fieldon a multinode Weyl semimetal (mWSM) of arbitrary integer monopole charge, with the two Weyl multinodes separated in-space. Besides type-I mWSMs, there exist type-II mWSMs which are characterized by the tilted minimal dispersion for low-energy excitations; the Weyl points in type-II mWSMs are still protected crossings but appear at the contact of the electron and hole pockets, after the Lifshitz transition. We find that the presence of a perpendicular magnetic field quantizes the occupation pockets due to the presence of Fermi tubes.

Quantum Capacitance of a Topological Insulator-Ferromagnet Interface.

We study the quantum capacitance in a topological insulator thin film system magnetized in the in-plane direction in the presence of an out-of-plane magnetic field and hexagonal warping. To first order, the modification in quantum capacitance due to hexagonal warping compared to the clean case, where both the in-plane magnetization and hexagonal warping are absent, is always negative, and increases in magnitude monotonically with the energy difference from the charge neutrality point. In contrast, the change in the quantum capacitance due to in-plane magnetization oscillates with the energy in general, except when a certain relation between the inter-surface coupling, out of plane Zeeman energy splitting and magnetic field strength is satisfied.

Unified Approach towards the Dynamics of Optical and Electron Vortex Beams.

We have proposed a unified framework towards the dynamics of optical and electron vortex beams from the perspective of the geometric phase and the associated Hall effects. The unification is attributed to the notion that the spin degrees of freedom of a relativistic particle, either massive or massless, are associated with a vortex line. Based on a cylindrical coordinate formulation, which leads to a local vortex structure related to orbital angular momentum (OAM), it can be shown that, when electron vortex beams (EVBs) move in an external electric field, paraxial beams give rise to an OAM Hall effect, and nonparaxial beams with tilted vortices initiate a spin Hall effect in free space as well as in an external field.

Relativistic Electron Vortex Beams in a Laser Field.

The orbital angular momentum Hall effect and the spin Hall effect of electron vortex beams (EVBs) have been studied for the EVBs interacting with a laser field. In the scenario of a paraxial beam, the cumulative effect of the orbit-orbit interaction of EVBs and laser fields drives the orbital Hall effect, which in turn produces a shift of the center of the beam from that of the field-free case towards the polarization axis of the photons. In addition, for nonparaxial beams one can also perceive a similar shift of the center of the beam owing to the spin Hall effect involving spin-orbit interaction.