Interface phenomena:
An interface between two different compounds exhibits new emergent properties that are absent in the bulk constituents. These new properties appear due to the interplay of different degrees of freedom (e.g. charge, spin, orbital and lattice). The interface properties include superconductivity, Rashba spin-orbit coupling, novel magnetic states, anomalous and topological Hall effects.

Majorana states:
The Majorana quasiparticles appear in topological superconductors, usually as zero-energy bound states. Because of their non-Abelian statistics, they are considered to be useful in the decoherence-free topological quantum computing. Several artificial geometries involving a superconductor-semiconductor heterostructure, and also some bulk superconductors have been theoretically proposed to be the host of the Majorana quasiparticles. Because these particles are ideally charge-less, spin-less and mass-less, it is a challenge to detect them in conventional experiments. The need is, therefore, to experimentally demonstrate their non-Abelian statistics. Theoretical simulations can help to identify a feasible geometry where such an experiment is possible. Manipulation strategies of these Majorana states will help to implement the quantum gates.

Orbital loop current:
Orbital loop current models time-reversal symmetry breaking effect associated with charge density wave ordering found in scanning tunneling microscopy experiments and muon spin-resonance spectroscopy experiments in kagome compounds AV3Sb5 (A=Cs, Rb, K). The loop current, when present with superconductivity, leads to a plethora of unconventional phenomena such as the formation of chiral pair density wave, in-gap states inside superconducting energy gap and putative topological superconducting state. Understanding this complex interplay of the orbital loop current and superconductivity is important to find out the mechanism of superconductivity and its pairing symmetry.

Magnetic Skyrmions:
Skyrmions are topologically stable field configurations of certain class of the non-linear field theory. In the context of condensed matter physics, they appear both isolated and in the form of a crystalline arrangement (skyrmion crystal) in magnetic materials where multiple exchange interactions compete with each other. A simple realization of a triangular skyrmion crystal can be obtained in a two-dimensional model, having Heisenberg exchange coupling, Dzyaloshinskii-Moriya exchange coupling and a magnetic field or a magnetic anisotropy. Such a skyrmion crystal brings interesting physical properties such as topological Hall effect and magnetic excitations. Also, they are considered to be useful in technological applications such as data storage application and probabilistic computation.

Topological magnons:
At low temperatures, magnetic materials exhibit a correlated phase that hosts collective and coherent magnetic excitations such as magnons. Topology appears in the magnons from the geometry of the underlying lattice and spin-orbit coupling (or Dzyaloshinskii-Moriya exchange coupling). Similar to the topological insulators and semimetals, the Berry phase associated with the magnetization dynamics leads to interesting spin and heat transport phenomena. Magnetic materials hosting the topological magnons offer a platform to investigate the interplay between topology, magnetic symmetry and electronic correlations. On the application side, in the emerging field of magnonics, topological magnons are proposed to be used as information carriers that do not suffer from conventional problems in magnonic devices.