Non-Hermiticity can equip unique topological phases that do not have Hermitian analogues, and they manifest some novel characteristics in the system. For instance, a recent study by Chen and Zhai has shown that the hall conductance of an NH Chern insulator has a non-universal bulk contribution. Weyl semimetal (WSM) is a three-dimensional topological material. In literature, it is well established that the Hall conductivity in the normal plane of the Weyl nodes of the Weyl semimetal (3D) is directly proportional to the distance between them. Hall conductivity remains quantized between these two nodes, and outside, it becomes zero because the insulator becomes trivial. We have been interested in studying what happens to the Weyl nodes and Hall conductivity if non-Hermiticity is added to the system in the form of nonreciprocal hopping. 

We are also working on Landau levels and magnetic field-induced transition between the Landau levels of different NH systems. For that, we are analytically using the NH linear response theory framework to determine the magneto-optical conductivity.

The ongoing study of NH systems has been able to answer questions such as how impurities and disorder affect various properties in materials. Recently, Sukhachov and Balatsky  have shown that the presence of NH impurities in Dirac systems change the spatial and frequency dependence of LDOS. We aim to develop a new framework to investigate topological properties of NH system in presence of various kinds of impurities. This involves generalizing the T-matrix formalism to NH case, i.e., using biorthogonal formalism. The presence of non-Hermiticity enhances the LDOS. Further, when real, imaginary and complex impurities are added to the system, the LDOS increases significantly as a function of non-Hermiticity strength and the spectral function distribution also gets modified. We  are studying to different NH models. 

Density matrix is of very high interest in statistical mechanics, quantum mechanics, many-body physics etc. It maps equilibrium statistical mechanics to quantum mechanics and vice versa via Wick rotation. In literature, the form of density matrix for free particle was well established. But hardly there was any explanation about the finite size effects on density matrix as well as quantum cluster expansions. In this work, we have analytically obtained 1-particle density matrices for ideal Bose and Fermi gases in both 3-D box geometries and the harmonically trapped geometries for the entire range of temperature. We have obtained quantum cluster expansions of the grand free energies in closed forms for the same systems in the restricted geometries. We have also shown generic form of quantum cluster integral. The cases where short-range interaction comes into the picture  have also been analyzed for quasi 1-D cases of Bose and Fermi gases in box geometries.