My research is in the area of theoretical quantum condensed matter physics focusing on strongly correlated systems. I am interested in understanding the properties of the different types of phases (both static and dynamical) that can exist in these systems and the transitions between them.
In recent times, there has been a lot of activity in understanding the phenomenon of many-body localization in correlated systems with important implications for our understanding of statistical mechanics. Systems displaying this phenomenon are the only ones known in nature that do not thermalize generically (i.e. without any fine tuning). A random or quasiperiodic potential is a key ingredient in these systems and a transition from an athermal many-body localized phase to a thermal delocalized phase can be effected by tuning the strength of the potential. I am interested in understanding the nature of this transition, which is dynamical in nature and very different from the quantum and classical phase transitions usually encountered in condensed matter physics. At the same time, I am also investigating how the nature of localization is different in random and quasiperiodic potentials. The presence of a quasiperiodic potential, especially in one dimension, admits the possibility of phases other the aforementioned many-body localized and thermal phases. These new phases are currently not well understood and their characterization is of great interest to me.
I have also been involved in studying aspects of transport in strongly correlated systems, especially those closely related to experiments. In particular, I have been looking at cross plane transport in twisted bilayer graphene with an eye on thermoelectric transport. Additionally, I have studied thermoelectric and electrical transport in monolayer graphene (with a view towards understanding the effect of magnetic fields) and in high temperature superconductors (to try to understand the physics of the vortex liquid). I have also been interested in understanding various aspects of Andreev reflection, especially to with the enhancement of crossed and specular Andreev reflection.
I am also interested in certain aspects of the physics of cold atomic systems, in particular the possibility of the occurrence of interesting quantum phases and phase transitions. Specific topics in this area that I have worked on include the effect of geometrical frustration in optical lattices on symmetry breaking and the dynamics of ordering, the physics of low dimensional superfluids and supersolids and the effect of disorder on lattice systems of interacting bosons.
I have also worked on the relation between quantum entanglement and thermalization, and quantum criticality off and on for several years and continue to be interested in the subject.
[5] R. Modak and S. Mukerjee, Many-body localization in the presence of a single particle mobility edge, Phys. Rev. Lett. 115, 230401 (2015).
[4] A. Dhar, M. Maji, T. Mishra, R. V. Pai, S. Mukerjee and A. Paramekanti, Bose-Hubbard model in a strong effective magnetic field: Emergence of a chiral Mott insulator ground state, Phys. Rev. A 85, 041602 (R) (2012).
[3] F. Pollmann, S. Mukerjee, A. Turner and J. E. Moore, Theory of finite-entanglement scaling at one-dimensional quantum critical points, Phys. Rev. Lett. 102, 255701 (2009).
[2] P. Murphy, S. Mukerjee and J. E. Moore, Optimal thermoelectric figure of merit of a molecular junction, Phys. Rev. B 78, 161406(R) (2008).
[1] S. Mukerjee, C. Xu and J. E. Moore, Topological defects and the superfluid transition of the S = 1 spinor condensate in two dimensions, Phys. Rev. Lett. 97, 120406 (2006).