These constitute two areas of investigations:

1) Electronic properties of magneto-electric materials

Magneto-electric materials are promising as one can exploit the coupling between two order parameters-electric order which gives rise to ferro-electricity and magnetic order which can be ferromagnetic or anti-ferromagnetic, for device applications.. The materials in which both, the electric and magnetic, order co-exist in the same phase, are called multi-ferroics. Our research is directed at investigating this coupling, determining the critical thickness for existence of an electric order (or ferro-electric properties) and possible influence of the magnetic order on the critical thickness in case of strong coupling and design of a super-lattices of ferroelectric and ferromagnetic materials for interface multi-ferroic properties. Room temperature multi-ferroics are rare and elusive (except BiFeO3 in which anti-ferro and ferro-electric order coexists). We have so far studied the ferroelectric properties of GeTe [1], influence of magnetic doping on the ferroelectric property of GeTe [2] and establishing the coupling of the two order parameter in a complex perovskite structured Bi₂NiMnO₆ [3]. These studies were carried out in order to understand the mechanism for existence of electric order in GeTe, role of cation vacancies and magnetic atom disorder on the magnetism in GeTe and their effect on ferro-electricity and whether there is any coupling of two order parameters in Bi based oxide perovskites.

Work is progress to 1) determine the critical thickness of BFO films (1,2,3) with metal electrodes, possibly to understand the role of electrical and mechanical boundary conditions on the intrinsic electric order with and without external electric fields [4] and 2) design an artificial multi-ferroic hetero-structure with robust order parameters at the interface with strong coupling [5]. We have designed two hetero-structures combining two complex oxides- one with strong electric order namely BaTiO₃ and one with strong magnetic orders (LaMnO₃ and YTiO₃). The holy-grail of physics so far is to find a room temperature multi-ferroic, possibly ferromagnetic ferroelectric, with strong coupling of two order parameters

Eventually, a transistor structure can be built with ferromagnetic metals as source and drain, graphene mono- or bi-layer as a channel and a suitable multi-ferroic material as a gate. The spin-polarized transport in the channel then can be tuned by applying an external electric field to the multi-ferroic gate, thus exploiting the coupling between electric and magnetic order which can then tune the exchange interaction between the spins in the channel, injected from source, and those in the multi-ferroic material.

2) Hetero-structures of Mott and band insulators:

Complex oxides, depending on the d-shell occupancies in transition metals and electron correlations, are either band insulators (such as LaAlO₃, SrTiO₃ etc.) or Mott insulators (YTiO₃, LaTiO₃, BaVO₃ etc.). Depending upon the stacking sequences, the interface between the band-insulators, sandwich structure consisting of polar and non-polar planes of LaAlO₃/SrTiO_3, are found either to be metallic or insulating  and the electronic charge transfer at the interface and oxygen vacancies are understood to be driving force behind such behaviors.  At the metallic interfaces, the carrier mobility and the carrier densities of the quasi-2DEG electron gas are high compared to that formed at the interfaces based on hetero-structures of III-V semiconductors. Moreover, they can be tuned, by altering the unit-cell thickness of the LaAlO₃ layers, from an insulating state to the metallic state, by external electric field. It was found that in a multi-layer structure, where both of these interfaces are present, a critical thickness of 6 unit cells is required to maintain the conductivity and carrier densities at the two separate interfaces, below which they are affected by electronic coupling between the two interfaces. In a structure consisting of band (SrTiO₃) and Mott (LaTiO₃) insulators, carrier doping at the interface is observed to take place by electron charge reconstruction across the interface caused by lattice relaxations and is driven by strong electron correlation in LaTiO₃.

Our interest is in the strongly correlated electron gas that is formed between the interfaces of two Mott insulators.  We begin to study the interface electronic structure of LaTiO₃/YTiO₃ and quantum well structure LaTiO₃/BaVO₃/LaTiO₃ using density functional theory with local Hubbard correlation on d-electrons to understand the role of lattice relaxation and strong correlation in charge reconstruction across the interface [6]. In order to probe the dynamic correlations and screeing, wherein, charge fluctuations at a given site at any given time and their interactions with strongly correlated orbitals drive a particular electronic phase at the interface, we will use DFT based dynamical field theory, a non-perturbative many-body technique which is able to capture all the electron-correlation regime from weak (band picture) to strong correlations (Mott picture) including paramagnetic strongly correlated metals. Realistic descriptions of lattice structure, electronic structure and strong correlations are necessary to probe the rich physics of quasi-2DEG electron gas formed at the interface of two Mott insulators.