Brief overview of my research activities 

The broad theme of my research: Theoretical Condensed Matter Physics.

Keywords: Flat bands, Fractal lattices, Quasiperiodic lattice models, Single-particle localization and delocalization, Spin dependent transport, Spin filter, Fractional quantum Hall physics in lattice, Anyons, Spin-orbit effect, Aharonov-Bohm effect, Aharonov-Casher effect. 

Below, I briefly describe some of my research activities: 

Flat bands in tight-binding lattice models

Physical properties and functionality of real-life materials are often determined by studying their band structure. We often observe nondispersive, completely or nearly flat lines (or surfaces) in the band structure of certain materials, known as the "flat bands". These flat bands are interesting as they offer highly degenerate manifold of single-particle states, which can act as an ideal platform to study various intriguing strongly correlated phenomena. We have investigated the appearance of multiple flat band states with interesting features in a variety of decorated two-dimensional lattice models, such as diamond-octagon lattice, extended Lieb lattice, lattice built of fractal geometry etc. We have demonstrated how one can tune the parameters of the underlying Hamiltonian representing such lattice geometries to engineer these flat bands, where the particles become completely immobile due to the vanishing group velocity and they form clusters of compact localized states (CLS). With the application of an external magnetic flux or an intrinsic spin-orbit interaction, these flat bands give rise to nontrivial topological properties and provide an ideal setup to probe integer or fractional quantum Hall effect in a lattice model. From the technological point of view, the flat band research can have important applications in the field of photonics. 

References : 

[1] B. Pal and K. Saha, Phys. Rev. B 97, 195101 (2018).

[2] B. Pal, Phys. Rev. B 98, 245116 (2018).

[3] A. Bhattacharya and B. Pal, Phys. Rev. B 100, 235145 (2019).

Spin dependent transport and spin filters

The ability to tune, manipulate and detect the spin degree of freedom of quantum mechanical particles in a controllable fashion plays an important role in the field "spintronics or spin-based electronics". In a spin-based electronic device, one can make use of the spin degree of freedom of the particles to gain several significant advantages, such as non-volatile memory, high storage density, low power consumption, faster access speed etc. as compared to the existing conventional charge-based electronic device technologies. To make the actual spin-based devices, simple prototype theoretical models can be really useful. To identify such prototype theoretical models, we have investigated the spin dependent transport in simple tight-binding lattice models comprising magnetic sites. We have shown that such simple models can act as potential spin filters which can infiltrate a desired spin component of the particles (i.e., produces spin-polarized particles). In addition to the conventional spin 1/2 states, we have elucidated the concept of higher-order spin states, such as spin 1, 3/2, 2, 5/2 etc. in such model spin filtering devices. This is really interesting and may be the first step towards fabricating spin-based devices with atomic gases of higher-order spin states.

References : 

[1] B. Pal, Phys. Rev. B 99, 134431 (2019).

[2] B. Pal and P. Dutta, Scientific Reports 6, 32543 (2016).

[3] B. Pal, R. A. Römer, and A. Chakrabarti, J. Phys.: Condens. Matter 28, 335301 (2016).

Nature of single-electron states in fractal lattices

Fractal lattices represent complex pattern with self-similarity at different length scales. Due to such complex geometrical structure, fractal lattices exhibit exotic electronic spectrum. Although deterministic fractal lattice geometries have well-defined growth rule as we grow the system from a lower generation to the higher generations, they always lack periodicity in their lattice structure. It is practically impossible to identify and exactly evaluate the energy eigenvalues of the localized states in such aperiodically ordered systems in the thermodynamic limit. A direct diagonalization of the Hamiltonian for a finite size of the system yields the eigenvalues of the localized states, but there is no guarantee that these eigenvalues will remain in the spectrum when the system grows in size and tends to infinity. We have addressed this issue for different fractal lattices and found a systematic scheme through which it is possible to exactly identify at least a subset of energy eigenvalues corresponding to the localized states in such fractal lattices in the thermodynamic limit. Using a well-known real space renormalization group (RSRG) technique, we have shown that the localization of the single-particle states corresponding to an energy eigenvalue is delayed over the fractal space as we move from one generation to another generation, and we have named such localization pattern as "staggered localization". In addition to this, we have studied the effect an external magnetic flux on the single-particle states and the two-terminal transmission characteristics for such fractal lattice geometries. 

References : 

[1] B. Pal and A. Chakrabarti, Phys. Rev. B 85, 214203 (2012).

[2] B. Pal and A. Chakrabarti, Eur. Phys. J. B 85, 307 (2012).

[3] B. Pal, P. Patra, J. P. Saha, and A. Chakrabarti, Phys. Rev. A 87, 023814 (2013).

[4] A. Nandy, B. Pal, and A. Chakrabarti, J. Phys.: Condens. Matter 27, 125501 (2015).

[5] A. Nandy, B. Pal, and A. Chakrabarti, Phys. Lett. A 378, 3144 (2014).

Delocalization of single-particle states in presence of disorder

Single-particle states are localized in disordered systems irrespective of the strength of the disorder. This was first observed by Philip Anderson and was named after him as the "Anderson localization". This is true for one- and two-dimensional systems and in three dimension there is a possibility of metal-insulator transition. We have studied some rare exceptions of the above situation, in which we have shown that it is possible to have absolutely continuous bands of extended single-particle states even in presence of disorder. We have worked out this for a variety of quasi-one dimensional tight-binding lattice models, the building blocks of which are arranged randomly or follow certain quasiperiodic sequences (e.g., Fibonacci sequence, copper mean sequence etc.), i.e., absence of any kind of long-range translational order. We have analytically shown that it is possible to have bands of completely delocalized (extended) states in such aperiodic lattices under certain numerical correlations between the parameters of the Hamiltonian. Our results put forward a strong exception to the canonical case of conventional Anderson localization where the localization of the electronic states in a disordered system is, in general, not meant to be sensitive on the numerical correlations of the parameters of the Hamiltonian. 

References : 

[1] B. Pal, S. K. Maiti, and A. Chakrabarti, Europhys. Lett. 102, 17004 (2013).

[2] B. Pal and A. Chakrabarti, Physica E 60, 188 (2014).

[3] B. Pal, Phys. Status Solidi B 251, 1401 (2014).

[4] B. Pal and A. Chakrabarti, Phys. Lett. A 378, 2782 (2014).

[5] A. Nandy, B. Pal, and A. Chakrabarti, Europhys. Lett. 115, 37004 (2016).

Fractional quantum Hall physics and anyons in fractal lattices

The fractional quantum Hall effect (FQHE) is an important physical phenomenon that is observed in two-dimensional electron gas subjected to very low temperature and strong magnetic field, in which the Hall conductance of the system shows precisely quantized plateaus at fractional values of e2/h. Fractional quantum Hall states have robust topological order that can be used to realize the topological quantum computers. The excitons of FQHE are new kind of quasiparticles with fractional elementary charges known as "anyon". Anyons are special type of quasiparticles which are neither bosons nor fermions, and when two anyons are exchanged, the corresponding many-body quantum state is transformed in a more complicated fashion than just multiplication of a pre-factor of plus or minus sign. The fractional quantum Hall states are usually realized in two-dimensions.  The possibility of changing the dimension to non-integer dimensions can be really interesting since the properties of a system, in general, depend strongly on the dimension of the system. To investigate this idea, we have implemented fractal lattices and we have constructed a new type of fractional quantum Hall state with an interesting property that it lives in fractal dimensions. We have numerically shown the existence of fractional quantum Hall states that can host anyons for a wide range of fractal lattice geometries with dimensions in between 1 and 2. 

References : 

[1] S. Manna*, B. Pal*, W. Wang*, and A. E. B. Nielsen, Phys. Rev. Research 2, 023401 (2020).