arXiv subjects

Sankalpa Ghosh

Publications and source records attributed to Sankalpa Ghosh.

54 records · Page 3Linked to original sources

arXiv2010

Electron transport and Goos-Hanchen shift in graphene with electric and magnetic barriers: optical analogy and band structure

Transport of massless Dirac fermions in graphene monolayers is analyzed in the presence of a combination of singular magnetic barriers and applied electrostatic potential. Extending a recently proposed (J Phys. Cond. Matt. Vol 21, 292204 (2009)) analogy between the transmission of light through a medium with modulated refractive index and electron transmission in graphene through singular magnetic barriers to the present case, we find the addition of a scalar potential profoundly changes the transmission. We calculate the quantum version of the Goos-Hänchen shift that the electron wave suffers upon being totally reflected by such barriers. The combined electric and magnetic barriers substantially modify the band structure near the Dirac point. This affects transport near the Dirac point significantly and has important consequences for graphene-based electronics.

cond-mat.mes-hall↗

arXiv2010

Cold atoms in rotating optical lattice with nearest neighbour interaction

Extended Bose Hubbard models with nearest neighbour interaction describe minimally the effect of long range interaction on ultra cold atoms in deep optical lattices. Rotation of such optical lattices subject such neutral cold atoms to the effect of an artificial magnetic field. The modification of the phase boundaries of the density wave and Mott Insulator phases due to this rotation are shown to be related to the edge spectrum of spinorial and scalar Harper equation. Corresponding profiles of the checkerboard vortex states with sublattice modulated superfluid order parameter near density wave phase boundary are calculated.

cond-mat.quant-gas↗

arXiv2009

Density, phase and coherence properties of a low dimensional Bose-Einstein systems moving in a disordered potential

We present a detailed numerical study of the dynamics of a disordered one-dimensional Bose-Einstein condensates in position and momentum space. We particularly focus on the region where non-linearity and disorder simultaneously effect the time propagation of the condensate as well as the possible interference between various parts of the matter wave. We report oscillation between spatially extended and localized behavior for the propagating condensate which dies down with increasing non-linearity. We also report intriguing behavior of the phase fluctuation and the coherence properties of the matter wave. We also briefly compare these behavior with that of a two-dimensional condensate. We mention the relevance of our results to the related experiments on Anderson localization and indicate the possibility of future experiments

cond-mat.mes-hall↗

arXiv2009

Electron optics with magnetic vector potential barriers in graphene

An analysis of electron transport in graphene is presented in the presence of various arrangement of delta-function like magnetic barriers. The motion through one such barrier gives an unusual non specular refraction leading to asymmetric transmission. The symmetry is restored by putting two such barriers in opposite direction side by side. Periodic arrangements of such barriers can be used as Bragg reflectors whose reflectivity has been calculated using a transfer matrix formalism. Such Bragg reflectors can be used to make resonant cavities. We also analyze the associated band structure for the case of infinite periodic structures.

cond-mat.mes-hall↗

arXiv2008

Effective field theory for spinor dipolar Bose Einstein condensates

We show that the effective theory of long wavelength low energy behavior of a dipolar Bose-Einstein condensate(BEC) with large dipole moments (treated as a classical spin) can be modeled using an extended Non-linear sigma model (NLSM) like energy functional with an additional non-local term that represents long ranged anisotropic dipole-dipole interaction. Minimizing this effective energy functional we calculate the density and spin-profile of the dipolar Bose-Einstein condensate in the mean-field regime for various trapping geometries. The resulting configurations show strong intertwining between the spin and mass density of the condensate, transfer between spin and orbital angular momentum in the form of Einstein-de Hass effect, and novel topological properties. We have also described the theoretical framework in which the collective excitations around these mean field solutions can be studied and discuss some examples qualitatively.

cond-mat.stat-mech↗

arXiv2007

Spinor dipolar Bose-Einstein condensates; Classical spin approach

Magnetic dipole-dipole interaction dominated Bose-Einstein condensates are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from large spin limit to obtain an effective minimal Hamiltonian; a version extended from a non-linear sigma model. By solving the Gross-Pitaevskii equation we find several novel spin textures where the mass density and spin density are strongly coupled, depending upon trap geometries due to the long-range and anisotropic natures of the dipole-dipole interaction.

cond-mat.other↗

arXiv2006

Numerical study of one-dimensional and interacting Bose-Einstein condensates in a random potential

We present a detailed numerical study of the effect of a disordered potential on a confined one-dimensional Bose-Einstein condensate, in the framework of a mean-field description. For repulsive interactions, we consider the Thomas-Fermi and Gaussian limits and for attractive interactions the behavior of soliton solutions. We find that the disorder average spatial extension of the stationary density profile decreases with an increasing strength of the disordered potential both for repulsive and attractive interactions among bosons. In the Thomas Fermi limit, the suppression of transport is accompanied by a strong localization of the bosons around the state k=0 in momentum space. The time dependent density profiles differ considerably in the cases we have considered. For attractive Bose-Einstein condensates, a bright soliton exists with an overall unchanged shape, but a disorder dependent width. For weak disorder, the soliton moves on and for a stronger disorder, it bounces back and forth between high potential barriers.

cond-mat.other↗

arXiv2006

Vortex Tunneling and Transport Theory In Two-Dimensional Bose Condensates

The tunneling rate t_v of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wavefunctions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, t_v = V exp(- pi n_s d^2/2), where n_s is the boson density. The analogy between vortex hopping in a superconducting film and 2D electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magneto-resistance. Using the 'Quantum Hall Insulator' analogy we argue that the -Hall conductivity- (rather than the inverse Hall resistivity) measures the effective carrier density in domains of mobile vortices. Details of vortex wavefunctions and overlap calculations, and a general derivation of the Magnus coefficient for any wavefunction on the sphere, are provided in appendices.

cond-mat.supr-con↗

arXiv2004

Bogomol'nyi bound and screw dislocations in a mesoscopic smectic-A

The de Gennes free energy functional of an infinite smectic-A liquid crystal at the dual point is shown to be topological and to depend only on the number of screw dislocations and the anisotropy. This result generalizes the existence of a Bogomol'nyi bound to an anisotropic system. The role of the boundary of a finite mesoscopic smectic is to provide a mechanism for the existence of thermodynamically stable screw dislocations. We obtain a closed expression for the corresponding free energy and a relation between the applied twist and the number of screw dislocations.

cond-mat.mes-hall↗

arXiv2004

Vortices in Atomic Bose-Einstein Condensates: an Introduction

The occurrence of vortices in atomic Bose-Einstein condensates (BEC) enables a description of their superfluid behaviour. In this article we present a pedagogical introduction to the vortex physics in trapped atomic BECs. The mechanism of the vortex nucleation in an atomic BEC is discussed in detail. We also discuss a recently proposed approach which treats the problem of vortex nucleation using a one-particle Schr$\ddot{o}$dinger equation with non-local and chiral boundary conditions.

cond-mat.mes-hall↗

arXiv2004

Vortex nucleation through edge states in finite Bose-Einstein condensates

We study the vortex nucleation in a finite Bose-Einstein condensate. Using a set of non-local and chiral boundary conditions to solve the Schr$\ddot{o}$dinger equation of non-interacting bosons in a rotating trap, we obtain a quantitative expression for the characteristic angular velocity for vortex nucleation in a condensate which is found to be 35% of the transverse harmonic trapping frequency.

cond-mat.mes-hall↗

arXiv2003

Composite Bosons description of rapidly rotating Bose-Einstein Condensates

Recently a novel phase transition has been observed \cite{jalin} in a rotating Bose-Einstein condensate when the rotating frequency $Ω$ reaches the transverse trap frequency $ω_{\bot}$ and eventually crosses it. We study certain aspects of this experiment in terms of the condensation of composite bosons and the corresponding vortex formation using a Chern-Simon Gross-Pitaevskii theory. %

cond-mat.mes-hall↗

arXiv2001

Solitons in one-dimensional interacting Bose-Einstein system

A modified Gross-Pitaevskii approximation was introduced recently for bosons in dimension $d\le2$ by Kolomeisky {\it et al.} (Phys. Rev. Lett. {\bf 85} 1146 (2000)). We use the density functional approach with sixth-degree interaction energy term in the Bose field to reproduce the stationary-frame results of Kolomeisky {\it et al.} for a one-dimensional Bose-Einstein system with a repulsive interaction. We also find a soliton solution for an attractive interaction, which may be boosted to a finite velocity by a Galilean transformation. The stability of such a soliton is discussed analytically. We provide a general treatment of stationary solutions in one dimension which includes the above solutions as special cases. This treatment leads to a variety of stationary wave solutions for both attractive and repulsive interactions.

cond-mat.stat-mech↗

arXiv2001

Twocomponent Fermi vapour in a 2D rotating trap

An exactly solvable model of two-component interacting Fermi vapour in two dimension within Thomas Fermi approach has been proposed. We assume a realistic off-diagonal s-wave interaction between fermions in the two hyperfine states. The interaction is taken to be given by a screened Coulomb interaction which is both relevant and is analytically tractable. There are two distinct limits in the case of trapped fermionic systems: When the rotating frequency is less than the trap frequency a Thomas-Fermi approach may be used for a reasonably large number of particles. In the case of rapidly rotating fermions, an alternative variational approach is used, where the local density approximation may be applied after projecting the system on to the lowest degenerate level. Analytic expressions for the relevant physical quantities are obtained and their significance is discussed in both these cases.

cond-mat.mes-hall↗

arXiv2000

Rotating fermions in two dimensions: Thomas Fermi approach

Properties of confined mesoscopic systems have been extensively studied numerically over recent years. We discuss an analytical approach to the study of finite rotating fermionic systems in two dimension. We first construct the energy functional for a finite fermionic system within the Thomas-Fermi approximation in two dimensions. We show that for specific interactions the problem may be exactly solved. We derive analytical expressions for the density, the critical size as well as the ground state energy of such systems in a given angular momentum sector.

cond-mat.mes-hall↗

arXiv2000

Quantum Hall Solitons with Intertwined Spin and Pseudospin at $ν= \ 1$

In this paper we study in detail different types of topological solitons which are possible in bilayer quantum Hall systems at filling fraction $ν=1$ when spin degrees of freedom are included. Starting from a microscopic Hamiltonian we derive an effective energy functional for studying such excitations. The gauge invariance and $CP^{3}$ character of this energy fuctional and their consequences are examined. Then we identify permissible classes of finite energy solutions which are topologically non-trivial. We also numerically evaulate a representative solution in which a pseudospin (layer degrees of freedom) bimeron in a given spin component is intertwined with spin-skyrmions in each layer, and and discuss whether it is energetically favoured as the lowest lying excitation in such system with some numerical results.

cond-mat.mes-hall↗

arXiv1998

Bimerons in Double Layer Quantum Hall Systems

In this paper we discuss bimeron pseudo spin textures for double layer quantum hall systems with filling factor $ν=1$. Bimerons are excitations corresponding to bound pairs of merons and anti-merons. Bimeron solutions have already been studied at great length by other groups by minimising the microsopic Hamiltonian between microscopic trial wavefunctions. Here we calculate them by numerically solving coupled nonlinear partial differential equations arising from extremisation of the effective action for pseudospin textures. We also calculate the different contributions to the energy of our bimerons, coming from pseudospin stiffness, capacitance and coulomb interactions between the merons. Apart from augmenting earlier results, this allows us to check how good an approximation it is to think of the bimeron as a pair of rigid objects (merons) with logarithmically growing energy, and with electric charge ${1 \over 2}$. Our differential equation approach also allows us to study the dependence of the spin texture as a function of the distance between merons, and the inter layer distance. Lastly, the technical problem of solving coupled nonlinear partial differential equations, subject to the special boundary conditions of bimerons is interesting in its own right.

cond-mat.mes-hall↗

arXiv1997

Meron Pseudospin Solutions in Quantum Hall Systems

In this paper we report calculations of some pseudospin textures for bilayer quantum hall systems with filling factor $ ν=1$. The textures we study are isolated single meron solutions. Meron solutions have already been studied at great length by others by minimising the microscopic Hamiltonian between microscopic trial wavefunctions. Our approach is somewhat different. We calculate them by numerically solving the nonlinear integro -differential equations arising from extremisation of the effective action for pseudospin textures. Our results can be viewed as augmenting earlier results and providing a basis for comparison.Our differential equation approach also allows us to dilineate the impact of different physical effects like the pseudospin stiffness and the capacitance energy on the meron solution.

cond-mat.mes-hall↗