arXiv subjects

K. Sengupta

Publications and source records attributed to K. Sengupta.

At least 55 records · Page 3Linked to original sources

arXiv2021

One-dimensional spin-orbit coupled Dirac system with extended $s$-wave superconductivity: Majorana modes and Josephson effects

Motivated by the spin-momentum locking of electrons at the boundaries of topological insulators, we study a one-dimensional system of spin-orbit coupled massless Dirac electrons with $s$-wave superconducting pairing. As a result of the spin-orbit coupling, our model has only two kinds of linearly dispersing modes, which we take to be right-moving spin-up and left-moving spin-down. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that the $s$-wave pairing has an extended form, with the nearest-neighbor pairing being larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. Next we study a lattice version of a model with both Schrödinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrödinger and Dirac terms. We then study a continuum system consisting of two $s$-wave superconductors with different phases of the pairing. Remarkably, we find that the system has a {\it single} Andreev bound state which is localized at the junction. When the pairing phase difference crosses a multiple of $2 π$, an Andreev bound state touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constant $V_0$ and a term which oscillates with a frequency $ω$. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequency $ω_J= 2eV_0/\hbar$ is a rational fraction of $ω$. We discuss experiments which can realize such junctions.

cond-mat.mes-hall↗

arXiv2021

Analytic approaches to periodically driven closed quantum systems: Methods and Applications

We present a brief overview of some of the analytic perturbative techniques for the computation of the Floquet Hamiltonian for a periodically driven, or Floquet, quantum many-body system. The key technical points about each of the methods discussed are presented in a pedagogical manner. They are followed by a brief account of some chosen phenomena where these methods have provided useful insights. We provide an extensive discussion of the Floquet-Magnus expansion, the adiabatic-impulse approximation, and the Floquet perturbation theory. This is followed by a relatively short discourse on the rotating wave approximation, a Floquet-Magnus resummation technique and the Hamiltonian flow method. We also provide a discussion of some open problems which may possibly be addressed using these methods.

cond-mat.str-el↗

arXiv2020

A Floquet perturbation theory for periodically driven weakly-interacting fermions

We compute the Floquet Hamiltonian $H_F$ for weakly interacting fermions subjected to a continuous periodic drive using a Floquet perturbation theory (FPT) with the interaction amplitude being the perturbation parameter. This allows us to address the dynamics of the system at intermediate drive frequencies $\hbar ω_D \ge V_0 \ll {\mathcal J}_0$, where ${\mathcal J}_0$ is the amplitude of the kinetic term, $ω_D$ is the drive frequency, and $V_0$ is the typical interaction strength between the fermions. We compute, for random initial states, the fidelity $F$ between wavefunctions after a drive cycle obtained using $H_F$ and that obtained using exact diagonalization (ED). We find that FPT yields a substantially larger value of $F$ compared to its Magnus counterpart for $V_0\le \hbar ω_D$ and $V_0\ll {\mathcal J}_0$. We use the $H_F$ obtained to study the nature of the steady state of an weakly interacting fermion chain; we find a wide range of $ω_D$ which leads to subthermal or superthermal steady states for finite chains. The driven fermionic chain displays perfect dynamical localization for $V_0=0$; we address the fate of this dynamical localization in the steady state of a finite interacting chain and show that there is a crossover between localized and delocalized steady states. We discuss the implication of our results for thermodynamically large chains and chart out experiments which can test our theory.

cond-mat.str-el↗

arXiv2020

Magnetization reversal in S/F/S Josephson junctions on a 3D topological insulator

We study a magnetization reversal by an electric current pulse in a superconductor/insulating ferromagnet/superconductor Josephson junction placed on top of a 3D topological insulator. It is demonstrated that such a system is perspective for low-dissipative spintronics because of the strong spin-momentum locking in the TI surface states. This property provides an ideally strong coupling between the orbital and spin degrees of freedom thus giving a possibility of efficient reversal of the magnetic moment by current pulse with amplitude lower than the critical current, that results in strongly reduced energy dissipation. The underlying physical mechanism of the reversal is discussed. The influence of the magnetic anisotropy on the controllability of the reversal by the pulse duration is investigated. In addition, a way of a simultaneous electrical detection of the reversal is proposed.

cond-mat.supr-con↗

arXiv2020

Dynamical Transition for a class of integrable models coupled to a bath

We study the dynamics of correlation functions of a class of $d-$dimensional integrable models coupled linearly to a fermionic or bosonic bath in the presence of a periodic drive with a square pulse protocol. It is well known that in the absence of the bath, these models exhibit a dynamical phase transition; all correlators decay to their steady state values as $n_0^{-(d+1)/2}$[$n_0^{-d/2}]$ above [below] a critical frequency $ω_c$, where $n_0$ is the number of drive cycles. We find that the presence of a linearly coupled fermionic bath which maintains integrability of the system preserves this transition. We provide a semi-analytic expression for the evolution operator for this system and use it to provide a phase diagram showing the different dynamical regimes as a function of the system-bath coupling strength and the bath parameters. In contrast, when such models are coupled to a bosonic bath which breaks integrability of the model, we find exponential decay of the correlators to their steady state. Our numerical analysis shows that this exponential decay sets in above a critical number of drive cycles $n_c$ which depends on the system-bath coupling strength and the amplitude of perturbation. Below $n_c$, the system retains the power-law behavior identical to that for the closed integrable models and the dynamical transition survives. We discuss the applicability of our results for interacting fermion systems and discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2020

Entanglement measures and non-equilibrium dynamics of quantum many-body systems: a path integral approach

We present a path integral formalism for expressing matrix elements of the density matrix of a quantum many-body system between any two coherent states in terms of standard Matsubara action with periodic(anti-periodic) boundary conditions on bosonic(fermionic) fields. We show that this enables us to express several entanglement measures for bosonic/fermionic many-body systems described by a Gaussian action in terms of the Matsubara Green function. We apply this formalism to compute various entanglement measures for the two-dimensional Bose-Hubbard model in the strong-coupling regime, both in the presence and absence of Abelian and non-Abelian synthetic gauge fields, within a strong coupling mean-field theory. In addition, our method provides an alternative formalism for addressing time evolution of quantum-many body systems, with Gaussian actions, driven out of equilibrium without the use of Keldysh technique. We demonstrate this by deriving analytical expressions of the return probability and the counting statistics of several operators for a class of integrable models represented by free Dirac fermions subjected to a periodic drive in terms of the elements of their Floquet Hamiltonians. We provide a detailed comparison of our method with the earlier, related, techniques used for similar computations, discuss the significance of our results, and chart out other systems where our formalism can be used.

cond-mat.str-el↗

arXiv2020

Dynamics of the vacuum state in a periodically driven Rydberg chain

We study the dynamics of the periodically driven Rydberg chain starting from the state with zero Rydberg excitations (vacuum state denoted by $|0\rangle$) using a square pulse protocol in the high drive amplitude limit. We show, using exact diagonalization for finite system sizes ($L\le 26$), that the Floquet Hamiltonian of the system, within a range of drive frequencies which we chart out, hosts a set of quantum scars which have large overlap with the $|0\rangle$ state. These scars are distinct from their counterparts having high overlap with the maximal Rydberg excitation state ($|\mathbb{Z}_2\rangle$); they coexist with the latter class of scars and lead to persistent coherent oscillations of the density-density correlator starting from the $|0\rangle$ state. We also identify special drive frequencies at which the system undergoes perfect dynamic freezing and provide an analytic explanation for this phenomenon. Finally, we demonstrate that for a wide range of drive frequencies, the system reaches a steady state with sub-thermal values of the density-density correlator. The presence of such sub-thermal steady states, which are absent for dynamics starting from the $|\mathbb{Z}_2\rangle$ state, imply a weak violation of the eigenstate thermalization hypothesis in finite sized Rydberg chains distinct from that due to the scar-induced persistent oscillations reported earlier. We conjecture that in the thermodynamic limit such states may exist as pre-thermal steady states that show anomalously slow relaxation. We supplement our numerical results by deriving an analytic expression for the Floquet Hamiltonian using a Floquet perturbation theory in the high amplitude limit which provides an analytic, albeit qualitative, understanding of these phenomena at arbitrary drive frequencies. We discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2020

Restoring coherence via aperiodic drives in a many-body quantum system

We study the unitary dynamics of randomly or quasi-periodically driven tilted Bose-Hubbard (tBH) model in one dimension deep inside its Mott phase starting from a $\mathbb{Z}_2$ symmetry-broken state. The randomness is implemented via a telegraph noise protocol in the drive period while the quasi-periodic drive is chosen to correspond to a Thue-Morse sequence. The periodically driven tBH model (with a square pulse protocol characterized by a time period $T$) is known to exhibit transitions from dynamical regimes with long-time coherent oscillations to those with rapid thermalization. Here we show that starting from a regime where the periodic drive leads to rapid thermalization, a random drive, which consists of a random sequence of square pulses with period $T+αdT$, where $α=\pm 1$ is a random number and $dT$ is the amplitude of the noise, restores long-time coherent oscillations for special values of $dT$. A similar phenomenon can be seen for a quasi-periodic drive following a Thue-Morse sequence where such coherent behavior is shown to occur for a larger number of points in the $(T, dT)$ plane due to the additional structure of the drive protocol. We chart out the dynamics of the system in the presence of such aperiodic drives, provide a qualitative analytical understanding of this phenomenon, point out the role of quantum scars behind it, and discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2020

Quantum dynamics with stochastic reset

We study non-equilibrium dynamics of integrable and non-integrable closed quantum systems whose unitary evolution is interrupted with stochastic resets, characterized by a reset rate $r$, that project the system to its initial state. We show that the steady state density matrix of a non-integrable system, averaged over the reset distribution, retains its off-diagonal elements for any finite $r$. Consequently a generic observable $\hat O$, whose expectation value receives contribution from these off-diagonal elements, never thermalizes under such dynamics for any finite $r$. We demonstrate this phenomenon by exact numerical studies of experimentally realizable models of ultracold bosonic atoms in a tilted optical lattice. For integrable Dirac-like fermionic models driven periodically between such resets, the reset-averaged steady state is found to be described by a family of generalized Gibbs ensembles (GGE s) characterized by $r$. We also study the spread of particle density of a non-interacting one-dimensional fermionic chain, starting from an initial state where all fermions occupy the left half of the sample, while the right half is empty. When driven by resetting dynamics, the density profile approaches at long times to a nonequilibrium stationary profile that we compute exactly. We suggest concrete experiments that can possibly test our theory.

cond-mat.stat-mech↗

arXiv2019

Josephson current between two $p$-wave superconducting nanowires in the presence of Rashba spin-orbit interaction and Zeeman magnetic fields

Josephson current between two one-dimensional nanowires with proximity induced $p$-wave superconducting pairing is calculated in the presence of Rashba spin-orbit interaction, in-plane and normal magnetic fields. We show that Andreev retro-tunneling is realized by means of three channels. The main contribution to the Josephson current gives a scattering in a conventional particle-hole channel, when an electron-like quasiparticle reflects to a hole-like quasiparticle with opposite spin yielding a current which depends only on the order parameters' phase differences $φ$ and oscillates with $4π$ period. Second anomalous particle-hole channel, corresponding to the Andreev reflection of an incident electron-like quasiparticle to an hole-like quasiparticle with the same spin orientation, survives only in the presence of the in-plane magnetic field. The contribution of this channel to the Josephson current oscillates with $4π$ period not only with $φ$ but also with orientational angle of the in-plane magnetic field $θ$ resulting in a magneto-Josephson effect. Third anomalous particle-particle channel, which represents a reflection of an electron-like (hole-like) quasiparticle to a electron-like (hole-like) quasiparticle with opposite spin-orientation, oscillates only with the in-plane magnetic field orientation angle $θ$. We present a detailed theoretical analysis of both DC and AC Josephson effects in such a system showing contributions from all these channels and discuss experiments which can test our theory.

cond-mat.supr-con↗

arXiv2019

Transport on a topological insulator surface with a time-dependent magnetic barrier

We study transport across a time-dependent magnetic barrier present on the surface of a three-dimensional topological insulator. We show that such a barrier can be implemented for Dirac electrons on the surface of a three-dimensional topological insulator by a combination of a proximate magnetic material and linearly polarized external radiation. We find that the conductance of the system can be tuned by varying the frequency and amplitude of the radiation and the energy of an electron incident on the barrier providing us optical control on the conductance of such junctions. We first study a $δ$-function barrier which shows a number of interesting features such as sharp peaks and dips in the transmission at certain angles of incidence. Approximate methods for studying the limits of small and large frequencies are presented. We then study a barrier with a finite width. This gives rise to some new features which are not present for a $δ$-function barrier, such as resonances in the conductance at certain values of the system parameters. We present a perturbation theory for studying the limit of large driving amplitude and use this to understand the resonances. Finally, we use a semiclassical approach to study transmission across a time-dependent barrier and show how this can qualitatively explain some of the results found in the earlier analysis. We discuss experiments which can test our theory.

cond-mat.mes-hall↗

arXiv2019

Josephson junctions of Weyl and multi-Weyl semimetals

We study a Josephson junction involving a Weyl and a multi-Weyl semimetal separated by a barrier region of width $d$ created by putting a gate voltage $U_0$ over the Weyl semimetal. The topological winding number of such a junction changes across the barrier. We show that $I_c R_N$ for such junctions, where $I_c$ is the critical current and $R_N$ the normal state resistance, in the thin barrier limit, has a universal value independent of the barrier potential. We provide an analytical expression of the Andreev bound states and use it to demonstrate that the universal value of $I_c R_N$ is a consequence of change in topological winding number across the junction. We also study AC Josephson effect in such a junction in the presence of an external microwave radiation, chart out its current-voltage characteristics, and show that the change in the winding number across the junction shapes the properties of its Shapiro steps. We discuss the effect of increasing barrier thickness $d$ on the above-mentioned properties and chart out experiments which may test our theory.

cond-mat.str-el↗

arXiv2019

Collapse and revival of quantum many-body scars via Floquet engineering

The presence of quantum scars, athermal eigenstates of a many-body Hamiltonian with finite energy density, leads to absence of ergodicity and long-time coherent dynamics in closed quantum systems starting from simple initial states. Such non-ergodic coherent dynamics, where the system does not explore its entire phase space, has been experimentally observed in a chain of ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg chain, that the drive frequency acts as a tuning parameter for several reentrant transitions between ergodic and non-ergodic regimes. The former regime shows rapid thermalization of correlation functions and absence of scars in the spectrum of the system's Floquet Hamiltonian. The latter regime, in contrast, has scars in its Floquet spectrum which control the long-time coherent dynamics of correlation functions. Our results open a new possibility of drive frequency-induced tuning between ergodic and non-ergodic dynamics in experimentally realizable disorder-free quantum many-body systems.

quant-ph↗

arXiv2019

Electrical control of magnetization in S/F/S junctions on a 3D topological insulator

Strong dependence of the Josephson energy on the magnetization orientation in Josephson junctions with ferromagnetic interlayers and spin-orbit coupling opens a way to control magnetization by Josephson current or Josephson phase. Here we investigate the perspectives of magnetization control in superconductor/ferromagnet/superconductor (S/F/S) Josephson junctions on the surface of a 3D topological insulator hosting Dirac quasiparticles. Due to the spin-momentum locking of these Dirac quasiparticles a strong dependence of the Josephson current-phase relation on the magnetization orientation is realized. It is demonstrated that this can lead to splitting of the ferromagnet's easy-axis in the voltage driven regime. We show that such a splitting can lead to stabilization of an unconventional four-fold degenerate ferromagnetic state.

cond-mat.supr-con↗

arXiv2019

Ferromagnetic resonance and magnetic precessions in $φ_0$ junction

The Josephson $φ_0$ junctions with the current-phase relation $I = I_c \sin (φ-φ_0)$, where the phase shift $φ_0$ is proportional to the magnetic moment perpendicular to the gradient of the asymmetric spin-orbit potential, demonstrate a number of unique features important for superconducting spintronics and modern informational technologies. Here we show that a current sweep along IV-characteristic of the $φ_0$ junction may lead to regular magnetization dynamics with a series of specific phase trajectories. The origin of these trajectories is related to a direct coupling between the magnetic moment and the Josephson oscillations in these junctions, and ferromagnetic resonance when Josephson frequency coincides with the ferromagnetic one. We demonstrate that an external electromagnetic field can control the dynamics of magnetic moment within a current interval corresponding to a Shapiro step and produce topological transformation of specific precession trajectories. We demonstrate the appearance of the DC component of superconducting current and clarify its role in the transformation of IV-characteristics in the resonance region. Good agreement between numerical and analytical results has been found in the ferromagnetic resonance region. The presented results might be used for developing novel resonance methods of determination of the spin-orbit coupling parameter in the non-centrosymmetric materials. We discuss experiments which can test our results.

cond-mat.supr-con↗

arXiv2019

Transport across junctions of a Weyl and a multi-Weyl semimetal

We study transport across junctions of a Weyl and a multi-Weyl semimetal (WSM and a MSM) separated by a region of thickness $d$ which has a barrier potential $U_0$. We show that in the thin barrier limit ($U_0 \to \infty$ and $d \to 0$ with $χ=U_0 d/(\hbar v_F)$ kept finite, where $v_F$ is velocity of low-energy electrons and $\hbar$ is Planck's constant), the tunneling conductance $G$ across such a junction becomes independent of $χ$. We demonstrate that such a barrier independence is a consequence of the change in the topological winding number of the Weyl nodes across the junction and point out that it has no analogue in tunneling conductance of either junctions of two-dimensional topological materials (such as graphene or topological insulators) or those made out of WSMs or MSMs with same topological winding numbers. We study this phenomenon both for normal-barrier-normal (NBN) and normal-barrier-superconductor (NBS) junctions involving WSMs and MSMs with arbitrary winding numbers and discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2019

Transport across junctions of pseudospin-one fermions

We study transport across ballistic junctions of materials which host pseudospin-one fermions as emergent low-energy quasiparticles. The effective low-energy Hamiltonians of such fermions are described by integer spin Weyl models. We show that current conservation in such integer spin-$s$ Weyl systems requires continuity across a boundary of only $2s$ (out of $2s+1$) components of the wave function. Using the current conservation conditions, we study the transport between normal metal-barrier-normal metal (NBN) and normal metal-barrier-superconductor (NBS) junctions of such systems in the presence of an applied voltage $eV$. We show that for a specific value of the barrier potential $U_0$, such NBN junctions act as perfect collimators; any quasiparticle which is incident on the barrier with a non-zero angle of incidence is reflected back with unit probability for any barrier width $d$. We discover an interesting symmetry of this system, namely, the conductance is invariant under $U_0 \to 2(μ_L \pm eV)-U_0$, where $μ_L$ is the chemical potential and the +(-) sign corresponds to particle (hole) mediated transport. For NBS junctions with a proximity-induced $s$-wave pairing potential, which also display such a collimation, we chart out the properties of the subgap tunneling conductance $G$ as a function of the barrier strength and applied voltage. We point out the effect of the collimation on the subgap tunneling conductance of these NBS junctions and discuss experiments which can test our theory.

cond-mat.str-el↗

arXiv2019

Thermal transitions of the modulated superfluid for spin-orbit coupled correlated bosons in an optical lattice

We investigate the thermal physics of a Bose-Hubbard model with Rashba spin-orbit coupling starting from a strong coupling mean-field ground state. The essential role of the spin-orbit coupling $\left(γ\right)$ is to promote condensation of the bosons at a finite wavevector ${k}_{0}$. We find that the bosons display either homogeneous or phase-twisted or orbital ordered superfluid phases, depending on $γ$ and the inter-species interaction strength $λ$. We show that an increase of $γ$ leads to suppression of the critical interaction $U_c$ for the superfluid to Mott insulator transition in the ground state, and a reduction of the $T_c$ for superfluid to Bose-liquid transition at a fixed interaction. We capture the thermal broadening in the momentum distribution function, and the real space profiles of the thermally disordered magnetic textures, including their homogenization for $T \gtrsim T_{c}$. We provide a Landau theory based description of the ground state phase boundaries and thermal transition scales, and discuss experiments which can test our theory.

cond-mat.str-el↗