arXiv subjects

Diptiman Sen

Publications and source records attributed to Diptiman Sen.

At least 73 records · Page 4Linked to original sources

arXiv2018

Topological magnons in a kagome lattice spin system with $XXZ$ and Dzyaloshinskii-Moriya interactions

We study the phases of a spin system on the Kagome lattice with nearest-neighbor $XXZ$ interactions with anisotropy ratio $Δ$ and Dzyaloshinsky-Moriya interactions with strength $D$. In the classical limit where the spin $S$ at each site is very large, we find a rich phase diagram of the ground state as a function of $Δ$ and $D$. There are five distinct phases which correspond to different ground state spin configurations in the classical limit. We use spin wave theory to find the bulk energy bands of the magnons in some of these phases. We also study a strip of the system which has infinite length and finite width; we find modes which are localized on one of the edges of the strip with energies which lie in the gaps of the bulk modes. In the ferromagnetic phase in which all the spins point along the $+ \hat z$ or $- \hat z$ direction, the bulk bands are separated from each other by finite energy gaps. This makes it possible to calculate the Berry curvature at all momenta, and hence the Chern numbers for every band; the number of edge states is related to the Chern numbers. Interestingly, we find that there are four different regions in this phase where the Chern numbers are different. Hence there are four distinct topological phases even though the ground state spin configuration is identical in all these phases. We calculate the thermal Hall conductivity of the magnons as a function of the temperature in the above ferromagnetic phase; we find that this can distinguish between the various topological phases. These results are valid for all values of $S$.In the other phases, there are no gaps between the different bands; hence the edge states are not topologically protected.

cond-mat.mes-hall↗

arXiv2018

Quantized transport in topological insulator n-p-n junctions

Electrical transport in three dimensional topological insulators(TIs) occurs through spin-momentum locked topological surface states that enclose an insulating bulk. In the presence of a magnetic field, surface states get quantized into Landau levels giving rise to chiral edge states that are naturally spin-polarized due to spin momentum locking. It has been proposed that p-n junctions of TIs in the quantum Hall regime can manifest unique spin dependent effects, apart from forming basic building blocks for highly functional spintronic devices. Here, for the first time we study electrostatically defined n-p-n junctions of bulk insulating topological insulator BiSbTe$_{1.25}$Se$_{1.75}$ in the quantum Hall regime. We reveal the remarkable quantization of longitudinal resistance into plateaus at 3/2 and 2/3 h/e$^2$, apart from several partially developed fractional plateaus. Theoretical modeling combining the electrostatics of the dual gated TI n-p-n junction with Landauer Buttiker formalism for transport through a network of chiral edge states explains our experimental data, while revealing remarkable differences from p-n junctions of graphene and two-dimensional electron gas systems. Our work not only opens up a route towards exotic spintronic devices but also provides a test bed for investigating the unique signatures of quantum Hall effects in topological insulators.

cond-mat.mes-hall↗

arXiv2017

Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain

We study the Floquet phase diagram of two-dimensional Dirac materials such as graphene and the one-dimensional (1D) spin-1/2 $XY$ model in a transverse field in the presence of periodic time-varying terms in their Hamiltonians in the low drive frequency ($ω$) regime where standard $1/ω$ perturbative expansions fail. For graphene, such periodic time dependent terms are generated via the application of external radiation of amplitude $A_0$ and time period $T = 2π/ω$, while for the 1D $XY$ model, they result from a two-rate drive protocol with time-dependent magnetic field and nearest-neighbor couplings between the spins. Using the adiabatic-impulse method, we provide several semi-analytic criteria for the occurrence of changes in the topology of the phase bands of such systems. For irradiated graphene, we point out the role of the symmetries of $H(t)$ and $U$ behind such topology changes. Our analysis reveals that at low frequencies, phase band topology changes may also happen at $t= T/3, 2T/3$ (apart from $t=T$). We chart out the phase diagrams at $t=T/3, 2T/3,\, {\rm and }\, T$ as a function of $A_0$ and $T$ using exact numerics, and compare them with the prediction of the adiabatic-impulse method. We show that several characteristics of these phase diagrams can be analytically understood from results obtained using the adiabatic-impulse method and point out the crucial contribution of the high-symmetry points in the graphene Brillouin zone to these diagrams. Finally we study the 1D $XY$ model with a two-rate driving protocol using the adiabatic-impulse method and exact numerics revealing a phase band crossing at $t=T/2$ and $k=π/2$. We also study the anomalous end modes generated by such a drive. We suggest experiments to test our theory.

cond-mat.mes-hall↗

arXiv2017

Effects of local periodic driving on transport and generation of bound states

We periodically kick a local region in a one-dimensional lattice and demonstrate, by studying wave packet dynamics, that the strength and the time period of the kicking can be used as tuning parameters to control the transmission probability across the region. Interestingly, we can tune the transmission to zero which is otherwise impossible to do in a time-independent system. We adapt the non-equilibrium Green's function method to take into account the effects of periodic driving; the results obtained by this method agree with those found by wave packet dynamics if the time period is small. We discover that Floquet bound states can exist in certain ranges of parameters; when the driving frequency is decreased, these states get delocalized and turn into resonances by mixing with the Floquet bulk states. We extend these results to incorporate the effects of local interactions at the driven site, and we find some interesting features in the transmission and the bound states.

cond-mat.mes-hall↗

arXiv2017

Aperiodically driven integrable systems and their emergent steady states

Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long time behavior of the local properties synchronize with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in at least two cases. While any typical realization of random noise causes eventual heating to an infinite temperature ensemble for all local properties in spite of the system being integrable, noise which is self-similar in time leads to an entirely different steady state, which we dub as "geometric generalized Gibbs ensemble", that emerges only after an astronomically large time scale. To understand the approach to steady state, we study the temporal behavior of certain coarse-grained quantities in momentum space that fully determine the reduced density matrix for a subsystem with size much smaller than the total system. Such quantities provide a concise description for any drive protocol in integrable systems that are reducible to a free fermion representation.

cond-mat.str-el↗

arXiv2017

Generating end modes in a superconducting wire by periodic driving of the hopping

We show that harmonic driving of either the magnitude or the phase of the nearest-neighbor hopping amplitude in a p-wave superconducting wire can generate modes localized near the ends of the wire. The Floquet eigenvalues of these modes can either be equal to $\pm 1$ (which is known to occur in other models) or can lie near other values in complex conjugate pairs which is unusual; we call the latter anomalous end modes. All the end modes have equal probabilities of particles and holes. If the amplitude of driving is small, we observe an interesting bulk-boundary correspondence: the Floquet eigenvalues and the peaks of the Fourier transform of the end modes lie close to the Floquet eigenvalues and momenta at which the Floquet eigenvalues of the bulk system have extrema.

cond-mat.mes-hall↗

arXiv2017

Density functional theory of the fractional quantum Hall effect

A conceptual difficulty in formulating the density functional theory of the fractional quantum Hall effect is that while in the standard approach the Kohn-Sham orbitals are either fully occupied or unoccupied, the physics of the fractional quantum Hall effect calls for fractionally occupied Kohn-Sham orbitals. This has necessitated averaging over an ensemble of Slater determinants to obtain meaningful results. We develop an alternative approach in which we express and minimize the grand canonical potential in terms of the composite fermion variables. This provides a natural resolution of the fractional-occupation problem because the fully occupied orbitals of composite fermions automatically correspond to fractionally occupied orbitals of electrons. We demonstrate the quantitative validity of our approach by evaluating the density profile of fractional Hall edge as a function of temperature and the distance from the delta dopant layer and showing that it reproduces edge reconstruction in the expected parameter region.

cond-mat.str-el↗

arXiv2017

Generating surface states in a Weyl semi-metal by applying electromagnetic radiation

We show that the application of circularly polarized electromagnetic radiation on the surface of a Weyl semi-metal can generate states at that surface. These states can be characterized by their surface momentum. The Floquet eigenvalues of these states come in complex conjugate pairs rather than being equal to $\pm 1$. If the amplitude of the radiation is small, we find some unusual bulk-boundary relations: the Floquet eigenvalues of the surface states lie at the extrema of the Floquet eigenvalues of the bulk system, and the peaks of the Fourier transforms of the surface state wave functions lie at the momenta where the bulk Floquet eigenvalues have extrema. For the case of zero surface momentum, we can analytically derive scaling relations between the decay length of the surface states and the amplitude and penetration length of the radiation. For topological insulators, we again find that circularly polarized radiation can generate states on the surfaces; these states have much larger decay lengths than the surface states which are present even in the absence of radiation. Finally, we show that radiation can generate surface states for trivial insulators also.

cond-mat.mes-hall↗

arXiv2017

Electron dynamics in graphene with spin-orbit couplings and periodic potentials

We use both continuum and lattice models to study the energy-momentum dispersion and the dynamics of a wave packet for an electron moving in graphene in the presence of spin-orbit couplings and either a single potential barrier or a periodic array of potential barriers. Both Kane-Mele and Rashba spin-orbit couplings are considered. A number of special things occur when the Kane-Mele and Rashba couplings are equal in magnitude. In the absence of a potential, the dispersion then consists of both massless Dirac and massive Dirac states. A periodic potential is known to generate additional Dirac points; we show that spin-orbit couplings generally open gaps at all those points, but if the two spin-orbit couplings are equal, some of the Dirac points remain gapless. We show that the massless and massive states respond differently to a potential barrier; the massless states transmit perfectly through the barrier at normal incidence while the massive states reflect from it. In the presence of a single potential barrier, we show that there are states localized along the barrier. Finally, we study the time evolution of a wave packet in the presence of a periodic potential. We discover special points in momentum space where there is almost no spreading of a wave packet; there are six such points in graphene when the spin-orbit couplings are absent.

cond-mat.mes-hall↗

arXiv2017

Effects of interactions on periodically driven dynamically localized systems

It is known that there are lattice models in which non-interacting particles get dynamically localized when periodic $δ$-function kicks are applied with a particular strength. We use both numerical and analytical methods to study the effects of interactions in three different models in one dimension. The systems we have considered include spinless fermions with interactions between nearest-neighbor sites, the Hubbard model of spin-1/2 fermions, and the Bose Hubbard model with on-site interactions. We derive effective Floquet Hamiltonians up to second order in the time period of kicking. Using these we show that interactions can give rise to a variety of interesting results such as two-body bound states in all three models and dispersionless many-body bound states for spinless fermions and bosons. We substantiate these results by exact diagonalization and stroboscopic time evolution of systems with a finite number of particles. We derive a low-energy pseudo-spin-1/2 limit of the Bose Hubbard system in the thermodynamic limit and show that a special case of this has an exponentially large number of ground states. Finally we study the effect of changing the strength of the $δ$-function kicks slightly away from perfect dynamical localization; we find that a single particle remains dynamically localized for a long time after which it moves ballistically.

cond-mat.mes-hall↗

arXiv2016

Signatures and conditions for phase band crossings in periodically driven integrable systems

We present generic conditions for phase band crossings for a class of periodically driven integrable systems represented by free fermionic models subjected to arbitrary periodic drive protocols characterized by a frequency $ω_D$. These models provide a representation for the Ising and $XY$ models in $d=1$, the Kitaev model in $d=2$, several kinds of superconductors, and Dirac fermions in graphene and atop topological insulator surfaces. Our results demonstrate that the presence of a critical point/region in the system Hamiltonian (which is traversed at a finite rate during the dynamics) may change the conditions for phase band crossings that occur at the critical modes. We also show that for $d>1$, phase band crossings leave their imprint on the equal-time off-diagonal fermionic correlation functions of these models; the Fourier transforms of such correlation functions, $F_{\vec k_0}( ω_0)$, have maxima and minima at specific frequencies which can be directly related to $ω_D$ and the time at which the phase bands cross at $\vec k = \vec k_0$. We discuss the significance of our results in the contexts of generic Hamiltonians with $N>2$ phase bands and the underlying symmetry of the driven Hamiltonian.

cond-mat.str-el↗

arXiv2016

Granular topological insulators

Granular conductors form an artificially engineered class of solid state materials wherein the microstructure can be tuned to mimic a wide range of otherwise inaccessible physical systems. At the same time, topological insulators (TIs) have become a cornerstone of modern condensed matter physics as materials hosting metallic states on the surface and insulating in the bulk. However it remains to be understood how granularity affects this new and exotic phase of matter. We perform electrical transport experiments on highly granular topological insulator thin films of Bi$_2$Se$_3$ and reveal remarkable properties. We observe clear signatures of topological surface states despite granularity with distinctly different properties from conventional bulk TI systems including sharp surface state coupling-decoupling transitions, large surface state penetration depths and exotic Berry phase effects. We present a model which explains these results. Our findings illustrate that granularity can be used to engineer designer TIs, at the same time allowing easy access to the Dirac-fermion physics that is inaccessible in single crystal systems.

cond-mat.mtrl-sci↗

arXiv2016

Effects of periodic kicking on dispersion and wave packet dynamics in graphene

We study the effects of $δ$-function periodic kicks on the Floquet energy-momentum dispersion in graphene. We find that a rich variety of dispersions can appear depending on the parameters of the kicking: at certain points in the Brillouin zone, the dispersion can become linear but anisotropic, linear in one direction and quadratic in the perpendicular direction, gapped with a quadratic dispersion, or completely flat (called dynamical localization). We show all these results analytically and demonstrate them numerically through the dynamics of wave packets propagating in graphene. We propose experimental methods for producing these effects.

cond-mat.mes-hall↗

arXiv2016

Transport across a system with three p-wave superconducting wires: effects of Majorana modes and interactions

We study the effects of Majorana modes and interactions between electrons on transport in a one-dimensional system with a junction of three p-wave superconductors (SCs) which are connected to normal metal leads. For sufficiently long SCs, there are zero energy Majorana modes at the junctions between the SCs and the leads,and, depending on the signs of the p-wave pairings in the three SCs, there can also be one or three Majorana modes at the junction of the three SCs. We show that the various sub-gap conductances have peaks occurring at the energies of all these modes; we therefore get a rich pattern of conductance peaks. Next, we use a renormalization group approach to study the scattering matrix of the system at energies far from the SC gap. The fixed points of the renormalization group flows and their stabilities are studied; we find that the scattering matrix at the stable fixed point is highly symmetric even when the microscopic scattering matrix and the interaction strengths are not symmetric. We discuss the implications of this for the conductances. Finally we propose an experimental realization of this system which can produce different signs of the p-wave pairings in the different SCs.

cond-mat.mes-hall↗

arXiv2016

Edge states, spin transport and impurity induced local density of states in spin-orbit coupled graphene

We study graphene which has both spin-orbit coupling (SOC), taken to be of the Kane-Mele form, and a Zeeman field induced due to proximity to a ferromagnetic material. We show that a zigzag interface of graphene having SOC with its pristine counterpart hosts robust chiral edge modes in spite of the gapless nature of the pristine graphene; such modes do not occur for armchair interfaces. Next we study the change in the local density of states (LDOS) due to the presence of an impurity in graphene with SOC and Zeeman field, and demonstrate that the Fourier transform of the LDOS close to the Dirac points can act as a measure of the strength of the spin-orbit coupling; in addition, for a specific distribution of impurity atoms, the LDOS is controlled by a destructive interference effect of graphene electrons which is a direct consequence of their Dirac nature. Finally, we study transport across junctions which separates spin-orbit coupled graphene with Kane-Mele and Rashba terms from pristine graphene both in the presence and absence of a Zeeman field. We demonstrate that such junctions are generally spin active, namely, they can rotate the spin so that an incident electron which is spin polarized along some direction has a finite probability of being transmitted with the opposite spin. This leads to a finite, electrically controllable, spin current in such graphene junctions. We discuss possible experiments which can probe our theoretical predictions.

cond-mat.mes-hall↗

arXiv2015

Majorana modes and transport across junctions of superconductors and normal metals

We study Majorana modes and transport in one-dimensional systems with a $p$-wave superconductor (SC) and normal metal leads. For a system with a SC lying between two leads, it is known that there is a Majorana mode at the junction between the SC and each lead. If the $p$-wave pairing $Δ$ changes sign or if a strong impurity is present at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the sub-gap conductance between the leads and the SC. We derive an analytical expression as a function of $Δ$ and the length $L$ of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the shifts oscillate and decay exponentially as $L$ is increased. The energy shifts exactly match the location of the peaks in the conductance. Using bosonization and the renormalization group method, we study the effect of interactions between the electrons on $Δ$ and the strengths of an impurity inside the SC or the barriers between the SC and the leads; this in turn affects the Majorana modes and the conductance. Finally we propose a novel experimental realization of these systems, in particular of a system where $Δ$ changes sign at one point inside the SC.

cond-mat.mes-hall↗

arXiv2015

Detection of a quantum particle on a lattice under repeated projective measurements

We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect it's arrival at a particular chosen set of sites. The projective measurements are made at regular time intervals $τ$, and we consider the evolution of the wave function till the time a detection occurs. We study the probabilities of its first detection at some time and conversely the probability of it not being detected (i.e., surviving) up to that time. We propose a general perturbative approach for understanding the dynamics which maps the evolution operator, consisting of unitary transformations followed by projections, to one described by a non-Hermitian Hamiltonian. For some examples, of a particle moving on one and two-dimensional lattices with one or more detection sites, we use this approach to find exact expressions for the survival probability and find excellent agreement with direct numerical results. A mean field model with hopping between all pairs of sites and detection at one site is solved exactly. For the one- and two-dimensional systems, the survival probability is shown to have a power-law decay with time, where the power depends on the initial position of the particle. Finally, we show an interesting and non-trivial connection between the dynamics of the particle in our model and the evolution of a particle under a non-Hermitian Hamiltonian with a large absorbing potential at some sites.

quant-ph↗

arXiv2015

Quantum phase transitions in transverse field spin models: from statistical physics to quantum information

We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of the spin-1/2 Ising and XY models in a transverse field. Beginning with an overview of quantum phase transitions, we introduce a number of model Hamiltonians. We provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies. We also discuss Kitaev models and some other exactly solvable spin systems. Studies of quantum phase transitions in the presence of quenched randomness and with frustrating interactions are presented in detail. We discuss novel phenomena like Griffiths-McCoy singularities. We then turn to more recent topics like information theoretic measures of the quantum phase transitions in these models such as concurrence, entanglement entropy, quantum discord and quantum fidelity. We then focus on non-equilibrium dynamics of a variety of transverse field systems across quantum critical points and lines. After mentioning rapid quenching studies, we dwell on slow dynamics and discuss the Kibble-Zurek scaling for the defect density following a quench across critical points and its modifications for quenching across critical lines, gapless regions and multicritical points. Topics like the role of different quenching schemes, local quenching, quenching of models with random interactions and quenching of a spin chain coupled to a heat bath are touched upon. The connection between non-equilibrium dynamics and quantum information theoretic measures is presented at some length. We indicate the connection between Kibble-Zurek scaling and adiabatic evolution of a state as well as the application of adiabatic dynamics as a tool of a quantum optimization technique known as quantum annealing. The final section is dedicated to a detailed discussion on recent experimental studies of transverse Ising-like systems.

cond-mat.stat-mech↗