arXiv subjects

Ranjani Seshadri

Publications and source records attributed to Ranjani Seshadri.

12 recordsLinked to original sources

arXiv2026

Mode-selective excitation in parametrically driven coupled quantum oscillators

A parametrically driven classical harmonic oscillator exhibits resonant instability when driven at twice its natural frequency, with the lowest energy configuration remaining unaffected by the drive. In contrast, the ground state of the quantum mechanical counterpart shows a non-trivial response to such a drive due to the spatial delocalization of the wavefunction. The standard realization of PR involves modulating the natural frequency of the oscillator. Here we study a different drive protocol in which the coupling between two such quantum harmonic oscillators is modulated parametrically. We show that the drive frequency can in principle be tuned to selectively excite any desired normal mode, while leaving the other close to its ground state. Only states with even quantum numbers in each normal mode are populated. Within the parametric resonance window the excitations follow a power-law decay with respect to occupation number, in contrast to the exponential decay observed off-resonance. We also briefly discuss how this framework can be extended to a system of N coupled oscillators

quant-ph↗

arXiv2024

Response of the Quantum Ground State to a Parametric Drive

The phenomenon of Parametric Resonance (PR) is very well studied in classical systems with one of the textbook examples being the stabilization of a Kapitza's pendulum in the inverted configuration when the suspension point is oscillated vertically. One important aspect that distinguishes between classical PR and ordinary resonance is that in the former, if the initial energy of the system is at its minimum (${\dot x}={x}=0$), the system does not evolve. In a quantum system, however, even when the system is in the minimum energy (ground) state, the system has non-trivial evolution under PR due to the delocalized nature of the ground state wavefunction. Here we study the evolution of such a system which exhibits a purely quantum effect with no classical analog. In particular, we focus on the quantum mechanical analog of PR by varying with time the parabolic potential i.e. the frequency of the quantum harmonic oscillator

quant-ph↗

arXiv2024

Josephson Junction of Nodal Superconductors with Rashba and Ising Spin-Orbit coupling

We study the effect of a Rashba spin-orbit coupling on the nodal superconducting phase of an Ising superconductor. Such nodal phase was predicted to occur when applying an in-plane field beyond the Pauli limit to a superconducting monolayer transition metal dichalcogenides (TMD). Generically, Rashba spin-orbit is known to lift the chiral symmetry that protects the nodal points, resulting in a fully gapped phase. However, when the magnetic field is applied along the $Γ-K $ line, a residual vertical mirror symmetry protects a nodal crystalline phase. We study a single-band tight-binding model that captures the low energy physics around the $Γ$ pocket of monolayer TMD. We calculate the topological properties, the edge state structure, and the current phase relation in a Josephson junction geometry of the nodal crystalline phase. We show that while the nodal crystalline phase is characterized by localized edge modes on non-self-reflecting boundaries, the current phase relation exhibits a trivial $2π$ periodicity in the presence of Rashba spin-orbit coupling.

cond-mat.mes-hall↗

arXiv2023

Optical conductivity of a topological system driven using a realistic pulse

The effect of a time-periodic perturbation, such as radiation, on a system otherwise at equilibrium has been studied in the context of Floquet theory with stationary states replaced by Floquet states and the energy replaced by quasienergy. These quasienergy bands in general differ from the energy bands in their dispersion and, especially in the presence of spin-orbit coupling, in their states. This may, in some cases, alter the topology when the quasienergy bands exhibit different topological invariants than their stationary counterparts. In this work, motivated by advances in pump-probe techniques, we consider the optical response of driven topological systems when the drive is not purely periodic but is instead multiplied by a pulse shape/envelope function. We use real time-evolved states to calculate the optical conductivity and compare it to the response calculated using Floquet theory. We find that the conductivity bears a memory of the initial equilibrium state even when the pump is turned on slowly and the measurement is taken well after the ramp. The response of the time-evolved system is interpreted as coming from Floquet bands whose population has been determined by their overlap with the initial equilibrium state. In particular, at band inversion points in the Brillouin zone the population of the Floquet bands is inverted as well.

cond-mat.mes-hall↗

arXiv2022

Floquet topological phases on a honeycomb lattice using elliptically polarized light

We study the effect of driving a two-dimensional honeycomb system out of equilibrium using an elliptically polarized light as a time-dependent perturbation. In particular, we try to understand the topological phase diagram of this driven system when the external drive is a vector potential given by ${\bf A}(t) = (A_{0x} \cos(Ωt), A_{0y} \cos(Ωt + ϕ_0))$. These topological phases are characterized by the Floquet Chern number which, in each of these phases, is related to the number of robust edge modes on a nanoribbon. We show that varying the ratio $A_{0x}/A_{0y}$ of the external drive is a possible way to take the system from a trivial to a topological phase and vice versa.

cond-mat.mes-hall↗

arXiv2022

Engineering Floquet topological phases using elliptically polarized light

We study a two-dimensional topological system driven out of equilibrium by the application of elliptically polarized light. In particular, we analyze the Bernevig-Hughes-Zhang model when it is perturbed using an elliptically polarized light of frequency $Ω$ described in general by a vector potential ${\bf A}(t) = (A_{0x} \cos(Ωt), A_{0y} \cos(Ωt + ϕ_0))$. (Linear and circular polarizations can be obtained as special cases of this general form by appropriately choosing $A_{0x}$, $A_{0y}$, and $ϕ_0$). Even for a fixed value of $ϕ_0$, we can change the topological character of the system by changing the ratio of the $x$ and $y$ components of the drive. We therefore find a rich topological phase diagram as a function of $A_{0x}$, $A_{0y}$ and $ϕ_0$. In each of these phases, the topological invariant given by the Chern number is consistent with the number of spin-polarized states present at the edges of a nanoribbon.

cond-mat.mes-hall↗

arXiv2022

Josephson junctions of topological nodal superconductors

Transition metal dichalcogenides (TMDs) offer a unique platform to study unconventional superconductivity, owing to the presence of strong spin-orbit coupling and a remarkable stability to an in-plane magnetic field. A recent study found that when an in-plane field applied to a superconducting monolayer TMD is increased beyond the Pauli critical limit, a quantum phase transition occurs into a topological nodal superconducting phase which hosts Majorana flat bands. We study the current-phase relation of this nodal superconductor in a Josephson junction geometry. We find that the nodal superconductivity is associated with an energy-phase relation that depends on the momentum transverse to the current direction, with a $4π$ periodicity in between pairs of nodal points. We interpret this response as a result of a series of quantum phase transitions, driven by the transverse momentum, which separate a topological trivial phase and two distinct topologically non-trivial phases characterized by different winding invariants. This analysis sheds light on the stability of the Majorana flat bands to symmetry-breaking perturbations.

cond-mat.supr-con↗

arXiv2019

Generating a second-order topological insulator with multiple corner states by periodic driving

We study the effects of periodic driving on a variant of the Bernevig-Hughes-Zhang (BHZ) model defined on a square lattice. In the absence of driving, the model has both topological and nontopological phases depending on the different parameter values. We also study the anisotropic BHZ model and show that, unlike the isotropic model, it has a nontopological phase which has states localized on only two of the four edges of a finite-sized square. When an appropriate term is added, the edge states get gapped and gapless states appear at the four corners of a square; we have shown that these corner states can be labeled by the eigenvalues of a certain operator. When the system is driven periodically by a sequence of two pulses, multiple corner states may appear depending on the driving frequency and other parameters. We discuss to what extent the system can be characterized by topological invariants such as the Chern number and a diagonal winding number. We have shown that the locations of the jumps in these invariants can be understood in terms of the Floquet operator at both the time-reversal invariant momenta and other momenta which have no special symmetries.

cond-mat.mes-hall↗

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↗

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↗

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↗

arXiv2014

Confining electrons on a topological insulator surface using potentials and a magnetic field

We study the effects of extended and localized potentials and a magnetic field on the Dirac electrons residing at the surface of a three-dimensional topological insulator. We use a lattice model to numerically study the various states; we show how the potentials can be chosen in a way which effectively avoids the problem of fermion doubling on a lattice. We show that extended potentials of different shapes can give rise to states which propagate freely along the potential but decay exponentially away from it. For an infinitely long potential barrier, the dispersion and spin structure of these states are unusual and these can be varied continuously by changing the barrier strength. In the presence of a magnetic field applied perpendicular to the surface, these states become separated from the gapless surface states by a gap, thereby giving rise to a quasi-one-dimensional system. Similarly, a magnetic field along with a localized potential can give rise to exponentially localized states which are separated from the surface states by a gap and thereby form a zero-dimensional system. Finally, we show that a long barrier and an impurity potential can produce bound states which are localized at the impurity, and an "L"-shaped potential can have both bound states at the corner of the "L" and extended states which travel along the arms of the potential.

cond-mat.mes-hall↗