arXiv subjects

Tanay Nag

Publications and source records attributed to Tanay Nag.

At least 73 records · Page 4Linked to original sources

arXiv2021

Dynamics of fluctuation correlation in periodically driven classical system

Having established the fact that interacting classical kicked rotor systems exhibit long-lived prethermal phase with quasi-conserved average Hamiltonian before entering into chaotic heating regime, we use spatio-temporal fluctuation correlation of kinetic energy to probe the above dynamic phases. We remarkably find the diffusive transport of fluctuation in the prethermal regime reminding us the underlying hydrodynamic picture in a generalized Gibbs ensemble with a definite temperature that depends on the driving parameter and initial conditions. On the other hand, the heating regime, characterized by a diffusive growth of kinetic energy, can sharply localize the correlation at the fluctuation center for all time. Consequently, we attribute non-diffusive and non-localize structure of correlation to the crossover regime, connecting the prethermal phase to the heating phase, where the kinetic energy displays complicated growth structure. We understand these numerical findings using the notion of relative phase matching where prethermal phase (heating regime) refers to an effectively coupled (isolated) nature of the rotors. We exploit the statistical uncorrelated nature of the angles of the rotors in the heating regime to find the analytical form of the correlator that mimics our numerical results in a convincing way.

cond-mat.stat-mech↗

arXiv2021

Anomalous and normal dislocation modes in Floquet topological insulators

Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For example, a suitable periodic drive can convert a trivial insulator into a Floquet topological insulator (FTI) that accommodates nondissipative dynamic gapless modes at the interfaces with vacuum. Here we theoretically demonstrate that dislocations, ubiquitous lattice defects in crystals, can probe FTIs as well as unconventional $π$-trivial insulator in the bulk of driven quantum systems by supporting normal and anomalous modes, localized near the defect core. Respectively, normal and anomalous dislocation modes reside at the Floquet zone center and boundaries. We exemplify these outcomes specifically for two-dimensional (2D) Floquet Chern insulator and $p_x+ip_y$ superconductor, where the dislocation modes are respectively constituted by charged and neutral Majorana fermions. Our findings should be therefore instrumental in probing Floquet topological phases in the state-of-the-art experiments in driven quantum crystals, cold atomic setups, and photonic and phononic metamaterials through bulk topological lattice defects.

cond-mat.mes-hall↗

arXiv2021

Eight fold quantum Hall phases in a time reversal symmetry broken tight binding model

We consider a time reversal symmetry (TRS) broken Kane-Mele model superimposed with Haldane model and chart out the phase diagram using spin Chern number to investigate the fate of quantum anomalous Hall insulator (QAHI) and quantum spin Hall insulator (QSHI) phases. Interestingly, in addition to QSHI and QAHI phase, the phase diagram unveils quantum anomalous spin Hall insulator (QASHI) phase where only one spin sector is topological. We also find multicritical points where three / four topological phase boundaries coalesce. These topological phases are protected by an effective TRS and a composite anti-unitary particle-hole symmetry leading to remarkable properties of edge modes. We find spin-selective, spin-polarized and spin-neutral edge transport in QASHI, QSHI and QAHI phases respectively. Our study indicates that the robustness of the topological phase mainly depends on the spin gap which does not necessarily vanish at the Dirac points across a topological phase transition. We believe that our proposals can be tested in near future using recent experimental advancements in solid state and cold atomic systems.

cond-mat.mes-hall↗

arXiv2021

Role of time reversal symmetry and tilting in circular photogalvanic responses

We study the role of time reversal symmetry (TRS) in the circular photogalvanic (CPG) responses considering chiral Weyl semimetal (WSM) while a quantized CPG response is guaranteed by broken of both inversion symmetry (IS) and mirror symmetries. The TRS broken WSM yields one left and one right chiral Weyl nodes (WNs) while there are two left and right chiral WNs for TRS invariant WSM. We show that these features can potentially cause the quantization of CPG response at higher values compared to the topological charge of the underlying WSM. This is further supported by the fact that Berry curvature and velocity behave differently whether the system preserves or breaks the TRS. We find the CPG responses for TRS invariant type-II WSM to be quantized at two and four times the topological charge of the activated WNs while the chemical potential are respectively chosen in the vicinity of energies associated with left and right chiral WNs. By contrast, irrespective of the above choice of the chemical potential, the quantization in CPG response is directly given by the topological charge of the activated WNs for TRS broken case. Interestingly, we notice non-quantized peak in CPG response when energies of WNs associated with opposite chiralities are close to each other as it is the case for TRS invariant type-I WSM considered here. Moreover, we show that the tilt can significantly modify the CPG response as velocity in the tilt direction changes which enters into the CPG tensor through the Fermi distribution function. Given these exciting outcomes, the second order CPG response emerges as a useful indicator to characterize the system under consideration. Furthermore, we investigate the momentum resolved structure of CPG response to relate with the final results and strengthen our analysis from the perspective of the lattice models.

cond-mat.mes-hall↗

arXiv2021

Hierarchy of higher-order Floquet topological phases in three dimensions

Following a general protocol of periodically driving static first-order topological phases (supporting surface states) with suitable discrete symmetry breaking Wilson-Dirac masses, here we construct a hierarchy of higher-order Floquet topological phases in three dimensions. In particular, we demonstrate realizations of both second-order and third-order Floquet topological states, respectively supporting dynamic hinge and corner modes at zero quasienergy, by periodically driving their static first-order parent states with one and two discrete symmetry breaking Wilson-Dirac mass(es). While the static surface states are characterized by codimension $d_c=1$, the resulting dynamic hinge (corner) modes, protected by \emph{antiunitary} spectral or particle-hole symmetries, live on the boundaries with $d_c=2$ $(3)$. We exemplify these outcomes for three-dimensional topological insulators and Dirac semimetals, with the latter ones following an arbitrary spin-$j$ representation.

cond-mat.mes-hall↗

arXiv2021

Floquet Second Order Topological Superconductor based on Unconventional Pairing

We theoretically investigate the Floquet generation of second-order topological superconducting (SOTSC) phase in the high-temperature platform both in two-dimension (2D) and three-dimension (3D). Starting from a $d$-wave superconducting pairing gap, we periodically kick the mass term to engineer the dynamical SOTSC phase within a specific range of the strength of the drive. Under such dynamical breaking of time-reversal symmetry (TRS), we show the emergence of the \textit{weak} SOTSC phase, harboring eight corner modes \ie two zero-energy Majorana per corner, with vanishing Floquet quadrupole moment. On the other hand, our study interestingly indicates that upon the introduction of an explicit TRS breaking Zeeman field, the \textit{weak} SOTSC phase can be transformed into \textit{strong} SOTSC phase, hosting one zero-energy Majorana mode per corner, with quantized quadrupole moment. We also compute the Floquet Wannier spectra that further establishes the \textit{weak} and \textit{strong} nature of these phases. We numerically verify our protocol computing the exact Floquet operator in open boundary condition and then analytically validate our findings with the low energy effective theory (in the high-frequency limit). The above protocol is applicable for 3D as well where we find one dimensional (1D) hinge mode in the SOTSC phase. We then show that these corner modes are robust against moderate disorder and the topological invariants continue to exhibit quantized nature until disorder becomes substantially strong. The existence of zero-energy Majorana modes in these higher-order phases is guaranteed by the anti-unitary spectral symmetry.

cond-mat.mes-hall↗

arXiv2021

Floquet generation of Second Order Topological Superconductor

We theoretically investigate the Floquet generation of second-order topological superconducting (SOTSC) phase, hosting Majorana corner modes (MCMs), considering a quantum spin Hall insulator (QSHI) with proximity induced superconducting $s$-wave pairing in it. Our dynamical prescription consists of the periodic kick in time-reversal symmetry breaking in-plane magnetic field and four-fold rotational symmetry breaking mass term while these Floquet MCMs are preserved by anti-unitary particle-hole symmetry. The first driving protocol always leads to four zero energy MCMs (i.e. one Majorana per corner) as a sign of a {\it{strong}} SOTSC phase. Interestingly, the second protocol can result in a {\it{weak}} SOTSC phase, harbouring eight zero energy MCMs (two Majorana states per corner), in addition to the {\it{strong}} SOTSC phase. We characterize the topological nature of these phases by Floquet quadrupolar moment and Floquet Wannier spectrum. We believe that relying on the recent experimental advancement in the driven systems and proximity induced superconductivity, our schemes may be possible to test in the future.

cond-mat.mes-hall↗

arXiv2020

Magneto-transport phenomena of type-I multi-Weyl semimetals in co-planar setups

Having the chiral anomaly induced magneto-transport phenomena extensively studied in single Weyl semimetal (WSM) as characterized by topological charge $n=1$, we here address the transport properties in the context of multi-Weyl semimetals (m-WSMs) where $n>1$. Using semiclassical Boltzmann transport formalism with the relaxation time approximation, we investigate several intriguing transport properties such as longitudinal magneto-conductivity (LMC), planar Hall conductivity (PHC), thermo-electric coefficients (TECs) and planar Nernst coefficient (PNC) for m-WSMs in the co-planar setups with external magnetic field, electric field and temperature gradient. Starting from the low-energy model, we show analytically that at zero temperature both LMC and PHC vary cubically with topological charge as $n^3$ while the finite temperature ($T \neq 0$) correction is proportional to $(n+n^2)T^2$. Interestingly, we find that both the longitudinal and transverse TECs vary quadratically with topological charge as $n^2$ and the PNC is found to vary non-monotonically as a function of $n$. Our study hence clearly suggests that the inherent properties of m-WSMs indeed show up distinctly through the chiral anomaly and the chiral magnetic effect induced transport coefficients in two different setups. Moreover, in order to obtain an experimentally realizable picture, we simultaneously verify our analytical findings through the numerical calculations using the lattice model of m-WSMs.

cond-mat.mes-hall↗

arXiv2020

Thermo-electric transport properties of Floquet multi-Weyl Semimetals

We discuss the circularly polarized light (of amplitude $A_0$ and frequency $ω$) driven thermo-electric transport properties of type-I and type-II multi-Weyl semimetals (mWSMs) in the high frequency limit. Considering the low energy model, we employ the Floquet-Kubo formalism to compute the thermal Hall and Nernst conductivities for both types of mWSMs. We show that the anisotropic nature of the dispersion for arbitrary integer monopole charge $n>1$ plays an important role in determining the effective Fermi surface behavior; interestingly, one can observe momentum dependent corrections in Floquet mWSMs in addition to momentum independent contribution as observed for Floquet single WSMs. Apart from the non-trivial tuning of the Weyl node position $\pm Q \to \pm Q- A_0^{2n}/ω$, our study reveals that the momentum independent terms result in leading order contribution in the conductivity tensor. This has the form of $n$ times the single WSMs results with effective chemical potential $μ\to μ-A_0^{2n}/ω$. On the other hand, momentum dependent corrections lead to sub-leading order terms which are algebraic function of $μ$ and are present for $n>1$. Remarkably, this analysis further allows us to distinguish type-I mWSMs from their type-II counterparts. For type-II mWSMs, we find that the transport coefficients for $n\geq 2$ exhibit algebraic dependence on the momentum cutoff in addition to the weak logarithmic dependence as noticed for $n=1$ WSMs. We demonstrate the variation and qualitative differences of transport coefficients between type-I and type-II mWSM as a function of external driving parameter $ω$.

cond-mat.mes-hall↗

arXiv2020

Many-body localization in long range model: Real space renormalization group study

We develop a real space renormalization group (RSRG) scheme by appropriately inserting the long range hopping $t\sim r^{-α}$ with nearest neighbour interaction to study the entanglement entropy and maximum block size for many-body localization (MBL) transition. We show that for $α<2$ there exists a localization transition with renormalized disorder that depends logarithmically on the finite size of the system. The transition observed for $α>2$ does not need a rescaling in disorder strength. Most importantly, we find that even though the MBL transition for $α>2$ falls in the same universality class as that of the short-range models, while transition for $α<2$ belongs to a different universality class. {Due to the intrinsic nature of the RSRG flow towards delocalization, MBL phase for $α>2$ might suffer an instability in the thermodynamic limit while the underlying systems support algebraic localization. Moreover, we verify these findings by inserting microscopic details to the RSRG scheme where we additionally find a more appropriate rescaling function for disorder strength; we indeed uncover a power law scaling with a logarithmic correction and a distinctly different stretched exponential scaling for $α<2$ and $α>2$, respectively, by analyzing system with finite size. This finding further suggests that microscopic RSRG scheme is able to give a hint of instability of the MBL phase for $α>2$ even considering systems of finite size.

cond-mat.dis-nn↗

arXiv2020

Many-body dynamics in long-range hopping model in the presence of correlated and uncorrelated disorder

Much have been learned about universal properties of entanglement entropy (EE) and participation ration (PR) for Anderson localization. We find a new sub-extensive scaling with system size of the above measures for algebraic localization as noticed in one-dimensional long-range hopping models in the presence of uncorrelated disorder. While the scaling exponent of EE seems to vary universally with the long distance localization exponent of single particle states (SPSs), PR does not show such university as it also depends on the short range correlations of SPSs. On the other hand, in presence of correlated disorder, an admixture of two species of SPSs (ergodic delocalized and non-ergodic multifractal or localized) are observed, which leads to extensive (sub-extensive) scaling of EE (PR). Considering typical many-body eigenstates, we obtain above results that are further corroborated with the asymptotic dynamics. Additionally, a finite time secondary slow growth in EE is witnessed only for correlated case while for uncorrelated case there exists only primary growth followed by the saturation. We believe that our findings from typical many-body eigenstate would remain unaltered even in the weakly interacting limit.

cond-mat.dis-nn↗

arXiv2020

Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics

Higher-order topological~(HOT) states,~hosting topologically protected modes on lower-dimensional boundaries,~such as hinges and corners, have recently extended the realm of the static topological phases.~Here we demonstrate the possibility of realizing a two-dimensional \emph{Floquet} second-order topological insulator, featuring corner-localized zero quasienergy modes and characterized by quantized Floquet qudrupolar moment $Q^{\rm Flq}_{xy}=0.5$, by periodically kicking a quantum spin Hall insulator (QSHI) with a discrete fourfold ($C_4$) and time-reversal (${\mathcal T}$) symmetry breaking Dirac mass perturbation.~Furthermore, we show that $Q^{\rm Flq}_{xy}$ becomes independent of the choice of origin as the system approaches the thermodynamic limit.~We also analyze the dynamics of a corner mode after a sudden quench, when the $C_4$ and ${\mathcal T}$ symmetry breaking perturbation is switched off, and find that the corresponding survival probability displays periodic appearances of complete, partial and no revival for long time, encoding the signature of corner modes in a QSHI.~Our protocol is sufficiently general to explore the territory of dynamical HOT phases in insulators and gapless systems.

cond-mat.mes-hall↗

arXiv2018

Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain

We study the non-equilibrium evolution of concurrence of a Bell pair constituted of two qubits, through the measurement of Loschmidt echo (LE) under the scope of generalized central spin model. Having detected the Griffiths phase via derivative of LE in equilibrium, we show that in the non-equilibrium situation, the spin chain requires a temporal window to realize the effect of disorder. We show that within this timescale, LE falls off exponentially and this decay is maximally controlled by the initial states and coupling strength. Our detail investigation suggests that there actually exist three types of exponential decay, a Gaussian decay in ultra short time scale followed by two exponential decay in the intermediate time with two different decay exponents. The effect of the disorder starts appearing in the late time power law fall of LE where the power law exponent is strongly dependent on disorder strength and the final state but almost independent of initial states and coupling strength. This feature allows us to indicate the presence of Griffiths phase. To be precise, continuously varying critical exponent and wide distribution of relaxation time imprint their effect in LE in the late time limit where the power law fall is absent for quenching to a Griffiths phase. Here, LE vanishes following the fast exponential fall. Interestingly, for off-critical quenching LE attains a higher saturation value for increasing disorder strength, otherwise vanishes for a clean spin chain, referring to the fact that disorder prohibits the rapid decay of entanglement in long time limit. Moreover, we show that disorder is also able to destroy the light cone like nature of post quench quasi-particles as LE does not sense the singular time scales appearing for clean spin chain with qubits coupled at symmetric positions.

cond-mat.mes-hall↗

arXiv2018

Dynamical synchronization transition in interacting electron systems

Synchronization is a ubiquitous phenomenon in nature and we propose its new perspective in ultrafast dynamics in interacting electron systems. In particular, using graphene irradiated by an intense bi-circular pulse laser as a prototypical and experimental viable example, we theoretically investigate how to selectively generate a coherent oscillation of electronic order such as charge density waves (CDW). The key is to use tailored fields that match the crystalline symmetry broken by the target order. After the pump, a macroscopic number of electrons start oscillating and coherence is built up through a transition. The resulting physics is detectable as a coherent light emission at the synchronization frequency and may be used as a purely electronic way of realizing Floquet states respecting exotic space time crystalline symmetries. In the process, we also explore possible flipping of existing static CDW orders and generation of higher harmonics. The general framework for the coherent electronic order is found to be analogous with the celebrated Kuramoto model, describing the classical synchronization of coupled pendulums.

cond-mat.str-el↗

arXiv2018

Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary

We investigate the effect of a time-reversal breaking impurity term on both the equilibrium and non-equilibrium critical properties of entanglement entropy (EE) in a three-spin interacting transverse Ising model which can be mapped to a one-dimensional p-wave superconductor with next-nearest-neighbor hopping. Due to the presence of next-nearest-neighbor hopping, a new topological phase with two zero-energy Majorana modes at each end of an open chain appears in the phase diagram. We show that the derivative of EE with respect to one of the parameters of the Hamiltonian can detect the quantum phase transitions by exhibiting cusp like structure at those points; impurity strength ($\la_d$) can substantially modify the peak/dip height associated with the cusp. Importantly, we find that the logarithmic scaling of the EE with block size remains unaffected by the application of the impurity term, although, the coefficient (i.e., central charge) varies logarithmically with the impurity strength for a lower range of $\la_d$ and eventually saturates with an exponential damping factor ($\sim \exp(-\la_d)$) for the phase boundaries shared with the phase containing two Majorana edge modes. On the other hand, it receives a linear correction in term of $\la_d$ for an another phase boundary. Finally, we focus to study the effect of the impurity in the time evolution of the EE for the critical quenching case where impurity term is applied only to the final Hamiltonian. Interestingly, it has been shown that for all the phase boundaries in contrary to the equilibrium case, the saturation value of the EE increases logarithmically with the strength of impurity in a certain region of $\la_d$ and finally, for higher values of $\la_d$, it increases very slowly which is dictated by an exponential damping factor.

cond-mat.stat-mech↗

arXiv2017

Survival probability in a quenched Majorana chain with an impurity

We investigate the dynamics of a one-dimensional $p$-wave superconductor with next-nearest-neighbor hopping and superconducting interaction derived from a three-spin interacting Ising model in transverse field by mapping to Majorana fermions. The next-nearest-neighbor hopping term leads a new topological phase containing two zero-energy Majorana modes at each end of an open chain, compared to a nearest-neighbor $p$-wave superconducting chain. We study the Majorana survival probability (MSP) of a particular Majorana edge state when the initial Hamiltonian ($H_i$) is changed to the quantum critical as well as off-critical final Hamiltonian ($H_f$) which additionally contains an impurity term ($H_{imp}$) that breaks the time-reversal invariance. For the off-critical quenching inside the new topological phase with $H_f= H_i +H_{imp}$, and small impurity strength ($λ_d$), we observe a perfect oscillation of the MSP as a function of time with a single frequency (determined by the impurity strength $λ_d$) that can be analyzed from an equivalent two-level problem. On the other hand, the MSP shows a beating like structure with time for quenching to the phase boundary separating the topological phase (with two edge Majoranas at each edge) and the non-topological phase where the additional frequency is given by inverse of the system size. We attribute this behavior of the MSP to the modification of the energy levels of the final Hamiltonian due to the application of the impurity term.

cond-mat.stat-mech↗

arXiv2016

Generation of concurrence between two qubits locally coupled to a one dimensional spin chain

We consider a generalized central spin model, consisting of two central qubits and an environmental spin chain (with periodic boundary condition) to which these central qubits are locally and weakly connected either at the same site or at two different sites separated by a distance $d$. Our purpose is to study the subsequent temporal generation of entanglement, quantified by concurrence, when initially the qubits are in an unentangled state. In the equilibrium situation, we show that the concurrence survives for a larger value of $d$ when the environmental spin chain is critical. Importantly, a common feature observed both in the equilibrium and the non-equilibrium situations while the latter is created by a sudden but global change of the environmental transverse field, is that the two qubits become maximally entangled for the critical quenching. Following a non-equilibrium evolution of the spin chain, our study for $d\neq 0$, indicates that there exists a threshold time above which concurrence attains a finite value. Additionally, we show that the number of independent decohering channels (DCs) is determined by $d$ as well as the local difference of the transverse field of the two underlying Hamiltonians governing the time evolution. The qualitatively similar behavior displayed by the concurrence for critical and off-critical quenches, as reported here, is characterized by analyzing the non-equilibrium evolution of these channels. The concurrence is maximum when the decoherence factor or the echo associated with the most rapidly DC decays to zero; on the contrary, the condition when the concurrence vanishes is determined non-trivially by the associated decay of one of the intermediate DCs. Analyzing the reduced density of a single qubit, we also explain the observation that the dephasing rate is always slower than the unentanglement rate.

cond-mat.stat-mech↗

arXiv2015

A study of excess energy and decoherence factor of a qubit coupled to a one dimensional periodically driven spin chain

We take a central spin model (CSM), consisting of a one dimensional environmental Ising spin chain and a single qubit connected globally to all the spins of the environment, to study numerically the excess energy (EE) of the environment and the logarithm of decoherence factor namely, dynamical fidelity susceptibility per site (DFSS), associated with the qubit under a periodic driving of the transverse field term of environment across its critical point using the Floquet technique. The coupling to the qubit, prepared in a pure state, with the transverse field of the spin chain yields two sets of EE corresponding to the two species of Floquet operators. In the limit of weak coupling, we derive an approximated expression of DFSS after an infinite number of driving period which can successfully estimate the low and intermediate frequency behavior of numerically obtained DFSS. Our main focus is to analytically investigate the effect of system-environment coupling strength on the EEs and DFSS and relate the behavior of DFSS to EEs as a function of frequency by plausible analytical arguments. We explicitly show that the low-frequency beating like pattern of DFSS is an outcome of two frequencies, causing the oscillations in the two branches of EEs, that are dependent on the coupling strength. In the intermediate frequency regime, dip structure observed in DFSS can be justified by the resonance peaks of EEs at those coupling parameter dependent frequencies; high frequency saturation value of EEs and DFSS are also connected to each other by the coupling strength.

cond-mat.stat-mech↗