arXiv subjects

Tanay Nag

Publications and source records attributed to Tanay Nag.

At least 55 records · Page 3Linked to original sources

arXiv2023

Topological characterization of special edge modes from the winding of relative phase

The symmetry-constrained topological invariant fails to explain the emergence of the special edge modes when system does not preserve discrete symmetries. The inversion or chiral symmetry broken SSH model is an example of one such system where one-sided edge state with finite energy appears at one end of the open chain. To investigate whether this special edge mode is of topological origin or not, we introduce a concept of relative phase between the components of a two-component spinor and define a winding number by the change of this relative phase over the one-dimensional Brillouin zone. The relative phase winds non-trivially (trivially) in accord with the presence (absence) of the one-sided edge mode inferring the bulk boundary correspondence. We extend this analysis to a two dimensional case where we characterize the non-trivial phase, hosting gapped one-sided edge mode, by the winding in relative phase only along a certain axis in the Brillouin zone. We demonstrate all the above findings from a generic parametric representation while topology is essentially determined by whether the underlying lower-dimensional projection includes or excludes the origin. Our study thus reveals a new paradigm of symmetry broken topological phases for future studies.

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arXiv2023

Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model

The higher-order corner modes for quantum anomalous Hall insulators in $C_3$ symmetry broken honeycomb lattice have been engineered recently. Here we consider an extended Haldane model in presence of inversion symmetry breaking sub-lattice mass, time-reversal symmetry breaking Zeeman field and spin-orbit coupling interaction where we find that only the quantum spin Hall insulator can host the second-order dipolar phase while the remaining two first-order topological phases do not morph into the latter. Remarkably, four-fold degeneracy of zero-energy dipolar states can be reduced to two-fold under the application (withdrawn) of sub-lattice mass (Zeeman field) term when the spin-orbit coupling is already present. On the other hand, the sub-lattice mass and Zeeman field terms compete with each other to pin down the two mid-gap states at zero-energy in the absence or presence of spin-orbit coupling. Interestingly, the bulk-polarization can topologically characterize the dipolar phase irrespective of the energy of the mid-gap states as long as inversion symmetry is preserved. The effective gap criterion can qualitatively mimic the extent of SOT phase originated by the interplay between finite Zeeman exchange field, sub-lattice mass, and SOC interaction.

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arXiv2023

Finite temperature dynamical quantum phase transition in a non-Hermitian system

We investigate the interplay between the non-Hermiticity and finite temperature in the context of mixed state dynamical quantum phase transition (MSDQPT). We consider a $p$-wave superconductor model, encompassing complex hopping and non-Hermiticity that can lead to gapless phases in addition to gapped phases, to examine the MSDQPT and winding number via the intra-phase quench. We find that the MSDQPT is always present irrespective of the gap structure of the underlying phase, however, the profile of Fisher zeros changes between the above phases. Such occurrences of MSDQPT are in contrast to the zero-temperature case where DQPT does not take place for the gapped phase. Surprisingly, the half-integer jumps in winding number at zero-temperature are washed away for finite temperature in the gapless phase. We study the evolution of the minimum time required by the system to experience MSDQPT with the inverse temperature such that gapped and gapless phases can be differentiated. Our study indicates that the minimum time shows monotonic (non-monotonic) behavior for the gapped (gapless) phase.

cond-mat.stat-mech↗

arXiv2023

Effect of chirality imbalance on Hall transport of PrRhC$_2$

Much has been learned about the topological transport in real materials. We investigate the interplay between magnetism and topology in the magneto-transport of PrRhC$_2$. The four-fold degeneracy reduces to two-fold followed by non-degenerate Weyl nodes when the orientation of the magnetic quantization axis is changed from easy axis to body-diagonal through face-diagonal. This engenders chirality imbalance between positive and negative chirality Weyl nodes around the Fermi energy. We observe a significant enhancement in the chiral anomaly mediated response such as planar Hall conductivity and longitudinal magneto-conductivity, due to the emergence of chirality imbalance upon orienting the magnetic quantization axis to body-diagonal. The angular variations of the above quantities for different magnetic quantization axis clearly refer to the typical signature of planar Hall effect in Weyl semimetals. We further investigate the profiles of anomalous Hall conductivities as a function of Fermi energy to explore the effects of symmetries as well as chirality imbalance on Berry curvature.

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arXiv2023

Time evolution of Majorana corner modes in Floquet second-order topological superconductor

We propose a practically feasible time-periodic sinusoidal drive protocol in onsite mass term to generate the two-dimensional~(2D) Floquet second-order topological superconductor, hosting both the regular $0$- and anomalous $π$-Majorana corner modes~(MCMs) while starting from a static 2D topological insulator/$d$-wave superconductor heterostructure setup. We theoretically study the local density spectra and the time dynamics of MCMs in the presence of such drive. The dynamical MCMs are topologically characterized by employing the average quadrupolar motion. Furthermore, we employ the Floquet perturbation theory~(FPT) in the strong driving amplitude limit to provide analytical insight into the problem. We compare our exact (numerical), and the FPT results in terms of the eigenvalue spectra and the time dynamics of the MCMs. We emphasize that the agreement between the exact numerical and the FPT results are more prominent in the higher frequency regime for close to the $0$-quasi-energy mode.

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arXiv2023

Topological characterization and stability of Floquet Majorana modes in Rashba nanowire

We theoretically investigate a practically realizable Floquet topological superconductor model, based on a one-dimensional Rashba nanowire and proximity induced $s$-wave superconductivity in the presence of a Zeeman field. The driven system hosts regular $0$- and anomalous $π$-Majorana end modes~(MEMs). By tuning the chemical potential and the frequency of the drive, we illustrate the generation of multiple MEMs in our theoretical set up. We utilize the chiral symmetry operator to topologically characterize these MEMs via a dynamical winding number constructed out of the periodized evolution operator. Interestingly, the robustness of the $0$- and $π$-MEMs is established in the presence of on-site time-independent random disorder potential. We employ the twisted boundary condition to define the dynamical topological invariant for this translational-symmetry broken system. The interplay between the Floquet driving and the weak disorder can stabilize the MEMs giving rise to a quantized value of the dynamical winding number for a finite range of drive parameters. This observation might be experimentally helpful in scrutinizing the topological nature of the Floquet MEMs. We showcase another driving protocol namely, a periodic kick in the chemical potential to study the generation of Floquet MEMs in our setup. Our work paves a realistic way to engineer multiple MEMs in a driven system.

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arXiv2022

Anomaly in dynamical quantum phase transition in non-Hermitian system with extended gapless phases

The dynamical quantum phase transitions (DQPTs) and the associated winding numbers have been extensively studied in the context Hermitian system. We consider the non-Hermitian analogue of $p$-wave superconductor, supporting Hermitian gapless phase with complex hopping, in presence of on-site or superconducting loss term. This allows us to investigate the effect of non-Hermitian gapless phases on the DQPTs in addition to the Hermitian gapless phases. Our findings indicate that contour analysis of the underlying Hamiltonian, enclosing the origin and/or exceptional points, can predict the occurrences of DQPTs except the quench within the gapless phases. For the Hermitian case with initial and final Hamiltonians both being Hermitian, we find non-monotonic integer jump for the winding number as the hallmark signature of the gapless phase there. For the hybrid case with initial and final Hamiltonians being Hermitian and non-Hermitian respectively, winding number exhibits integer spike in addition to the non-monotonic integer jumps. For the non-Hermitian case with initial and final Hamiltonians both being non-Hermitian, the winding number show half-integer jumps for lossy superconcuctivity that does not have any Hermitian analogue. On the other hand, the integer jumps in winding number is observed for lossy chemical potential. We understand our findings by connecting them with the profile of Fisher zeros and number of exceptional points and/or origin.

cond-mat.stat-mech↗

arXiv2022

Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics

Being motivated by intriguing phenomena such as the breakdown of conventional bulk boundary correspondence and emergence of skin modes in the context of non-Hermitian (NH) topological insulators, we here propose a NH second-order topological superconductor (SOTSC) model that hosts Majorana zero modes (MZMs). Employing the non-Bloch form of NH Hamiltonian, we topologically characterize the above modes by biorthogonal nested polarization and resolve the apparent breakdown of the bulk boundary correspondence. Unlike the Hermitian SOTSC, we notice that the MZMs inhabit only one corner out of four in the two-dimensional NH SOTSC. We extend the static MZMs into the realm of Floquet drive. We find anomalous $π$-mode following low-frequency mass-kick in addition to the regular $0$-mode that is usually engineered in a high-frequency regime. We further characterize the regular $0$-mode with biorthogonal Floquet nested polarization. Our proposal is not limited to the $d$-wave superconductivity only and can be realized in the experiment with strongly correlated optical lattice platforms.

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arXiv2022

Understanding the three-dimensional quantum Hall effect in generic multi-Weyl semimetals

The quantum Hall effect in three-dimensional Weyl semimetal (WSM) receives significant attention for the emergence of the Fermi loop where the underlying two-dimensional Hall conductivity, namely, sheet Hall conductivity, shows quantized plateaus. Considering the tilted lattice models for multi Weyl semimetals (mWSMs), we systematically study the Landau levels (LLs) and magneto-Hall conductivity in the presence of parallel and perpendicular (with respect to the Weyl node's separation) magnetic field, i.e., $\mathbf{ B}\parallel z$ and $\mathbf{B}\parallel x$, to explore the impact of tilting and non-linearity in the dispersion. We make use of two (single) node low-energy models to qualitatively explain the emergence of mid-gap chiral (linear crossing of chiral) LLs on the lattice for $\mathbf{ B}\parallel z$ ($\mathbf{ B}\parallel x$). Remarkably, we find that the sheet Hall conductivity becomes quantized for $\mathbf{ B}\parallel z$ even when two Weyl nodes project onto a single Fermi point in two opposite surfaces, forming a Fermi loop with $k_z$ as the good quantum number. On the other hand, the Fermi loop, connecting two distinct Fermi points in two opposite surfaces, with $k_x$ being the good quantum number, causes the quantization in sheet Hall conductivity for $\mathbf{ B}\parallel x$. The quantization is almost lost (perfectly remained) in the type-II phase for $\mathbf{ B}\parallel x$ ($\mathbf{ B}\parallel z$). Interestingly, the jump profiles between the adjacent quantized plateaus change with the topological charge for both of the above cases. The momentum-integrated three-dimensional Hall conductivity is not quantized; however, it bears the signature of chiral LLs as resulting in the linear dependence on $μ$ for small $μ$. The linear zone (its slope) reduces (increases) as the tilt (topological charge) of the underlying WSM increases.

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arXiv2022

Correlated disorder induced anomalous transport in magnetically doped topological insulators

We examine the transport properties of magnetically doped topological insulator (TI) thin films subject to correlated non-magnetic disorder. For the disorder we choose a quasi-periodic potential with a random phase. We restrict the disorder to a central region, which is coupled to two leads in a clean quantum spin Hall insulator (QSHI) state and concentrate on different orientations of the quasi-periodicity in the two-dimensional central region. In the case of a diagonally oriented or purely longitudinal quasi-periodicity we find different topological Anderson insulator (TAI) phases, with a quantum anomalous Hall insulator (QAHI), a quantum spin Chern insulator (QSCI), or a QSHI phase being realized before the Anderson insulation takes over at large disorder strength. Quantized transport from extended bulk states is found for diagonal quasi-periodicity in addition to the above TAI phases that are also observed for the case of uncorrelated disorder. For a purely transverse orientation of the quasi-periodicity the emerging QSHI and QSCI phases persist to arbitrarily strong disorder potential. These topological phase transitions (except to the Anderson insulator phase), can be understood from a self consistent Born approximation.

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arXiv2022

Distinct signatures of particle-hole symmetry breaking in transport coefficients for generic multi-Weyl semimetals

We propose and study generic multi-Weyl semimetal (mWSM) lattice Hamiltonians that break particle-hole symmetry. These models fall into two categories: model I (model II) where the gap and tilt terms are coupled (decoupled) can host type-I and type-II Weyl nodes simultaneously (separately) in a hybrid phase (type-I and type-II phases, respectively). We concentrate on the question of how anisotropy and non-linearity in the dispersions, gaps and tilt terms influence diffusive second order transport quantities namely, the circular photogalvanic effect (CPGE) and the Berry curvature dipole (BCD) as well as first order Magnus Hall effect (MHE) in the ballistic limit. The signatures of topological charges are clearly imprinted in the quantized CPGE response for the hybrid mWSM phase in model I. Such a quantization is also found in the type-I WSM phase for model II, however, the frequency profiles of the CPGE in these two cases is distinctively different owing to their different band dispersion irrespective of the identical topological properties. The contributions from the vicinity of Weyl nodes and away from the WNs are clearly manifested in the BCD response, respectively, for model I model II. The Fermi surface properties for the activated momentum lead to a few hallmark features on the MHE for both the models. Furthermore, we identify distinguishing signatures of the above responses for type-I, type-II and hybrid phases to provide an experimentally viable probe to differentiate these WSMs phases.

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arXiv2022

Dynamical construction of Quadrupolar and Octupolar topological superconductors

We propose a three-step periodic drive protocol to engineer two-dimensional~(2D) Floquet quadrupole superconductors and three-dimensional~(3D) Floquet octupole superconductors hosting zero-dimensional Majorana corner modes~(MCMs), based on unconventional $d$-wave superconductivity. Remarkably, the driven system conceives four phases with only $0$ MCMs, no MCMs, only anomalous $π$ MCMs, and both regular $0$ and anomalous $π$ MCMs. To circumvent the subtle issue of characterizing $0$ and $π$ MCMs separately, we employ the periodized evolution operator to architect the dynamical invariants, namely quadrupole and octupole motion in 2D and 3D, respectively, that can distinguish different higher order topological phases unambiguously.Our study paves the way for the realization of dynamical quadrupolar and octupolar topological superconductors.

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arXiv2022

Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators

After extensive investigation on the Floquet second-order topological insulator (FSOTI) in two dimension (2D), here we propose two driving schemes to systematically engineer the hierarchy of Floquet first-order topological insulator, FSOTI, and Floquet third-order topological insulator in three dimension (3D). Our driving protocols allow these Floquet phases to showcase regular $0$, anomalous $π$, and hybrid $0$-$π$-modes in a unified phase diagram, obtained for both 2D and 3D systems, while staring from the lower order topological or non-topological phases. Both the step drive and the mass kick protocols exhibit the analogous structure of the evolution operator around the high symmetry points. These eventually enable us to understand the Floquet phase diagrams analytically and the Floquet higher order modes numerically based on finite size systems. The number of $0$ and $π$-modes can be tuned irrespective of the frequency in the step drive scheme while we observe frequency driven topological phase transitions for the mass kick protocol. We topologically characterize some of these higher order Floquet phases (harboring either $0$ or anomalous $π$ mode) by suitable topological invariant in 2D and 3D cases.

cond-mat.mes-hall↗

arXiv2021

Electronic structure and unconventional non-linear response in double Weyl semimetal SrSi$_2$

Considering a non-centrosymmetric, non-magnetic double Weyl semimetal (WSM) SrSi$_2$, we investigate the electron and hole pockets in bulk Fermi surface behavior that enables us to characterize the material as a type-I WSM. We study the structural handedness of the material and correlate it with the distinct surface Fermi surface at two opposite surfaces following an energy evolution. The Fermi arc singlet becomes doublet with the onset of spin orbit coupling that is in accordance with the topological charge of the Weyl Nodes (WNs). A finite energy separation between WNs of opposite chirality in SrSi$_2$ allows us to compute circular photogalvanic effect (CPGE). Followed by the three band formula, we show that CPGE is only quantized for Fermi level chosen in the vicinity of WN residing at higher value of energy. Surprisingly, for the other WN of opposite chirality in the lower value of energy, CPGE is not found to be quantized. Such a behavior of CPGE is in complete contrast to the time reversal breaking WSM where CPGE is quantized to two opposite plateau depending on the topological charge of the activated WN. We further analyze our finding by examining the momentum resolved CPGE. Finally we show that two band formula for CPGE is not able to capture the quantization that is apprehended by the three band formula.

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arXiv2021

Floquet engineering of low-energy dispersions and dynamical localization in a periodically kicked three-band system

Much having learned about Floquet dynamics of pseudospin-$1/2$ system namely, graphene, we here address the stroboscopic properties of a periodically kicked {three-band fermionic system such as $α$-T$_3$ lattice. This particular model provides an interpolation between graphene and dice lattice via the continuous tuning of the parameter $α$ from 0 to 1.} In the case of dice lattice ($α=1$), we reveal that one can, in principle, engineer various types of low energy dispersions around some specific points in the Brillouin zone by tuning the kicking parameter in the Hamiltonian along a particular direction. Our analytical analysis shows that one can experience different quasienergy dispersions for example, Dirac type, semi-Dirac type, gapless line, absolute flat quasienergy bands, depending on the specific values of the kicking parameter. Moreover, we numerically study the dynamics of a wave packet in dice lattice. The quasienergy dispersion allows us to understand the instantaneous structure of wave packet at stroboscopic times. We find a situation where absolute flat quasienergy bands lead to a complete dynamical localization of the wave packet. {Aditionally, we calculate the quasienergy spectrum numerically for $α$-T$_3$ lattice. A periodic kick in a perpendicular (planar) direction breaks (preserves) the particle-hole symmetry for $0<α<1$. Furthermore, it is also revealed that the dynamical localization of wave packet does not occur at any intermediate $α\ne 0,\,1$.}

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arXiv2021

Periodic and aperiodic dynamics of flat bands in diamond-octagon lattice

We drive periodically a two-dimensional diamond-octagon lattice model by switching between two Hamiltonian corresponding two different magnetic flux piercing through diamond plaquette to investigate the generation of topological flat bands. We show that in this way, the flatness and topological nature of all the bands of the model can be tuned and Floquet quasi-sates can be made topologically flat while its static counterpart does not support the existence of topology and flatness together. By redefining the flatness accordingly in the context of non-equilibrium dynamics and correctly justifying it using the Floquet joint density of states, one indeed obtains a better control of the desired result when the input parameter space composed of temporal window associated with the step Hamiltonian and flux becomes larger than the static parameter space consisting of magnetic flux only. Interestingly, we find the generation of flux current. We systematically analyse the work done and flux current in the asymptotic limit as a function of input parameters to show that topology and flatness both share a close connection to the flux current and work done, respectively. We finally extend our investigation to the aperiodic array of step Hamiltonian, where we find that the heating up problem can be significantly reduced if the initial state is substantially flat as initial the large degeneracy of states prevents the system from absorbing energy easily from the aperiodic driving. We additionally show that the heating can be reduced if the values of the magnetic flux in the step Hamiltonian are small, the duration of these flux are unequal and on the initial flatness of the band. We successfully explain our finding by plausible analytical arguments.

cond-mat.stat-mech↗

arXiv2021

Hierarchy of higher-order topological superconductors in three dimensions

After exploring much on two-dimensional higher-order topological superconductors (HOTSCs) hosting Majorana corner modes (MCMs) only, we propose a simple fermionic model based on a three-dimensional topological insulator proximized with $s$-wave superconductor to realize Majorana hinge modes (MHMs) followed by MCMs under the application of appropriate Wilson-Dirac perturbations. We interestingly find that the second-order topological superconductor, hosting MHMs, appears above a threshold value of the first type perturbation while the third-order topological superconducting phase, supporting MCMs, immediately arises incorporating infinitesimal perturbation of the second kind. Thus, a hierarchy of HOTSC phases can be realized in a single three-dimensional model. Additionally, the application of bulk magnetic field is found to be instrumental in manipulating the number of MHMs, leaving the number for MCMs unaltered. We analytically understand these above-mentioned numerical findings by resorting to the low energy model. We further characterize these topological phases with a distinct structure of the Wannier spectra. From the practical point of view, we manifest quantized transport signatures of these higher-order modes. Finally, we construct Floquet engineering to generate the hierarchy of HOTSC phases by kicking the same perturbations as considered in their static counterpart.

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arXiv2021

Topological Magnus responses in two and three dimensional systems

Recently, time-reversal symmetric but inversion broken systems with non-trivial Berry curvature in the presence of a built-in electric field have been proposed to exhibit a new type of linear Hall effect in ballistic regime, namely, the Magnus Hall effect. The transverse current here is caused by the Magnus velocity that is proportional to the built-in electric field allowing us to examine the Magnus Hall conductivity and Magnus Nernst conductivity with chemical potential. Starting with two-dimensional (2D) topological systems, we find that warping induced asymmetry in both the Fermi surface and Berry curvature can in general enhance the Magnus Hall response for monolayer graphene and surface states of topological insulator. Interestingly, strain can change the Fermi surface character substantially that further results in distinct behavior of Magnus transport coefficients as we observe in bilayer graphene. Going beyond 2D systems, we also investigate the Magnus Hall and Nernst responses in three-dimensional multi-Weyl semimetals (mWSMs). Remarkably, Magnus responses can only survive for the tilted WSMs, and therefore can be measured as a tool to distinguish between the untilted and tilted WSMs in experiments. In addition, we find that the Magnus Hall responses get suppressed with increasing the non-linearity associated with the band touching around multi-Weyl node.

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