Department of Physics
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Item Transport properties in a two-dimensional Su–Schrieffer–Heeger model in quantum Hall regime(IOP, 2025-09) Bandyopadhyay, Jayendra N.; Sarkar, NiladriWe investigate the transport properties of a two-dimensional Su–Schrieffer–Heeger (2D SSH) model in the quantum Hall regime using non-equilibrium Green’s function formalism. The device Hamiltonian, where the 2D SSH model serves as the channel, is constructed using a nearest-neighbor tight-binding model. The effect of an external perpendicular magnetic field is incorporated into the contacts via Peierls substitution. We observe a transition from a gapped phase to a flat band regime at zero energy by varying the magnetic field. This transition is characterized by the emergence of highly localized states in the bulk or edges, which we observe by calculating local density-of-states. We analyze transport in the system along two directions (x and y) via transmission measurements, indicating a magnetic field-induced transition from insulating to metallic phase. The study of the energy spectrum of the system shows the formation of Landau levels (LLs). Moreover, the quantum number of the non-degenerate and degenerate LLs (transmission modes) can be any integer or an odd integer, depending on diagonal, inter-cell, and intra-cell hopping strengths. From the analysis of the transport properties along the y-direction, we find that edge modes play a crucial role in facilitating ballistic transport.Item Superconducting p-wave pairing effects on one-dimensional non-Hermitian quasicrystals with power law hopping(APS, 2025-05) Bandyopadhyay, Jayendra N.We study the effects of superconducting 𝑝 -wave pairing on the non-Hermitian Aubry-André-Harper model with power-law hopping. For the case of short-range hopping, weak pairing leads to oscillating quasi-Majorana zero modes, turning to edge-localized Majorana zero modes as pairing strength increases. For the case of long-range hopping, we observe the emergence of massive Dirac modes having oscillatory behavior, similar to Majorana modes with weak pairing. The massive Dirac modes localize at the edges as the pairing strength grows. The superconducting pairing spoils the plateaus observed in the fractal dimension of all the energy eigenstates of the Aubry-André-Harper model with power-law hopping. The number of plateaus decreases with the increasing pairing strength for the weak non-Hermiticity in the system. The phase diagram of the system reveals that real and complex energy spectra correlate differently with the localization properties of the eigenstates, depending on the strength of pairing and hopping range.Item Topological in-gap states in a non-Hermitian quasicrystal with p-wave pairing(APS, 2025-09) Bandyopadhyay, Jayendra N.The interplay of onsite quasiperiodic potential, superconductivity, and non-Hermiticity is explored in a non-Hermitian unconventional superconducting quasicrystal described by the Aubry-André-Harper model with 𝑝 -wave pairing. Importantly, here the asymmetry is introduced in the hopping to break the reciprocity, leading to the explicit breaking of particle-hole symmetry. In the zero-pairing limit, the model hosts an exact triple-phase transition where the topological, metal-insulator, and real-to-complex spectral transitions coincide. With weak (perturbative) pairing, this coincidence survives only approximately and is progressively destroyed as the pairing strength increases. Additionally, instead of the Majorana zero modes (MZMs) found in the symmetric hopping case, we observe the emergence of in-gap states under open boundary conditions. These in-gap states are robust against disorder, underscoring their topological protection. Therefore, unlike the MZMs, which are very challenging to experimentally realize, these in-gap states can be used in topological quantum computational protocols.Item Entanglement signatures of gapless topological phases in a -wave superconductor(2025-09) Bandyopadhyay, Jayendra N.We explore the gapless topological phases of a -wave superconductor, probing its rich topologically ordered phases and underlying quantum phenomena. The topological order of the system is characterized by studying its entanglement properties. This study confirms the bulk-boundary correspondence in the entanglement spectrum, even without a full bulk gap. For contractible bipartitions, the entanglement entropy varies non-monotonically with the chemical potential, displaying pronounced peaks at points where the bulk gap closes and reopens, signaling topological quantum phase transitions. This behavior remains robust in the thermodynamic limit. The entanglement entropy grows with system size for non-contractible bipartitions, indicating long-range entanglement in the gapless phase. These findings reveal the subtle interplay between symmetry, entanglement, and topology in gapless systems, and emphasize the role of entanglement-based diagnostics in identifying unconventional topological phases beyond the gapped paradigm.Item Harmonic emission as a probe to coherent transitions in the topological superconductors(2025-07) Bandyopadhyay, Jayendra N.; Holkundkar, Amol R.We investigate the dynamical behavior of a topological superconducting system, demonstrating that its static configuration undergoes a transition driven by an intrinsic supercurrent. By analyzing the band population, we confirm the quasiparticle nature of the system both in the presence and absence of an external laser field. Under laser driving, we observe an enhancement in static emission forming a plateau-like structure, accompanied by multiple coherent transitions in the population. These transitions exhibit Rabi-like oscillations, attributed to the presence of Majorana bound states (MBS), further reinforcing the quasiparticle character of the model. Our results highlight the efficacy of laser driving as a probe of the system's topological and dynamical stability.Item Engineering harmonic emission through spatial modulation in a Kitaev chain(APS, 2025-09) Bandyopadhyay, Jayendra N.; Holkundkar, Amol R.We investigate high-harmonic generation (HHG) in a dimerized Kitaev chain. The dimerization in the model is introduced through a site-dependent modulating potential, determined by a parameter 𝜆∈[−1:1] . This parameter also determines the strength of the hopping amplitudes and tunes the system's topology. Depending upon the parameter 𝜆 , the HHG emission spectrum can be classified into three segments. The first segment exhibits two plateau structures, with the dominant one resulting from transitions to the chiral partner state, consistent with quasiparticle behavior in the topological superconducting phase. The second segment displays multiple plateaus, where intermediate states enable various transition pathways to higher conduction bands. Finally, the third segment presents broader plateaus, indicative of active interband transitions. In the 𝜆≤0 regime, we observe the midgap states (MGSs) hybridize with the bulk, suppressing the earlier observed harmonic enhancements. This highlights the key role of the intermediate states, particularly when MGSs are isolated. These results demonstrate that harmonic emission profiles can be selectively controlled through the modulating parameter 𝜆 , offering new prospects for tailoring HHG in topological systems.Item Investigating topological in-gap states in non-Hermitian quasicrystal with unconventional p-wave pairing(2025-01) Bandyopadhyay, Jayendra N.The interplay of onsite quasiperiodic potential, superconductivity, and non-Hermiticity is explored in a non-Hermitian unconventional superconducting quasicrystal described by Aubry-André-Harper (NHAAH) model with p-wave pairing. In previous studies, the non-Hermiticity was only considered at the onsite quasiperiodic potential of the NHAAH model, and Majorana zero modes (MZMs) were observed under open boundary conditions (OBC) in this model. In this work, we study an NHAAH model with p-wave pairing, where non-Hermiticity is considered onsite by introducing complex quasiperiodic potential and asymmetry at the hopping part. Our analysis uncovers triple-phase transitions, where topological, metal-insulator, and unconventional real-to-complex transitions coincide at weak p-wave pairing strength. Additionally, instead of the MZMs observed in the symmetric hopping case, we observe the emergence of in-gap states under OBC in this model. These in-gap states are robust against disorder, underscoring their topological protection. Therefore, unlike the MZMs, which are very challenging to experimentally realize, these in-gap states can be used in topological quantum computational protocols.Item Probing topological phase transitions in the Aubry-Andre-Harper model via high-harmonic generation(APS, 2024-09) Holkundkar, Amol R.; Bandyopadhyay, Jayendra N.We study the high-harmonic generation (HHG) in the Aubry-Andre-Harper (AAH) model. The modulating phase of the AAH model is used as a control parameter while preserving the chiral symmetry hosting the zero-energy edge states. The harmonic yield in a particular energy range exhibits a strong dependence on the control parameter with a clear separation of the region of topologically trivial and nontrivial phases of the system. The threshold for the harmonic yield is found to serve as an all-optical tool for detecting topological phases. We extended our study with broken chiral symmetry by including the onsite potential. The introduction of the onsite potential lifts the degeneracy in the edge states, which affects the harmonic enhancement. Furthermore, it is also observed that the system's onsite strength can control the HHG yieldItem Role of interband and intraband current in laser interaction with bichromatic quasiperiodic crystals(APS, 2024-04) Bandyopadhyay, Jayendra N.; Holkundkar, Amol R.We study the role of the inter- and intraband current in the laser interaction with the bichromatic quasiperiodic crystals. The interaction dynamics are simulated by solving the time-dependent Schrödinger equation in the 𝑘 space, and time evolution of the inter- and intraband current is obtained in a gauge-invariant form. We observed that for certain bichromatic potential ratios, the energy band structure of the “valence band” and the “conduction band” facilitates the interband transitions only at the center or at the edge of the Brillouin zone, which leads to a very interesting population transfer mechanism between the bands. The temporal profile of the inter- and intraband current gives a detailed account of the interaction. The higher-order harmonic generation is also studied for these bichromatic optical lattices, and the resultant harmonic yield is commented upon.Item Adiabatic modulation of driving protocols in periodically driven quantum systems(ARXIV, 2024-04) Sarkar, Tapomoy Guha; Bandyopadhyay, Jayendra N.We consider a periodically driven system where the high-frequency driving protocol consists of a sequence of potentials switched on and off at different instants within a period. We explore the possibility of introducing an adiabatic modulation of the driving protocol by considering a slow evolution of the instants when the sequence of potentials is switched on/off. We examine how this influences the long-term dynamics of periodically driven quantum systems. By assuming that the slow and fast timescales in the problem can be decoupled, we derive the stroboscopic (effective) Hamiltonian for a four-step driving sequence up to the first order in perturbation theory. We then apply this approach to a rigid rotor, where the adiabatic modulation of the driving protocol is chosen to produce an evolving emergent magnetic field that interacts with the rotor's spin. We study the emergence of diabolical points and diabolical loci in the parameter space of the effective Hamiltonian. Further, we study the topological properties of the maps of the adiabatic paths in the parameter space to the eigenspace of the effective Hamiltonian. In effect, we obtain a technique to tune the topological properties of the eigenstates by selecting various adiabatic evolution of the driving protocol characterized by different paths in the parameter space. This technique can be applied to any periodic driving protocol to achieve desirable topological effects.