arXiv subjects

Sayan Jana

Publications and source records attributed to Sayan Jana.

13 recordsLinked to original sources

arXiv2025

Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices

The time evolution of initially localized wavepackets in the discrete Hatano-Nelson lattice displays a rich dynamical structure shaped by the interplay between dispersion and nonreciprocity. Our analysis reveals a characteristic evolution of the wave-packet center of mass, which undergoes an initial acceleration, subsequently slows down, and ultimately enters a regime of uniform motion, accompanied throughout by exponential amplification of the wave-packet amplitude. To capture this behavior, we develop a continuum approximation that incorporates higher-order dispersive and nonreciprocal effects and provides accurate analytical predictions across all relevant time scales. Building on this framework, we then demonstrate the existence of a non-Hermiticity-induced jump - an abrupt spatial shift of the wave-packet center even in the absence of disorder - and derive its underlying analytical foundation. The analytical predictions are in excellent agreement with direct numerical simulations of the Hatano-Nelson chain. Our results elucidate the interplay between dispersion and nonreciprocity in generating unconventional transport phenomena, and pave the way for controlling wave dynamics in nonreciprocal and non-Hermitian metamaterials.

cond-mat.mes-hall↗

arXiv2025

Fast wave transport in two-dimensional $\mathcal{PT}$-symmetric lattices

We present a theoretical investigation of wave dynamics in two-dimensional non-Hermitian $\mathcal{PT}$-symmetric lattices, where onsite, as well as inter-site control couplings are employed. Our analysis shows that these couplings can be tuned to achieve a direction-sensitive group velocity enhancement beyond what is possible in the uncontrolled (Hermitian) counterpart, while ensuring that the wave packet evolution remains bounded and dynamically stable. We derive a dedicated relation between the control parameters, providing a systematic condition under which stability is guaranteed. We then study the topological properties of the non-Hermitian system at hand, and use an experimental-ready topoelecric metamaterial platform to demonstrate the non-Hermitian couplings realization, and the resulting wave dynamics. This framework paves the way to designing stable and fast wave transport in planar non-Hermitian media.

cond-mat.mes-hall↗

arXiv2025

Realizing non-Hermitian tunneling phenomena using non-reciprocal active acoustic metamaterials

Non-reciprocal systems have been shown to exhibit various interesting wave phenomena, such as the non-Hermitian skin effect, which causes accumulation of modes at boundaries. Recent research on discrete systems showed that this effect can pose a barrier for waves hitting an interface between reciprocal and non-reciprocal systems. Under certain conditions, however, waves can tunnel through this barrier, similar to the tunneling of particles in quantum mechanics. This work proposes and investigates an active acoustic metamaterial design to realize this tunneling phenomenon in the acoustical wave domain. The metamaterial consists of an acoustic waveguide with microphones and loudspeakers embedded in its wall. Starting from a purely discrete non-Hermitian lattice model of the system, a hybrid continuous-discrete acoustic model is derived, resulting in distributed feedback control laws to realize the desired behavior for acoustic waves. The proposed control laws are validated using frequency and time domain finite element method simulations, which include lumped electro-acoustic loudspeaker models. Additionally, an experimental demonstration is performed using a waveguide with embedded active unit cells and a digital implementation of the control laws. In both the simulations and experiments the tunneling phenomenon is successfully observed.

physics.app-ph↗

arXiv2025

Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems

We present a mechanism to generate unidirectional pulse-shaped propagating waves, tamed to exponential growth and dispersion, in active systems with nonreciprocal and nonlinear couplings. In particular, when all bulk modes are exponentially localized at one side of the lattice (skin effect), it is expected that wave dynamics is governed by amplification or decay until reaching the boundaries, even in the presence of dissipation. Our analytical results, and experimental demonstrations in an active electrical transmission line metamaterial, reveal that nonlinearity is a crucial tuning parameter in mediating a delicate interplay between nonreciprocity, dispersion, and dissipation. Consequently, undistorted unidirectional solitonic pulses are supported both for low and high nonreciprocity and pulse amplitude strength. The proposed mechanism facilitates robust pulse propagation in signal processing and energy transmission applications.

cond-mat.mes-hall↗

arXiv2024

Controlled fast wavepackets in non-Hermitian lattices

We report the propagation of fast wavepackets in classical non-Hermitian lattices, where the group velocity is controlled by the non-Hermiticity parameters, and can be made higher than in the Hermitian counterpart. Specifically, we obtain a square root dependence of the group velocity on the gain/loss parameter, similarly to the dependence of quantum wavepackets in stretched graphene-like lattices subjected to gain and loss. We derive a targeted mapping from the quantum to the classical Hamiltonian to realize this phenomenon in a dynamically stable form. As a result, fast wavepackets of any frequency supported by the lattice are propagating in time domain with a non-growing amplitude. We demonstrate the system experimentally in a topoelectrical metamaterial, where the non-Hermiticity is generated by embedded operational amplifiers in a feedback setup. Our design paves the way to realize increased group velocities, and other wave phenomena inspired by quantum systems in a form that preserves the original system properties, while supporting an inherently stable dynamics.

cond-mat.mes-hall↗

arXiv2023

Tunneling-like wave transmission in non-Hermitian lattices with mirrored nonreciprocity

We report a peculiar tunneling phenomenon that occurs in lattices with nonreciprocal couplings. The nonreciprocity holds for an inner portion of the lattice, constituting a non-Hermitian interface between outer Hermitian sections. The couplings are mirrored about the interface center. As a standalone system that was widely studied in recent years, each section of the interface supports the non-Hermitian skin effect, in which modes are accumulated at one boundary. Here, we investigate what happens to a wave that propagates along the lattice and hits the interface. The skin mode accumulation, which effectively constitutes a barrier, forbids wave penetration into the interface, but surprisingly, under certain conditions the wave is transmitted to the other side, keeping the interface dark, as if the wave invisibly tunneled through it. Remarkably, the tunneling is independent of the interface length, and a perfect transmission can be achieved independently of frequency and nonreciprocity strength. We derive the phenomenon both for quantum and classical systems, and realize it experimentally in an active topoelectric metamaterial. Our study fosters the research of wave tunneling through other types of non-Hermitian interfaces, which may also include nonlinearities, time-dependence and more.

cond-mat.mes-hall↗

arXiv2023

Gravitational lensing and tunneling of mechanical waves in synthetic curved spacetime

Black holes are considered among the most fascinating objects that exist in our universe, since in the classical formalism nothing, even no light, can escape from their vicinity due to gravity. The gravitational potential causes the light to bend towards the hole, which is known by gravitational lensing. Here we present a synthetic realization of this phenomenon in a lab-scale two-dimensional network of mechanical circuits, based on analogous condensed matter formalism of Weyl semimetals with inhomogeneous nodal tilt profiles. Some of the underlying network couplings turn out as unstable and non-reciprocal, and are implemented by embedded active feedback interactions in an overall stabilized structure. We demonstrate the lensing by propagating mechanical wavepackets through the network with a programmed funnel-like potential, achieving wave bending towards the circle center. We then demonstrate the versatility of our platform by reprogramming it to mimic quantum tunneling of particles through the event horizon, known by Hawking radiation, achieving an exceptional correspondence to the original mass loss rate within the hole. The network couplings and the potential can be further reprogrammed to realize other curvatures and associated relativistic phenomena.

quant-ph↗

arXiv2023

Emerging exceptional point with breakdown of skin effect in non-Hermitian systems

We study the interplay of two distinct non-Hermitian parameters: directional coupling and onsite gain-loss, together with topology, in coupled one-dimensional (1D) non-Hermitian Su-Schrieffer-Heeger (SSH) chains. The SSH model represents one of the simplest two-band models that features boundary localized topological modes. Our study shows how the merging of two topological modes can lead to a striking spectral feature of non-Hermitian systems, namely exceptional point (EP). We reveal the existence EP as a singularity in the parameter space of non-Hermitian couplings carrying a half-integer topological charge. We also demonstrate two different localization behaviors observed in the bulk and hybridized topological modes. While the bulk states and individual topological modes remain localized at the boundaries due to skin effect, the competition between the constituent non-Hermitian parameters can overcome the strength of skin effect and lead to the complete \textit{delocalization} of these hybridized modes. We obtain explicit analytic solutions for the eigenfunction and the eigenenergy of the hybridized modes, which exactly match the numerical results and successfully reveal the underlying cause of delocalization and the emergence of EP.

cond-mat.mes-hall↗

arXiv2022

Non-local spin entanglement in a fermionic chain

An effective two-spin density matrix (TSDM) for a pair of spin-$1/2$ degree of freedom, residing at a distance of $R$ in a spinful Fermi sea, can be obtained from the two-electron density matrix following the framework prescribed in Phys. Rev. A 69, 054305 (2004). We note that the single spin density matrix (SSDM) obtained from this TSDM for generic spin-degenerate systems of free fermions is always pinned to the maximally mixed state $i.e.$ $(1/2) \ \mathbb{I}$, independent of the distance $R$ while the TSDM confirms to the form for the set of maximally entangled mixed state (the so called "X-state") at finite $R$. The X-state reduces to a pure state (a singlet) in the $R\rightarrow 0$ limit while it saturates to an X-state with largest allowed value of von-Neumann entropy of $2 \ln2$ as $R \rightarrow \infty$ independent of the value of chemical potential. However, once an external magnetic field is applied to lift the spin-degeneracy, we find that the von-Neumann entropy of SSDM becomes a function of the distance $R$ between the two spins. We also show that the von-Neumann entropy of TSDM in the $R\rightarrow \infty$ limit becomes a function of the chemical potential and it saturate to $2 \ln2$ only when the band in completely filled unlike the spin-degenerate case. Finally we extend our study to include spin-orbit coupling and show that it does effect these asymptotic results. Our findings are in sharp contrast with previous works which were based on continuum models owing to physics which stem from the lattice model.

quant-ph↗

arXiv2021

Emergence of exceptional points and their spectroscopic signature in Dirac semimetal-dirty Superconductor heterojunction

We theoretically investigate the emergence of non-hermitian physics at the heterojunction of a type-II Dirac semi-metal (DSM) and a dirty superconductor (DSC). The non-hermiticity is introduced in the DSM through the self-energy term incorporated via the dirtiness of the superconducting material. This causes the spectra of the effective Hamiltonian to become complex, which gives rise to the appearance of the exceptional points (EPs). This complex self energy, apart from having a frequency dependence, also acquires spatial dependence as well, which is unique and can provide interesting effects related to non-hermitian physics in spectral function analysis. At an appropriate distance from the normal metal-superconductor junction of the DSC, non-hermitian degeneracies appear and a single Dirac point splits into two EPs. In the spectral function analysis, apart from the EPs, a Fermi-arc like structure also emerges, which connects the two degeneracies (EPs). The results discussed here are distinctive and possibly can be realized in spectroscopy measurements.

cond-mat.mes-hall↗

arXiv2020

Tailoring Metal Insulator Transitions $\&$ Band Topology via Off-resonant Periodic Drive in an Interacting Triangular Lattice

A triangular lattice with onsite Coulomb interaction $U$ present only on one sub-lattice, is periodically driven by electromagnetic field with a frequency $Ω\gg (t,~U)$ at half filling. In this high frequency limit, the electromagnetic vector potential, with an amplitude $A$, modifies the bare hopping and generates new next nearest neighbour hopping parameters. For $U=0$, the driving acts like an emergent intrinsic spin-orbit coupling term and stabilises three dispersive bands with the lower and upper bands having non zero Chern numbers. Within a slave rotor mean field theory, we show that while $U$ freezes out charge fluctuations on the interacting sub-lattice, it does not open up a charge gap without the external drive. In presence of the drive, and small $U$, the system exhibits repeated metal insulator transitions as a function of the amplitude $A$. For large $U$, we establish that the freezing of charge fluctuations on the interacting sub-lattice stabilizes an emergent, low energy \textit{half filled non-interacting Kane-Mele model}, whose band gaps can be tuned by varying $A$. In this limit, we show that the external drive provides an handle to engineer periodic band inversions at specific values of $A$ accompanied by topological phase transitions that are characterised by swapping of band Chern numbers.

cond-mat.str-el↗

arXiv2019

Jackiw-Rebbi zero modes in non-uniform topological insulator nanowire

We theoretically investigate the emergence of Jackiw-Rebbi zero modes and their conductance signature in non-uniform topological insulator nano-wires. We modelled the non-uniform nano-wires as junction between two cylindrical nano-wires with different radius. In the limit of wire length being much larger than its radius, the surface state of the nanowire splits into one dimensional Dirac modes propagating along the axis of the cylinder owing to radial confinement. The sign of the mass gap in each of these Dirac mode is decided by angular momentum quantum number corresponding to the rotational motion of the electron about the axis of the cylindrical. Application of an external magnetic flux through the cylindrical nanowires enables us to tune the mass gap from positive to negative value across the junction. Due to this flux tunable band inversion, controlled by the external magnetic filed, Jackiw-Rebbi zero modes can be made to appear or disappear at the junction. We compute differential conductance of our topological insulator nanowire junction and show that a quantized conductance peak appears at zero-energy (zero-bias) in the presence of the Jackiw-Rebbi mode.

cond-mat.mes-hall↗

arXiv2019

Impact of strong correlations on a band topological insulator on the Lieb lattice

The Lieb lattice possesses three bands and with intrinsic spin orbit coupling $λ$, supports topologically non-trivial band insulating phases. At half filling the lower band is fully filled, while the upper band is empty. The chemical potential lies in the flat band (FB) located at the middle of the spectrum, thereby stabilizing a flat band insulator. At this filling, we introduce on-site Hubbard interaction $U$ on all sites. Within a slave rotor mean field theory we show that, in spite of the singular effect of interaction on the FB, the three bands remain stable up to a fairly large critical correlation strength ($U_{crit}$), creating a correlated flat band insulator. Beyond $U_{crit}$, there is a sudden transition to a Mott insulating state, where the FB is destroyed due to complete transfer of spectral weight from the FB to the upper and lower bands. We show that all the correlation driven insulating phases host edge modes with linearly dispersing bands along with a FB passing through the Dirac point, exhibiting that the topological nature of the bulk band structure remains intact in presence of strong correlation. Furthermore, in the limiting case of $U$ introduced only on one sublattice where $λ=0$, we show that the Lieb lattice can support mixed edge modes containing contributions from both spinons and electrons, in contrast to purely spinon edge modes arising in the topological Mott insulator.

cond-mat.str-el↗