arXiv subjects

Arunava Chakrabarti

Publications and source records attributed to Arunava Chakrabarti.

At least 19 recordsLinked to original sources

arXiv2024

Engineering complete delocalization of single particle states in a class of one dimensional aperiodic lattices: a quantum dynamical study

We study quantum dynamics of a wave packet on a class of one dimensional decorated aperiodic lattices, described within a tight binding formalism. We look for the possibility of finding extended single particle states even in the absence of any translational periodicity. The chosen lattices are stubbed with one or more atoms, tunnel coupled to the backbone, thereby introducing a minimal quasi-one dimensionality. It is seen that, for a group of such lattices a certain correlation between the numerical values of the hopping amplitudes leads to a complete delocalization of single particle states. In some other cases, a special value of a magnetic flux trapped in the loops present in the geometries delocalize the states, leading to a flux driven insulator to metal transition. The mean square displacement, temporal autocorrelation function, the time dependence of the inverse participation ratio, or the information entropy - the so-called hallmarks of studying localization based on dynamics - all of them indicate such a complete turnover in the nature of the single particle states and the character of the energy spectrum under suitable conditions. The results shown in this work using quasiperiodic lattices of the Fibonacci family are much more general and hold good even for a randomly disordered arrangement of the building blocks of the systems considered, and indicate a subtle universality class under which these lattices can be grouped.

cond-mat.mes-hall↗

arXiv2024

Topological properties of a class of generalized Su-Schrieffer-Heeger networks: chains and meshes

We analyze the topological properties of a family of generalized Su-Schrieffer-Heeger (SSH) chains and mesh geometries. In both the geometries the usual staggering in the distribution of the two overlap integrals is delayed (in space) by the inclusion of a third (additional) hopping term. A tight-binding Hamiltonian is used to unravel the topological phases, characterized by a topological invariant. While in the linear chains, the topological invariant (the Zak phase) always appears to be quantized, in the quasi-one dimensional strip geometries and the generalized SSH mesh patterns the quantization of the Zak phase is sensitive to the strength of the additional interaction (the `extra' hopping integral). We study its influence thoroughly and explore the edge states and their robustness against disorder in the cross-linked generalized SSH mesh geometries. The systems considered here can be taken to model (though crudely) two-dimensional polymers where the cross-linking brings in non-trivial modification of the energy bands and transport properties. In addition to the topological features studied, we provide a prescription to unravel any flat, non-dispersive energy bands in the mesh geometries, along with the structure and distribution of the compact localized eigenstates. Our results are analytically exact.

cond-mat.mes-hall↗

arXiv2023

Complete escape from localization on a hierarchical lattice: A Koch fractal with all states extended

An infinitely large Koch fractal is shown to be capable of sustaining only extended, Bloch-like eigenstates, if certain parameters of the Hamiltonian describing the lattice are numerically correlated in a special way, and a magnetic flux of a special strength is trapped in every loop of the geometry. We describe the system within a tight binding formalism and prescribe the desired correlation between the numerical values of the nearest neighbor overlap integrals, along with a special value of the magnetic flux trapped in the triangular loops decorating the fractal. With such conditions, the lattice, despite the absence of translational order of any kind whatsoever, yields an absolutely continuous eigenvalue spectrum, and becomes completely transparent to an incoming electron with any energy within the allowed band. The results are analytically exact. An in-depth numerical study of the inverse participation ratio and the two-terminal transmission coefficient corroborates our findings. Our conclusions remain valid for a large set of lattice models, built with the same structural units, but beyond the specific geometry of a Koch fractal, unraveling a subtle universality in a variety of such low dimensional systems.

cond-mat.mes-hall↗

arXiv2023

Designer quantum states on a fractal substrate: compact localization, flat bands and the edge modes

Compact localized single particle eigenstates on a deterministic fractal substrate, modelled by a triangular Sierpinski gasket of arbitrarily large size, are unravelled and examined analytically. We prescribe an exact real space renormalization group (RSRG) decimation scheme within a tight binding formalism to discern these states, and argue that the number of such states can be infinite if the fractal substrate is enlarged to its thermodynamic limit. Interestingly, these localized states turn out to populate the non-dispersive, flat bands in a periodic array of Sierpinski gasket motifs, however large they may be. Our results match and corroborate the recently observed compact localized, flat band states engineered on two dimensional photonic waveguide networks with a fractal geometry, and provide a whole subset of them, which, in principle, should be observable in fractal photonic lattice experiments.

cond-mat.mes-hall↗

arXiv2022

Flat bands, edge states and possible topological phases in a branching fractal

We address the problem of analytically extracting a countable infinity of flat, non-dispersive bands in a periodic array of cells that comprise branching Vicsek geometries of higher and higher generations. Through a geometric construction, followed by an exact real space renormalization scheme we unravel clusters of compact localized states, corresponding to densely packed groups of flat bands, sometimes in close proximity with the dispersive ones, as the unit cells accommodate Vicsek fractal motifs of higher and higher generations. In such periodic arrays, energy bands close and open at energies that can be calculated exactly, and the precise correlation between the overlap integrals describing the tight binding systems can be worked out. The possibility of a topological phase transition is pointed out through an explicit construction of the edge states, weakly protected against disorder, though it is argued that the typical bulk-boundary correspondence is not holding good in such cases.

cond-mat.mes-hall↗

arXiv2021

Tailoring flat bands and topological phases in a multi-strand Creutz network

We prove that, a suitable correlation between the system parameters can trigger topological phase transition and flat bands in a multi strand Creutz ladder network, when a staggered second neighbor interaction is included along the x axis. An appropriate change of basis maps such a finite N strand mesh into N or N 1 decoupled Su Schrieffer Heeger chains, depending onNeven or odd. A simple intuitive method, using a real space decimation scheme turns out to be very powerful in analytically extracting the flat bands, explaining their degeneracy or a lifting of the same. Our results are analytically exact, and may inspire experiments in photonics and ultracold atomic systems.

cond-mat.quant-gas↗

arXiv2021

Topological properties of a class of Su-Schrieffer-Heeger variants

We investigate the edge states and the topological phase transitions in a class of tight binding lattices in one dimension where a Su-Schrieffer-Heeger (SSH) model exists in disguise. The unit cells of such lattices may have an arbitrarily intricate staggering pattern woven in the hopping integrals, that apparently masks the basic SSH structure. We unmask the SSH character in such lattices using a simple real space decimation of a subset of the degrees of freedom. The decimation not only allows us to recognize the familiar SSH geometry, but at the same time enables us to determine, in an analytically exact way, the precise energy eigenvalues at which the gaps open up (or close) at the Brillouin zone boundaries. It is argued that, a topological phase transition and the existence of the protected edge states can be observed in such lattices only under definite numerical correlations between the hopping integrals decorating the unit cell. Such a correlation, achievable in a variety of ways, brings different such models under a kind of a universality class.

cond-mat.dis-nn↗

arXiv2021

Engineering insulator-metal transition in a class of decorated aperiodic lattices: a quantum dynamical study

We investigate the quantum dynamics of wave packets in a class of decorated lattices, both quasiperiodic and random, where a nominal quasi-one dimensionality is introduced at local levels, bringing in a deterministic or even random variations in the distribution of the coordination number throughout the system. We show that certain correlations in the numerical values of the system Hamiltonian can cause a drastic change in the dynamical evolution of the wave packet, revealing a complete delocalization, independent of the energy of the travelling particle, even in the absence of any translational invariance. We use an exact decimation of a selected subset of the degrees of freedom, and an analysis of the commutation of the $2 \times 2$ transfer matrices on a renormalized version of the parent systems within a tight binding framework. An in-depth analysis of the mean square displacement, temporal autocorrelation function and the inverse participation ratio establishes the gross change in the behaviour of the wave packet dynamics. The consequence is the occurrence of a parameter-driven insulator-metal transition over the full (or a major) range of the energy spectrum in each case. In certain cases, inclusion of an external magnetic flux enables us to control the transition. The observation is general, and, to our mind, can inspire experiments involving photonics or matter wave localization.

cond-mat.dis-nn↗

arXiv2020

Ring-localized states, radial aperiodicity and quantum butterflies on a Cayley tree

We present an analytical method, based on a real space decimation scheme, to extract the exact eigenvalues of a macroscopically large set of pinned localized excitations in a Cayley tree fractal network. Within a tight binding scheme we exploit the above method to scrutinize the effect of a deterministic deformation of the network, first through a hierarchical distribution in the values of the nearest neighbor hopping integrals, and then through a radial Aubry Andre Harper quasiperiodic modulation. With increasing generation index, the inflating loop less tree structure hosts pinned eigenstates on the peripheral sites that spread from the outermost rings into the bulk of the sample, resembling the spread of a forest fire, lighting up a predictable set of sites and leaving the rest unignited. The penetration depth of the envelope of amplitudes can be precisely engineered. The quasiperiodic modulation yields hitherto unreported quantum butterflies, which have further been investigated by calculating the inverse participation ratio for the eigenstates, and a multifractal analysis. The applicability of the scheme to photonic fractal waveguide networks is discussed at the end.

cond-mat.dis-nn↗

arXiv2020

Localization, transport and edge states in a two-strand ladder network in an aperiodically staggered magnetic field

We investigate the spectral and transport properties of a two-arm tight-binding ladder perturbed by an external magnetic field following an Aubry-André-Harper profile. The varying magnetic flux trapped in consecutive ladder-cells simulates an axial twist that enables us, in principle, to probe a wide variety of systems ranging from a ribbon Hofstadter geometry to helical DNA chains. We perform an in-depth numerical analysis, using a direct diagonalization of the lattice Hamiltonian to study the electronic spectra and transport properties of the model. We show that such a geometry creates a self-similar multifractal pattern in the energy landscape. The spectral properties are analyzed using the local density of states and a Green's function formalism is employed to obtain the two-terminal transmission probability. With the standard multifractal analysis and the evaluation of inverse participation ratio we show that, the system hosts both critical and extended phase for a slowly varying aperiodic sequence of flux indicating a possible mobility edge. Finally, we report signatures of topological edge modes that are found to be robust against a correlated perturbation given to the nearest neighbor hopping integrals. Our results can be of importance in experiments involving ladder-like quantum networks, realized with cold atoms in an optical trap setup.

cond-mat.mes-hall↗

arXiv2020

Engineering topological phase transition and Aharonov-Bohm caging in a flux-staggered lattice

A tight binding network of diamond shaped unit cells trapping a staggered magnetic flux distribution is shown to exhibit a topological phase transition under a controlled variation of the flux trapped in a cell. A simple real space decimation technique maps a binary flux staggered network into an equivalent Su-Shrieffer-Heeger (SSH) model. In this way, dealing with a subspace of the full degrees of freedom, we show that a topological phase transition can be initiated by tuning the applied magnetic field that eventually simulates an engineering of the numerical values of the overlap integrals in the paradigmatic SSH model. Thus one can use an external agent, rather than monitoring the intrinsic property of a lattice to control the topological properties. This is advantageous from an experimental point of view. We also provide an in-depth description and analysis of the topologically protected edge states, and discuss how, by tuning the flux from outside one can enhance the spatial extent of the Aharonov-Bohm caging of single particle states for any arbitrary period of staggering. This feature can be useful for the study of transport of quantum information. Our results are exact.

cond-mat.mes-hall↗

arXiv2019

Spin-selective Aharonov-Casher caging in a topological quantum network

A periodic network of connected rhombii, mimicking a spintronic device, is shown to exhibit an intriguing spin selective extreme localization, when submerged in a uniform out of plane electric field. The topological Aharonov Casher phase acquired by a travelling spin is seen to induce a complete caging, triggered at a special strength of the spin orbit coupling, for half odd integer spins s \ge n\hbar/2, with n odd, sparing the integer spins. The observation finds exciting experimental parallels in recent literature on caged, extreme localized modes in analogous photonic lattices. Our results are exact.

cond-mat.dis-nn↗

arXiv2019

Spin-polarized localization in a magnetized chain

We investigate a simple tight-binding Hamiltonian to understand the stability of spin-polarized transport of states with an arbitrary spin content in the presence of disorder. The general spin state is made to pass through a linear chain of magnetic atoms, and the localization lengths are computed. Depending on the value of spin, the chain of magnetic atoms unravels a hidden transverse dimensionality that can be exploited to engineer energy regimes where only a selected spin state is allowed to retain large localization lengths. An analysis is carried out to understand the roles played by the spin projections in different energy regimes of the range of states. We introduce a new measure, viz, a spin-resolved localization length for this purpose. We study uncorrelated disorder in the potential profile offered by the magnetic substrate or in the orientations of the magnetic moments concerning a given direction in space. Our results show that the spin filtering effect is robust against weak disorder and hence the proposed systems should be good candidates for experimental realizations of spin-selective transport.

cond-mat.dis-nn↗

arXiv2018

Controlled trapping of single particle states on a periodic substrate by deterministic stubbing

A periodic array of atomic sites, described within a tight binding formalism is shown to be capable of trapping electronic states as it grows in size and gets stubbed by an atom or an atomic clusters from a side in a deterministic way. We prescribe a method based on a real space renormalization group method, that unravels a subtle correlation between the positions of the side coupled atoms and the energy eigenvalues for which the incoming particle finally gets trapped. We discuss how, in such conditions, the periodic backbone gets transformed into an array of infinite quantum wells in the thermodynamic limit. We present a case here, where the wells have a hierarchically distribution of widths, hosing standing wave solutions in the thermodynamic limit.

cond-mat.dis-nn↗

arXiv2018

Flux driven and geometry controlled spin filtering for arbitrary spins in aperiodic quantum networks

We demonstrate that an aperiodic array of certain quantum networks comprising magnetic and non-magnetic atoms can act as perfect spin filters for particles with arbitrary spin state. This can be achieved by introducing minimal quasi-one dimensionality in the basic structural units building up the array, along with an appropriate tuning of the potential of the non-magnetic atoms, the tunnel hopping integral between the non-magnetic atoms and the backbone, and, in some cases, by tuning an external magnetic field. This latter result opens up the interesting possibility of designing a flux controlled spin demultiplexer using quantum networks. The proposed networks have close resemblance with a family of recently developed photonic lattices, and the scheme for spin filtering can thus be linked, in principle, to a possibility of suppressing any one of the two states of polarization of a single photon, almost at will. We use transfer matrices and a real space renormalization group scheme to unravel the conditions under which any aperiodic arrangement of such topologically different structures will filter out any given spin projection. Our results are analytically exact, and corroborated by extensive numerical calculations of the spin polarized transmission and the density of states of such systems.

cond-mat.dis-nn↗

arXiv2017

Engineering electronic states of periodic and quasiperiodic chains by buckling

The spectrum of spinless, non-interacting electrons on a linear chain that is buckled in a non- uniform manner giving it a flavor of a topologically disordered lattice, is investigated within a tight binding formalism. We have addressed two specific cases, viz., a perfectly periodic chain wrinkled in a quasiperiodic Fibonacci pattern, and a quasiperiodic Fibonacci chain, where the buckling also takes place in a Fibonacci pattern. The buckling brings distant neighbors in the parent chain to close proximity, which is simulated by a tunnel hopping amplitude. It is seen that, in the perfectly ordered case, increasing the strength of the tunnel hopping (that is, bending the segments more) absolutely continuous density of states is retained towards the edges of the band, while the central portion becomes fragmented and host subbands of narrowing widths containing extended, current carrying states, and multiple isolated bound states formed as a result of the bending. A switching on and off of the electronic transmission can thus be engineered by buckling. On the other hand, in the second example of a quasiperiodic Fibonacci chain, imparting a quasiperiodic buckling is found to generate continuous subband(s) destroying the usual multifractality of the energy spectrum. We present exact results based on a real space renormalization group analysis, that is corroborated by explicit calculation of the two terminal electronic transport.

cond-mat.dis-nn↗

arXiv2017

Phase controlled metal-insulator transition in multi-leg quasiperiodic optical lattices

A tight-binding model of a multi-leg ladder network with a continuous quasiperiodic modulation in both the site potential and the inter-arm hopping integral is considered. The model mimics optical lattices where ultra-cold fermionic or bosonic atoms are trapped in double well potentials. It is observed that, the relative phase difference between the on-site potential and the inter-arm hopping integral, which can be controlled by the tuning of the interfering laser beams trapping the cold atoms, can result in a mixed spectrum of one or more absolutely continuous subband(s) and point like spectral measures. This opens up the possibility of a re-entrant metal-insulator transition. The subtle role played by the relative phase difference mentioned above is revealed, and we corroborate it numerically by working out the multi-channel electronic transmission for finite two-, and three-leg ladder networks. The extension of the calculation beyond the two-leg case is trivial, and is discussed in the work.

cond-mat.mes-hall↗

arXiv2016

Controlled delocalization of electronic states in a multi-strand quasiperiodic lattice

Finite strips, composed of a periodic stacking of infinite quasiperiodic Fibonacci chains, have been investigated in terms of their electronic properties. The system is described by a tight binding Hamiltonian. The eigenvalue spectrum of such a multi-strand quasiperiodic network is found to be sensitive on the mutual values of the intra-strand and inter-strand tunnel hoppings, whose distribution displays a unique three-subband self-similar pattern in a parameter subspace. In addition, it is observed that special numerical correlations between the nearest and the next-nearest neighbor hopping integrals can render a substantial part of the energy spectrum absolutely continuous. Extended, Bloch like functions populate the above continuous zones, signalling a complete delocalization of single particle states even in such a non-translationally invariant system, and more importantly, a phenomenon that can be engineered by tuning the relative strengths of the hopping parameters. A commutation relation between the potential and the hopping matrices enables us to work out the precise correlation which helps to engineer the extended eigenfunctions and determine the band positions at will.

cond-mat.dis-nn↗