arXiv subjects

Amrita Mukherjee

Publications and source records attributed to Amrita Mukherjee.

18 recordsLinked to original sources

arXiv2026

Type-II Mirror Chern Insulator in Altermagnets

Altermagnets with momentum-dependent spin splitting despite zero net magnetization can support unique topological states under broken time-reversal symmetry. We predict a mirror-symmetry-protected topological crystalline insulator with momentum-separated edge modes in a two-dimensional altermagnet. Using a square-octagon lattice model, we show that altermagnetic order generates symmetry-related valley-polarized Dirac nodes, which are gapped by spin-orbit coupling to yield a mirror Chern insulator with $C_{\mathcal{M}}=2$. In contrast to conventional mirror Chern insulators, where the two mirror-protected edge modes cross at the same momentum to form a Dirac cone, altermagnetic spin splitting and valley-selective band inversion separate these edge modes in momentum. We refer to this phase as a type-II mirror Chern insulator. We further propose a PbSe/$\mathrm{V_2Se_2O}$ heterobilayer as a candidate material for realizing this phase through the altermagnetic proximity effect. Our results establish altermagnetism as a route to mirror-protected topological phases with momentum-separated edge modes.

cond-mat.mes-hall↗

arXiv2025

Topologically nontrivial flat bands and quantum Hall crossovers in square-octagon lattice materials

Coexistence of nontrivial topology and flat electronic bands provides a fertile platform for correlated quantum states. The square-octagon lattice hosts Dirac nodes and flat bands at half-filling, yet the effects of intrinsic spin-orbit coupling (SOC) and staggered magnetic flux on its electronic and topological properties remain largely unexplored. Here, using tight-binding models incorporating SOC and staggered magnetic flux, we uncover a rich topological phase diagram in this lattice, comprising a quantum spin Hall phase with spin Chern number $C_s=1$, crossovers to quantum anomalous Hall phases with $C=1$ and $C=2$, and higher-order topological insulator phases with quantized quadrupolar corner charges. The initially dispersionless flat bands evolve into quasi-flat topological bands with nearly uniform quantum geometry and large flatness ratios, making them promising candidates for fractional Chern insulator states. We further identify realistic materials, including octagraphene, transition-metal dichalcogenides, synthetic $\mathrm{MoSi_2N_4}$, and magnetic $\alpha$-MnO$_2$, that may realize these tunable topological phases intertwined with flat-band physics, opening new opportunities for correlated topological matter.

cond-mat.mes-hall↗

arXiv2025

Proximity-induced flat bands and topological properties in a decorated diamond chain

In the present study, we propose a unique scheme to generate and control multiple flat bands in a decorated diamond chain by using a strain-induced proximity effect between the diagonal sites of each diamond plaquette. This is in complete contrast to the conventional diamond chain, in which the interplay between the lattice topology and an external magnetic flux leads to an extreme localization of the single-particle states, producing the flat bands in the energy spectrum. Such a strain-induced proximity effect will enable us to systematically control one of the diagonal hoppings in the decorated diamond chain, which will lead to the formation of both gapless and gapped flat bands in the energy spectrum. These gapless or gapped flat bands have been corroborated by the computation of the compact localized states amplitude distribution as well as the density of states of the system using a real space calculation. We have also shown that these flat bands are robust against the introduction of small amounts of random onsite disorder in the system. In addition to this, we have also classified the nontrivial topological properties of the system by calculating the winding numbers and edge states for the gapped energy spectrum. These findings could be easily realized experimentally using the laser-induced photonic lattice platforms.

cond-mat.str-el↗

arXiv2025

High-order van Hove singularities and nematic instability in the kagome superconductor CsTi$_3$Bi$_5$

ATi$_3$Bi$_5$ (A = Cs or Rb) are emerging topological kagome metals that exhibit superconductivity and nematicity without intertwining translational symmetry-breaking charge orders. In this work, we explore the fermiology of their titanium kagome electrons and identify a set of sublattice-pure, high-order van Hove singularities (VHSs) that can suppress charge ordering and enhance electronic correlations and superconductivity. Our calculations of charge susceptibility for kagome bands with both normal and high-order VHSs emphasize the role of these VHSs in driving electronic nematicity in CsTi$_3$Bi$_5$. Additionally, we compute the phonon spectrum and electron-phonon interactions for CsTi$_3$Bi$_5$ under pristine, doped, and kagome-exposed surface conditions, revealing its robustness against structural instabilities while enhancing the superconducting transition temperature. Our work positions ATi$_3$Bi$_5$ as a key platform for investigating superconductivity and electronic nematicity without translational symmetry-breaking states in kagome metals.

cond-mat.mtrl-sci↗

arXiv2024

Topological flat bands and higher-order topology in square-octagon lattice

Extensive recent research on Lieb and kagome lattices highlights their unique physics characterized by the coexistence of Dirac points, van Hove singularities, and flat bands. In these models, flat bands are typically pinned at the center of the Lieb spectrum or the extrema of kagome bands, offering limited tunability. In this work, we investigate the square-octagon lattice and demonstrate that flat bands generated through next-nearest-neighbor (NNN) hoppings can be tuned with intercell hoppings or staggered magnetic fluxes. Importantly, the introduction of staggered magnetic fluxes leads to the emergence of a Chern insulator phase and a higher-order topological insulator (HOTI) state at half-filling. An appropriate magnetic flux combined with NNN hopping can generate topological flat bands in the Chern insulator phase, exhibiting nontrivial Chern number and chiral edge states. The HOTI phase, in contrast, is characterized by topological corner states with quantized quadrupole moment within the bulk and edge states gap. We also present phase diagrams for the square-octagon lattice as functions of NNN and intercell hoppings under staggered magnetic fluxes. Our results indicate that the square-octagon lattice offers a promising platform for realizing topological flat bands, HOTI, and other topological and nontopological phases.

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↗

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

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

Flux modulated flat band engineering in square-kagome ladder network

The origin of non-dispersive flat band modes for a quasi-one dimensional square-kagome ladder network is explored analytically by virtue of the real space renormalization group (RSRG) technique. A section of the eigenstates is non-diffusive i.e., localized within a cluster of sub-lattice sites partly by the destructive type of quantum interference and partly by the physical divider formed by the sites with zero wave function amplitude. By making the amplitude vanish at the selective sites it becomes possible to confine the incoming excitation within the trapping cell leading to the formation of compact localized states. The effective mass of the particle becomes infinitely large corresponding to those self-localized modes and hence the mobility of the wave train becomes vanishingly small. This quenched kinetic energy leads to a momentum independent contribution to a dispersion curve. The present analysis is corroborated by numerical calculation of spectral landscape and the corresponding dispersion profile. The application of uniform magnetic flux may lead to a comprehensive engineering of the position as well as the curvature of the band. Also, one-to-one mapping between electronic case and photonic case within the tight-binding framework helps us to study the photonic localization in an analogous single mode wave guide system. The concept of slow light eventually introduces the possibility of spatial compression of light energy.

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↗

arXiv2018

Spectral engineering and tunable thermoelectric behavior in a quasiperiodic ladder network

Double stranded quasiperiodic copper mean arrangement has been studied in respect of their electronic property and thermoelectric signature. The two-arm network is demonstrated by a tight binding Hamiltonian. The eigenspectrum of such aperiodic mesh that does not convey translational invariance, is significantly dependent on the parameters of the Hamiltonian. It is observed that specific correlation between the parameters obtained from the commutation relation between the on-site energy and overlap integral matrices can eventually modify the spectral nature and generate absolutely continuous energy spectrum. This part is populated by atypical extended states that has a large localization length substantiated by the flow of the hopping integral under successive real space renormalization group method steps. This sounds delocalization of single particle energy states in such nontranslationally invariant networks. Further this can be engineered at will by selective choice of the relative strengths of the parameters. This precise correlation has a crucial impact on the thermoelectric behavior. Anomalous nature of thermoelectric coefficient may inspire the experimentalists to frame tunable thermodevices. Specific correlations can help us to tune the continuous band and determine the band position at will.

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

Outage Analysis for SWIPT-Enabled Two-Way Cognitive Cooperative Communications

In this paper, we study a cooperative cognitive radio network (CCRN) where the secondary user-transmitter (SU-Tx) assists bi-directional communication between a pair of primary users (PUs) following the principle of two-way relaying. In return, it gets access to the spectrum of the PUs to enable its own transmission to SU-receiver (SU-Rx). Further, in order to support sustainable operation of the network, SU-Tx is assumed to harvest energy from the RF signals received from the PUs, using the technique of simultaneous wireless information and power transfer (SWIPT). Assuming a decode-and-forward behaviour and power-splitting based relaying protocol at SU-Tx, closed form expressions for outage probability of PU and SU are obtained. Simulation results validate our analytical results and illustrate spectrum-efficiency and energy-efficiency advantages of the proposed system over one-way relaying.

cs.NI↗

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↗