arXiv subjects

Krishanu Roychowdhury

Publications and source records attributed to Krishanu Roychowdhury.

At least 19 recordsLinked to original sources

arXiv2025

Anomalous Landau Levels in Inhomogeneous Fluxes and Emergent Supersymmetry

Two-dimensional systems in magnetic fields host rich physics, most notably the quantum Hall effect arising from Landau level quantization. In a broad class of two-dimensional models, flat bands with topologically nontrivial band degeneracies give rise to anomalous Landau level quantization under homogeneous fields. Ascribed to the underlying quantum geometry, these are classified as singular flat bands, exhibiting unusual wavefunction localization, and anomalous quantization of Landau levels. We investigate the response of gapless singular flat bands to inhomogeneous fluxes, bridging continuum and lattice descriptions. Our analysis reveals a mechanism to controllably manipulate the anomalous Landau levels via flux inhomogeneity. We further uncover an emergent supersymmetry in the parameter space where the tower of anomalous Landau levels collapses to zero energy, rendering a lattice analog of the Aharonov-Casher theorem on degenerate zero modes in perpendicular fluxes, with wavefunction localization partly similar to Aharonov-Bohm caging. With the addition of strong correlations, these findings will have implications for realizing exotic topological and charge-ordered phases.

cond-mat.mes-hall↗

arXiv2024

A topological route to engineering robust and bright supersymmetric laser arrays

In recent years, several proposals that leverage principles from condensed matter and high-energy physics for engineering laser arrays have been put forward. The most important among these concepts are topology, which enables the construction of robust zero-mode laser devices, and supersymmetry (SUSY), which holds the potential for achieving phase locking in laser arrays. In this work, we show that the relation between supersymmetric coupled bosonic and fermionic oscillators on one side, and bipartite networks (and hence chiral symmetry) on another side can be exploited together with non-Hermitian engineering for building one- and two-dimensional laser arrays with in-phase synchronization. To demonstrate our strategy, we present a concrete design starting from the celebrated Su-Schrieffer-Heeger (SSH) model to arrive at a SUSY laser structure that enjoys two key advantages over those reported in previous works. Firstly, the design presented here features a near-uniform geometry for both the laser array and supersymmetric reservoir (i.e. the widths and distances between the cavity arrays are almost the same). Secondly, the uniform field distribution in the presented structure leads to a far-field intensity that scales as N^2 where N is the number of lasing elements. Taken together, these two features can enable the implementation of higher-power laser arrays that are easy to fabricate, and hence provide a roadmap for pushing the frontier of SUSY laser arrays beyond the proof-of-concept phase.

physics.optics↗

arXiv2024

Stretched-Exponential Melting of a Dynamically Frozen State Under Imprinted Phase Noise in the Ising Chain in a Transverse Field

Dynamical freezing is a phenomenon where a set of local observables emerges as approximate but stable conserved quantities (freezes) under a strong periodic drive in a closed quantum system. The expectation values of these emergent conserved quantities exhibit small fluctuations around their respective initial values. These fluctuations do not grow with time, and their magnitude can be tuned down sharply by tuning the drive parameters. In this work, we probe the resilience of dynamical freezing to random perturbations added to the relative phases between the interfering states (elements of a natural basis) in the time-evolving wave function after each drive cycle. We study this in an integrable Ising chain in a time-periodic transverse field. Our key finding is, that the imprinted phase noise melts the dynamically frozen state, but the decay is "slow": a stretched-exponential decay rather than an exponential one. Stretched-exponential decays (also known as Kohlrausch relaxation) are usually expected in complex systems with time-scale hierarchies due to strong disorders or other inhomogeneities resulting in jamming, glassiness, or localization.

cond-mat.stat-mech↗

arXiv2022

Volkov-Pankratov states on the edge of a quantum spin Hall system

Volkov-Pankratov (VP) states are a family of sub-gap states which appear at the smooth interface/domain wall between topologically distinct gapped states. We study the emergence of such states in the edge spectrum of a quantum spin Hall system subjected to a smoothly varying mass term (Zeeman field) that switches sign at a given spatial point. Both the VP states at non-zero energy and the zero energy Jackiw-Rebbi mode stay localized at the interfacial region, however, the former feature several distinctive signatures compared to the latter such as non-trivial spin textures that can be characterized by a winding number in real space. On applying an electric field, the texture deforms leaving its winding number unaltered. Moreover, the VP states exhibit an intriguing interplay between the electric and the magnetic field with a collapse of the spectrum onto the zero mode when they are equal in magnitude. Quantum transport simulations on a 2D lattice model are performed to undergird our theoretical prediction.

cond-mat.mes-hall↗

arXiv2022

Supersymmetry on the lattice: Geometry, Topology, and Flat Bands

In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons, and fermions defined by local rules. Here we apply it to find connections between bosonic and fermionic lattice models in the realm of condensed matter physics and uncover a novel 5-fold way topology it demands in these systems. At the single-particle level, our connections pair a bosonic and fermionic lattice model, either describing the hopping of number-conserving particles or local couplings between fermion parity-conserving particles. The pair are isospectral except for zero modes, such as flat bands, quadratic band touchings, and nexus points, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences. Notably, in this framework, the supercharge operator that generates SUSY is Hermitian and can itself be interpreted as a hopping Hamiltonian on a bipartite lattice, a feature that enables the discovery of materials or model lattices hosting the SUSY partners. To illustrate the power of SUSY, we present 16 use cases of SUSY, that span topics including frustrated magnets, Kitaev spin liquids, and topological superconductors, the majority of which turn out to provide insights into the discovery and design of flat bands and topological materials.

cond-mat.str-el↗

arXiv2021

Dynamics and correlations at a quantum phase transition beyond Kibble-Zurek

Kibble-Zurek theory (KZ) stands out as the most robust theory of defect generation in the dynamics of phase transitions. KZ utilizes the structure of equilibrium states away from the transition point to estimate the excitations due to the transition using adiabatic and impulse approximations. Here we show, the actual nonequilibrium dynamics lead to a qualitatively different scenario from KZ, as far correlations between the defects (rather than their densities) are concerned. For a quantum Ising chain, we show, this gives rise to a Gaussian spatial decay in the domain wall (kinks) correlations, while KZ would predict an exponential fall. We propose a simple but general framework on top of KZ, based on the "quantum coarsening" dynamics of local correlators in the supposed impulse regime. We outline how our picture extends to generic interacting situations.

cond-mat.str-el↗

arXiv2021

Entanglement dualities in supersymmetry

We derive a general relation between the bosonic and fermionic entanglement in the ground states of supersymmetric quadratic Hamiltonians. For this, we construct canonical identifications between bosonic and fermionic subsystems. Our derivation relies on a unified framework to describe both, bosonic and fermionic Gaussian states in terms of so-called linear complex structures $J$. The resulting dualities apply to the full entanglement spectrum between the bosonic and the fermionic systems, such that the von Neumann entropy and arbitrary Renyi entropies can be related. We illustrate our findings in one and two-dimensional systems, including the paradigmatic Kitaev honeycomb model. While typically SUSY preserves features like area law scaling of the entanglement entropies on either side, we find a peculiar phenomenon, namely, an amplified scaling of the entanglement entropy ("super area law") in bosonic subsystems when the dual fermionic subsystems develop almost maximally entangled modes.

quant-ph↗

arXiv2021

Spin-polarized voltage probes for helical edge state: a model study

Theoretical models of a spin-polarized voltage probe (SPVP) tunnel-coupled to the helical edge states (HES) of a quantum spin Hall system (QSHS) are studied. Our first model of the SPVP comprises $N_{P}$ spin-polarized modes (subprobes), each of which is locally tunnel-coupled to the HES, while the SPVP, as a whole, is subjected to a self-consistency condition ensuring zero average current on the probe. We carry out a numerical analysis which shows that the optimal situation for reading off spin-resolved voltage from the HES depends on the interplay of the probe-edge tunnel-coupling and the number of modes in the probe ($N_P$). We further investigate the stability of our findings by introducing Gaussian fluctuations in {\it{(i)}} the tunnel-coupling between the subprobes and the HES about a chosen average value and {\it{(ii)}} spin-polarization of the subprobes about a chosen direction of the net polarization of SPVP. We also perform a numerical analysis corresponding to the situation where four such SPVPs are implemented in a self-consistent fashion across a ferromagnetic barrier on the HES and demonstrate that this model facilitates the measurements of spin-resolved four-probe voltage drops across the ferromagnetic barrier. As a second model, we employ the edge state of a quantum anomalous Hall state (QAHS) as the SPVP which is tunnel-coupled over an extended region with the HES. A two-dimensional lattice simulation for the quantum transport of the proposed device setup comprising a junction of QSHS and QAHS is considered and a feasibility study of using the edge of the QAHS as an efficient spin-polarized voltage probe is carried out in presence of an optimal strength of the disorder.

cond-mat.mes-hall↗

arXiv2021

Effects of surface potentials on Goos-Haenchen and Imbert-Fedorov shifts in Weyl semimetals

Weyl semimetals exhibit exotic transport responses, among which, recently Goos-Haenchen (GH) and Imbert-Fedorov (IF) effects have received a revived attention, which are, otherwise, well-studied phenomena in optical systems and certain electronic systems. Besides the usual parametric dependence of the shifts inherited from the underlying Hamiltonian to describe the Weyl system and/or that induced by external controls, the IF shift further carries a topological identity -- it depends on the chirality of the Weyl cones. A realistic system of Weyl semimetal naturally accommodates surface potentials induced by impurities present on its surface that could pose impediments to observe clean transport signatures predicted in theoretical models. Classifying these potentials, we study their effects on GH and IF shifts to provide useful guidance to future experiments that are tuned to the objective of characterizing Weyl semimetals and for a possible realisation of novel devices based on these phenomena. A transfer matrix-based approach is invoked to study the profile of Weyl wavefunctions across the interface which is hosting the impurity potentials, revealing that such potentials can lead to several discerning effects which, in certain cases, extend even to nullifying the IF shift completely and giving rise to phenomenon like valley inversion.

cond-mat.mes-hall↗

arXiv2021

Topology in non-linear mechanical systems

Many advancements have been made in the field of topological mechanics. The majority of the works, however, concerns the topological invariant in a linear theory. We, in this work, present a generic prescription of defining topological indices which accommodates non-linear effects in mechanical systems without taking any approximation. Invoking the tools of differential geometry, a Z-valued quantity in terms of the Poincare-Hopf index, that features the topological invariant of non-linear zero modes (ZMs), is predicted. We further identify one type of topologically protected solitons that are robust to disorders. Our prescription constitutes a new direction of searching for novel topologically protected non-linear ZMs in the future.

cond-mat.soft↗

arXiv2020

Spin Berry phase in a helical edge state: Sz nonconservation and transport signatures

Topological protection of edge state in quantum spin Hall systems relies only on time-reversal symmetry. Hence, S z conservation on the edge can be relaxed which can have an interferometric manifestation in terms of spin Berry phase. Primarily it could lead to the generation of spin Berry phase arising from a closed loop dynamics of electrons. Our work provides a minimal framework to generate and detect these effects by employing both spin-unpolarized and spin-polarized leads. We show that spin-polarized leads could lead to resonances or anti-resonances in the two-terminal conductance of the interferometer. We further show that the positions of these anti-resonances (as a function of energy of the incident electron) get shifted owing to the presence of spin Berry phase. Finally, we present simulations of a device setup using KWANTpackage which put our theoretical predictions on firm footing.

cond-mat.mes-hall↗

arXiv2020

Doping effects on the magnetic frustration in the honeycomb iridates

We investigate the doping effects of magnetic and nonmagnetic impurities injected to the honeycomb iridate sample of Na2IrO3 . Both the doping result in changing the ordering temperature as well as the Curie-Weiss temperature of the parent sample as a consequence of enhancement of the lattice frustration, screening of the Ir atoms and spin-orbit effects that reflects in the susceptibility and specific heat measurements. Our findings are corroborated by a detailed comparative study of various magnetic and nonmagnetic impurity atoms that have notable effects on different electronic properties of the doped compounds.

cond-mat.str-el↗

arXiv2018

Topological Mechanics from Supersymmetry

In topological mechanics, the identification of a mechanical system's rigidity matrix with an electronic tight-binding model allows to infer topological properties of the mechanical system, such as the occurrence of `floppy' boundary modes, from the associated electronic band structure. Here we introduce an approach to systematically construct topological mechanical systems by an exact supersymmetry (SUSY) that relates the bosonic (mechanical) and fermionic (e.g. electronic) degrees of freedom. As examples we discuss mechanical analogues of the Kitaev honeycomb model and of a second-order topological insulator with floppy corner modes. Our SUSY construction naturally defines hitherto unexplored topological invariants for bosonic (mechanical) systems, such as bosonic Wilson loop operators that are formulated in terms of a SUSY-related fermionic Berry curvature.

cond-mat.str-el↗

arXiv2018

Topology and geometry of spin origami

Kagome antiferromagnets are known to be highly frustrated and degenerate when they possess simple, isotropic interactions. We consider the entire class of these magnets when their interactions are spatially anisotropic. We do so by identifying a certain class of systems whose degenerate ground states can be mapped onto the folding motions of a generalized "spin origami" two-dimensional mechanical sheet. Some such anisotropic spin systems, including Cs2ZrCu3F12, map onto flat origami sheets, possessing extensive degeneracy similar to isotropic systems. Others, such as Cs2CeCu3F12, can be mapped onto sheets with non-zero Gaussian curvature, leading to more mechanically stable corrugated surfaces. Remarkably, even such distortions do not always lift the entire degeneracy, instead permitting a large but sub-extensive space of zero-energy modes. We show that for Cs2CeCu3F12, due to an additional point group symmetry associated with structure, these modes are 'Dirac' line nodes with a double degeneracy protected by a topological invariant. The existence of mechanical analogs thus serves to identify and explicate the robust degeneracy of the spin systems.

cond-mat.str-el↗

arXiv2018

A classification of magnetic frustration and metamaterials from topology

We study the relationship between the physics of topology and zero modes in frustrated systems and metama- terials. Zero modes that exist in topological matters are distinct from the ones arising from symmetry breaking. Incidentally, a prominent aspect of frustrated systems and metamaterials also is to harbor such kind of zero modes in form of an accidental degeneracy. Taking cues from these two apparently different phenomena, we ask a simple question: are the robust features of frustration topologically protected and if so can we classify different types of frustration using topology? In answering these questions we invoke the tools of topological mechanics to identify the key agent at play, namely the rigidity matrix, which is a non-Hermitian matrix and decides the topology of spin-wave zero modes in a frustrated magnet or phonon modes in metamaterials. Further developments of the theory rely on combining the recent developments in our understanding of Maxwell constraint counting and generalizing the ten-fold way classification of Hermitian matrices to non-Hermitian matrices. The result is a three-fold way classification for each Maxwell counting index. We illustrate the clas- sification by demonstrating the existence of a new vortex-like invariant for real rigidity matrices using random matrices and through example frustrated spin models. So by classifying all the rigidity matrices, we answer the question of the origin of frustration (i.e. zero modes in the form of accidental degeneracy) in a wide class of frustrated magnets and metamaterials by linking it to topological invariants.

cond-mat.str-el↗

arXiv2017

Tunable multi-electron Pancharatnam phase in intensity interferometry

Pancharatnam phase was discovered in the context of polarization optics in nineteen fifties. However, its full realization in quantum many-body systems still eludes us. This is primarily due to the fact that electron spin is not easily tunable. In the present proposal, we suggest that edge states of quantum spin Hall effect (QSHE) in conjunction with spin polarized electrodes (SPE) provide us with a unique opportunity to explore the Pancharatnam phase. We demonstrate the possibility of generating and detecting the multi-electron version of this phase that can as well be interpreted as multi-particle Aharonov-Bohm (A-B) effect in spin space arising solely due to spin dynamics. We further show that our proposed set-up leads to a robust interference pattern which survives orbital dephasing.

cond-mat.mes-hall↗

arXiv2016

Pseudospin-valve effect on transport in junctions of three-dimensional topological insulator surfaces

We show that the surface states of pristine 3D topological insulators (TIs) are analogs of ferromagnetic half metals due to complete polarization of an emergent momentum independent pseudospin (SU(2)) degree of freedom on the surface. To put this claim on firm footing, we present results for TI surfaces perpendicular to the crystal growth axis, which clearly show that the tunneling conductance between two such TI surfaces of the same TI material is dominated by this half metallic behavior leading to physics reminiscent of a spin-valve. Further using the generalized tunnel magnetoresistance derived in this work we also study the tunneling current between arbitrary TI surfaces. We also perform a comprehensive study of the effect of all possible surface potentials allowed by time reversal symmetry on this spin-valve effect and show that it is robust against most of such potentials.

cond-mat.mes-hall↗

arXiv2016

Quantum Hall realization of polarized intensity interferometry

We combine the ideas of intensity interferometry, polarization optics and Bell's measurement into an experimental proposal which is hosted in a $ν\,$=$\,2$ quantum Hall (QH) edge state. Our interferometer comprises of a single gate, that separates the spin resolved edge states of $ν$\,=\,$2$ state. An analog of waveplate (from polarization optics) is realized by exposing the individual edges to nano-magnets over a finite length which facilitates coherent manipulation of the electron spin on the edge. We show that the in-plane rotation of magnetization direction of the nano-magnets results in oscillations observed solely in the cross-correlated noise which arises from two particle interference. Through numerical simulations we demonstrate that our proposal is well within the reach of recent experimental developments of spin manipulations on the QH edge.

cond-mat.mes-hall↗