arXiv subjects

Pallab Goswami

Publications and source records attributed to Pallab Goswami.

At least 19 recordsLinked to original sources

arXiv2026

Entangling Power: A Probe of Symmetry and Integrability in Quantum Many-Body Systems

The entangling power of a unitary operator quantifies its ability to generate entanglement from product states and provides a natural probe of quantum many-body dynamics. Entanglement extremization at points of enhanced symmetry has previously been observed in high-energy scattering. In this work we compute the time-averaged entangling power of anisotropic Heisenberg spin chains across two-site models and finite-size systems, as well as the entangling power of the two-magnon $S$-matrix in the thermodynamic limit. For two-site models we establish a monotonic hierarchy: the entangling power decreases as the symmetry group grows, reaching its minimum at the $SU(2)$ XXX point. Finite-size XXZ chains exhibit sharp dips at the $SU(2)$ points $\Delta=\pm 1$ and the free-fermion point $\Delta=0$, with the free-fermion dip decaying much more slowly with system size. In the thermodynamic limit, we decompose the two-magnon $S$-matrix into quantum logic gates -- Identity, SWAP, and $\sigma_z\otimes\sigma_z$ -- and show that the entangling power vanishes for all scattering energies at the $SU(2)$ points, where the $S$-matrix reduces to the Identity gate, while the free-fermion point achieves the maximum -- the opposite of the finite-size many-body behavior. The entangling power can serve as an {\em operator} diagnostic for symmetry and selected aspects of integrability in quantum simulations of spin-chain dynamics.

quant-ph↗

arXiv2024

Nonlinear Hall Effect in KTaO$_3$ Two-Dimensional Electron Gases

The observation of a Hall effect, a finite transverse voltage induced by a longitudinal current, usually requires the breaking of time-reversal symmetry, for example through the application of an external magnetic field or the presence of long range magnetic order in a sample. Recently it was suggested that under certain symmetry conditions, the presence of finite Berry curvatures in the band structure of a system with time-reversal symmetry but without inversion symmetry can give rise to a nonlinear Hall effect in the presence of a probe current. In order to observe the nonlinear Hall effect, one requires a finite component of a so-called Berry dipole along the direction of the probe current. We report here measurements of the nonlinear Hall effect in two-dimensional electron gases fabricated on the surface of KTaO$_3$ with different surface crystal orientations as a function of the probe current, a transverse electric field and back gate voltage. For all three crystal orientations, the transverse electric field modifies the nonlinear Hall effect. We discuss our results in the context of the current understanding of the nonlinear Hall effect as well as potential experimental artifacts that may give rise to the same effects.

cond-mat.mes-hall↗

arXiv2024

Intrinsic magnetism in KTaO$_3$ heterostructures

There has been intense recent interest in the two-dimensional electron gases (2DEGs) that form at the surfaces and interfaces of KTaO$_3$ (KTO), with the discovery of superconductivity at temperatures significantly higher than those of similar 2DEGs based on SrTiO$_3$ (STO). Like STO heterostructures, these KTO 2DEGs are formed by depositing an overlayer on top of appropriately prepared KTO surfaces. Some of these overlayers are magnetic, and the resulting 2DEGs show signatures of this magnetism, including hysteresis in the magnetoresistance (MR). Here we show that KTO 2DEGs fabricated by depositing AlO$_x$ on top of KTO also show hysteretic MR, indicative of long range magnetic order, even though the samples nominally contain no intrinsic magnetic elements. The hysteresis appears in both the transverse and longitudinal resistance in magnetic fields both perpendicular to and in the plane of the 2DEG. The hysteretic MR has different characteristic fields and shapes for surfaces of different crystal orientations, and vanishes above a few Kelvin. Density functional theory (DFT) calculations indicate that the magnetism likely arises from Ta$^{4+}$ local moments created in the presence of oxygen vacancies.

cond-mat.mes-hall↗

arXiv2023

Solitons and real-space screening of bulk topology of quantum materials

Recent years have seen multiple high-throughput studies reveal an immense number of topological materials through use of symmetry indicators. Despite this success, three-dimensional topological insulators (TI) admitting a band-gap larger than Bi$_{2}$Se$_{3}$ and two-dimensional TIs admitting a band gap larger than $β$-bismuthene, two of the originally proposed TIs, remain extremely rare. Simultaneously, a significant effort has been made to understand and identify topological phases ``invisible" to symmetry indicators. Such phases offer a unique opportunity to expand the search for a large band-gap TI, however their identification requires sophisticated probes of bulk topology. Magnetic flux tubes or vortices have emerged as one such probe in two-dimensions when inserted into the bulk. In this work, we develop an automated workflow to perform vortex insertion and apply it to a current database of high-quality, experimentally realized, two-dimensional insulators. The results reveal multiple novel two-dimensional topological insulators supporting large bands gaps, including the 1H-MX$_{2}$ (M=Mo,W) and (X=S,Se,Te) family of transition metal dichalcogenides. Our work has broad implications for current theoretical and experimental efforts to employ these materials in superconducting and Moire systems.

cond-mat.mtrl-sci↗

arXiv2023

Colossal Spontaneous Hall Effect and Emergent Magnetism in KTaO$_3$ Two-Dimensional Electron Gases

There has been intense recent interest in the two-dimensional electron gases (2DEGs) that form at the surfaces and interfaces of KTaO$_3$ (KTO), with the discovery of superconductivity at temperatures significantly higher than those of similar 2DEGs based on SrTiO$_3$ (STO). Here we demonstrate that KTO 2DEGs fabricated under conditions that suppress the superconductivity show a large spontaneous Hall effect at low temperatures. The transverse response is asymmetric in an applied perpendicular magnetic field and becomes hysteretic at millikelvin temperatures. The hysteresis is due to long range magnetic order arising from local Ta$^{4+}$ moments. However, the most striking features of the data are the asymmetry of the transverse response and the large spontaneous transverse resistance at zero field, which can be a significant fraction of the longitudinal resistance and depends on crystal orientation. Both effects are due to the presence of a dominant contribution to the transverse response that is symmetric in perpendicular field, suggesting that its origin is topological in nature. We argue that this contribution arises from Berry curvature dipoles coupled with nonequilibrium conditions induced by the measuring current.

cond-mat.mes-hall↗

arXiv2023

Fundamentals of crystalline Hopf insulators

Three-dimensional, crystalline Hopf insulators are generic members of unitary Wigner-Dyson class, which can break all global discrete symmetries and point group symmetries. In the absence of first Chern number for any two-dimensional plane of Brillouin zone, the Hopf invariant $N_H \in \mathbb{Z}$. But in the presence of Chern number $N_H \in \mathbb{Z}_{2q}$, where $q$ is the greatest common divisor of Chern numbers for $xy$, $yz$, and $xz$ planes of Brillouin zone. How does $N_H$ affect topological quantization of isotropic, magneto-electric coefficient? We answer this question with calculations of Witten effect for a test, magnetic monopole. Furthermore, we construct $N$-band tight-binding models of Hopf insulators and demonstrate their topological stability against spectral flattening.

cond-mat.mes-hall↗

arXiv2022

Part II: Witten effect and $\mathbb{Z}$-classification of axion angle $θ=n π$

The non-trivial third homotopy class of three-dimensional topological insulators leads to quantized, magneto-electric coefficient or axion angle $θ= n π$, with $n \in \mathbb{Z}$. In Part I, we developed tools for computing $n$ from a staggered symmetry-indicator $κ_{AF,j}$ and Wilson loops of non-Abelian, Berry connection in momentum-space, which clearly distinguished between magneto-electrically trivial ($n=0$), and non-trivial ($n=2s$) topological crystalline insulators. In this work, we perform $\mathbb{Z}$-classification of real-space, topological response or $θ$ by carrying out thought experiments with magnetic, Dirac monopoles. We demonstrate this for non-magnetic and magnetic topological insulators by computing induced electric charge on monopoles or Witten effect. We show that both first- and higher- order topological insulators can exhibit quantized, magneto-electric response, irrespective of the presence of gapless surface-states, and corner-states. Special attention is paid to the response of octupolar higher-order topological insulator, which was originally predicted to be magneto-electrically trivial. The important roles of fermion zero-modes, $\mathcal{CP}$, and flavor symmetries are critically addressed. Our work outlines a unified theoretical framework for addressing dc topological response and topological quantum phase transitions, which cannot be reliably predicted by symmetry-based classification scheme.

cond-mat.mes-hall↗

arXiv2022

Non-Abelian Stokes theorem and quantized Berry flux

Band topology of anomalous quantum Hall insulators can be precisely addressed by computing Chern numbers of constituent non-degenerate bands that describe quantized, Abelian Berry flux through two-dimensional Brillouin zone. Can Chern numbers be defined for $SU(2)$ Berry connection of two-fold degenerate bands of materials preserving space-inversion ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetries or combined $\mathcal{PT}$ symmetry, without detailed knowledge of underlying basis? We affirmatively answer this question by employing a non-Abelian generalization of Stokes' theorem and describe a manifestly gauge-invariant method for computing magnitudes of quantized $SU(2)$ Berry flux (spin-Chern number) from eigenvalues of Wilson loops. The power of this method is elucidated by performing $\mathbb{N}$-classification of \emph{ab initio} band structures of three-dimensional, Dirac materials. Our work outlines a unified framework for addressing first-order and higher-order topology of insulators and semimetals, without relying on detailed symmetry data.

cond-mat.mtrl-sci↗

arXiv2022

Spin-charge separation and quantum spin Hall effect of $β$-bismuthene

Field theory arguments suggest the possibility of $\mathbb{Z}$-classification of quantum spin Hall effect with magnetic flux tubes, that cause separation of spin and charge degrees of freedom, and pumping of spin or Kramers pair. However, the \emph{proof of principle} demonstration of spin-charge separation is yet to be accomplished for realistic, \emph{ab initio} band structures of spin-orbit-coupled materials, lacking spin-conservation law. In this work, we perform thought experiments with magnetic flux tubes on $β$-bismuthene to demonstrate spin-charge separation, and quantized pumping of spin for three insulating states that can be accessed by tuning filling fractions. With a combined analysis of momentum-space topology and real-space response, we identify important role of topologically non-trivial bands, supporting even integer winding numbers, which cannot be inferred from symmetry-based indicators. Our work sets a new standard for prediction of two-dimensional, quantum spin-Hall materials, based on precise bulk invariant and universal topological response.

cond-mat.mes-hall↗

arXiv2022

Part I: Staggered index and 3D winding number of Kramers-degenerate bands

For three-dimensional (3D) crystalline insulators, preserving space-inversion ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetries, the third homotopy class of two-fold, Kramers-degenerate bands is described by a 3D winding number $n_{3,j} \in \mathbb{Z}$, where $j$ is the band index. It governs space group symmetry-protected, instanton or tunneling configurations of $SU(2)$ Berry connection, and the quantization of magneto-electric coefficient $θ_j = n_{3,j} π$. We show that $|n_{3,j}|$ for realistic, \emph{ab initio} band structures can be identified from a staggered symmetry-indicator $κ_{AF,j} \in \mathbb{Z}$ and the gauge-invariant spectrum of $SU(2)$ Wilson loops. The procedure is elucidated for $4$-band and $8$-band tight-binding models and \emph{ab initio} band structure of Bi, which is a $\mathbb{Z}_2$-trivial, higher-order, topological crystalline insulator. When the tunneling is protected by $C_{nh}$ and $D_{nh}$ point groups, the proposed method can also identify the signed winding number $n_{3,j}$. Our analysis distinguishes between magneto-electrically trivial ($θ=0$) and non-trivial ($θ=2 s π$, with $s \neq 0$) topological crystalline insulators. In Part II, we demonstrate $\mathbb{Z}$-classification of $θ$ by computing induced electric charge (Witten effect) on magnetic Dirac monopoles.

cond-mat.mtrl-sci↗

arXiv2022

Topology of three-dimensional Dirac semimetals and generalized quantum spin Hall systems without gapless edge modes

Usually the quantum spin Hall states are expected to possess gapless, helical edge modes. Are there clean, non-interacting, quantum spin Hall states without gapless, edge modes? We show the generic, $n$-fold-symmetric, momentum planes of three-dimensional, stable Dirac semi-metals, which are orthogonal to the direction of nodal separation are examples of such generalized quantum spin Hall systems. We demonstrate that the planes lying between two Dirac points and the celebrated Bernevig-Zhang-Hughes model support identical quantized, non-Abelian Berry flux of magnitude $2 π$. Consequently, both systems exhibit spin-charge separation in response to electromagnetic, $π$-flux vortex. The Dirac points are identified as the unit-strength, monopoles of $SO(5)$ Berry connection, describing topological quantum phase transitions between generalized, quantum spin Hall and trivial insulators. Our work identifies precise bulk invariant and quantized response of Dirac semimetals and shows that many two-dimensional higher-order topological insulators can be understood as generalized quantum spin Hall systems, possessing gapped edge states.

cond-mat.mes-hall↗

arXiv2022

Mixed-order topology of Benalcazar-Bernevig-Hughes models

Benalcazar-Bernevig-Hughes (BBH) models, defined on $D$-dimensional simple cubic lattice, are paradigmatic toy models for studying $D$-th order topology and corner-localized, mid-gap states. Under periodic boundary conditions, the Wilson loops of non-Abelian Berry connection of BBH models along all high-symmetry axes have been argued to exhibit gapped spectra, which predict gapped surface-states under open boundary conditions. In this work, we identify 1D, 2D, and 3D topological invariants for characterizing higher order topological insulators. Further, we demonstrate the existence of cubic-symmetry-protected, gapless spectra of Wilson loops and surface-states along the body diagonal directions of the Brillouin zone of BBH models. We show the gapless surface-states are described by $2^{D-1}$-component, massless Dirac fermions. Thus, BBH models can exhibit the signatures of first and $D$-th order topological insulators, depending on the details of externally imposed boundary conditions.

cond-mat.mes-hall↗

arXiv2021

Insulator-metal quantum phase transition in heavy topological insulators

Exponentially localized surface states are the most distinctive property of a crystal with non-trivial band topology. Such surface states play a key role in characterizing topological insulators (TIs), both in theory and experiments. TIs resulting from the hybridization of heavy (or nearly flat) and light (or dispersive) bands are automatically tuned to the vicinity of an insulator-to-metal phase transition (IMT), which is not accompanied by a change in bulk band-topology. By formulating a scaling theory for IMTs in such "heavy" TIs, we show that the proximity to an IMT manifests most dramatically in the behavior of the surface states, viz. (i) the strength of spin-orbital locking is strongly suppressed; (ii) the surface conduction and valence bands support vastly different number of states; (iii) the surface states penetrate deep into the bulk and the penetration depth diverges at the IMT point. Thus, the surface states in heavy TIs coexist with bulk scattered states, and may no longer serve as an useful determinant of their bulk band-topology. The mechanism of degradation of surface states discussed here is generic, and expected to hold in both heavy TIs and semimetals.

cond-mat.str-el↗

arXiv2021

Mechanism of skyrmion condensation and pairing for twisted bi-layer graphene

When quantum flavor Hall insulator phases of itinerant fermions are disordered by strong quantum fluctuations, the condensation of skyrmion textures of order parameter fields can lead to superconductivity. In this work, we address the mechanism of skyrmion condensation by considering the scattering between (2+1)-dimensional, Weyl fermions and hedgehog type tunneling configurations of order parameters that violate the skyrmion-number conservation law. We show the quantized, flavor Hall conductivity ($σ^f_{xy}$) controls the degeneracy of topologically protected, fermion zero-modes, localized on hedgehogs, and the overlap between zero-mode eigenfunctions or 't Hooft vertex determines the nature of pairing. We demonstrate the quantum-disordered, flavor Hall insulators with $σ^f_{xy}= 2 N$ lead to different types of charge $2 N e^-$ superconductivity. Some implications for the competition among flavor Hall insulators, the charge $2e^-$ paired states in BCS and pair-density-wave channels, and the composite, charge $4e^-$ superconductors for twisted bilayer graphene are outlined.

cond-mat.supr-con↗

arXiv2018

Giant anomalous Nernst effect and quantum-critical scaling in a ferromagnetic semimetal

In metallic ferromagnets, the Berry curvature of underlying quasiparticles can cause an electric voltage perpendicular to both magnetization and an applied temperature gradient, a phenomenon called the anomalous Nernst effect (ANE). Here, we report the observation of a giant ANE in the full-Heusler ferromagnet Co$_2$MnGa, reaching $S_{yx}\sim -6$ $μ$V/K at room $T$, one order of magnitude larger than the maximum value reported for a magnetic conductor. With increasing temperature, the transverse thermoelectric conductivity or Peltier coefficient $α_{yx}$ shows a crossover between $T$-linear and $-T \log(T)$ behaviors, indicating the violation of Mott formula at high temperatures. Our numerical and analytical calculations indicate that the proximity to a quantum Lifshitz transition between type-I and type-II magnetic Weyl fermions is responsible for the observed crossover properties and an enhanced $α_{yx}$. The $T$ dependence of $α_{yx}$ in experiments and numerical calculations can be understood in terms of a quantum critical scaling function predicted by the low energy effective theory over more than a decade of temperatures. Moreover, the observation of chiral anomaly or an unsaturated positive longitudinal magnetoconductance also provide evidence for the existence of Weyl fermions in Co$_2$MnGa.

cond-mat.mtrl-sci↗

arXiv2018

Itinerant quantum multi-criticality of two dimensional Dirac fermions

We analyze emergent quantum multi-criticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders, which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break $O(S_1)$ and $O(S_2)$ symmetries in the ordered phase. Performing a renormalization group analysis by using the $ε=(3-d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an \emph{enlarged} $O(S_1+S_2)$ chiral symmetry. Such a fixed point acts as an exotic quantum multi-critical point (MCP), governing the \emph{continuous} semimetal-insulator as well as insulator-insulator (for example antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either $O(S_1)$ or $O(S_2)$ chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher dimensional Dirac fermions is also outlined.

cond-mat.str-el↗

arXiv2017

Skyrmion defects and competing singlet orders in a half-filled antiferromagnetic Kondo-Heisenberg model on the honeycomb lattice

Due to the interaction between topological defects of an order parameter and underlying fermions, the defects can possess induced fermion numbers, leading to several exotic phenomena of fundamental importance to both condensed matter and high energy physics. One of the intriguing outcome of induced fermion number is the presence of fluctuating competing orders inside the core of topological defect. In this regard, the interaction between fermions and skyrmion excitations of antiferromagnetic phase can have important consequence for understanding the global phase diagrams of many condensed matter systems where antiferromagnetism and several singlet orders compete. We critically investigate the relation between fluctuating competing orders and skyrmion excitations of the antiferromagnetic insulating phase of a half-filled Kondo-Heisenberg model on honeycomb lattice. By combining analytical and numerical methods we obtain exact eigenstates of underlying Dirac fermions in the presence of a single skyrmion configuration, which are used for computing induced chiral charge. Additionally, by employing this nonperturbative eigenbasis we calculate the susceptibilities of different translational symmetry breaking charge, bond and current density wave orders and translational symmetry preserving Kondo singlet formation. Based on the computed susceptibilities we establish spin Peierls and Kondo singlets as dominant competing orders of antiferromagnetism. We show favorable agreement between our findings and field theoretic predictions based on perturbative gradient expansion scheme which crucially relies on adiabatic principle and plane wave eigenstates for Dirac fermions. The methodology developed here can be applied to many other correlated systems supporting competition between spin-triplet and spin-singlet orders in both lower and higher spatial dimensions.

cond-mat.str-el↗

arXiv2017

Chiral anomaly and longitudinal magnetotransport in type-II Weyl semimetals

In the presence of parallel electric and magnetic fields, the violation of separate number conservation laws for the three dimensional left and right handed Weyl fermions is known as the chiral anomaly. The recent discovery of Weyl and Dirac semimetals has paved the way for experimentally testing the effects of chiral anomaly via longitudinal magneto-transport measurements. More recently, a type-II Weyl semimetal (WSM) phase has been proposed, where the nodal points possess a finite density of states due to the touching between electron- and hole- pockets. It has been suggested that the main difference between the two types of WSMs (type-I and type-II) is that in the latter, chiral anomaly and the associated longitudinal magneto-resistance are strongly anisotropic, vanishing when the applied magnetic field is perpendicular to the direction of tilt of Weyl fermion cones in a type-II WSM. We analyze chiral anomaly in a type-II WSM in quasiclassical Boltzmann framework, and find that the chiral anomaly induced positive longitudinal magneto-conductivity is present along any arbitrary direction.

cond-mat.mes-hall↗