arXiv subjects

Vatsal Dwivedi

Publications and source records attributed to Vatsal Dwivedi.

At least 19 recordsLinked to original sources

arXiv2025

Magnetotransport across Weyl semimetal grain boundaries

A clean interface between two Weyl semimetals features a universal, field-linear tunnel magnetoconductance of $(e^2/h)N_\mathrm{ho}$ per magnetic flux quantum, where $N_\mathrm{ho}$ is the number of chirality-preserving topological interface Fermi arcs. In this work we show that the linearity of the magnetoconductance is robust with to interface disorder. The slope of the magnetoconductance changes at a characteristic field strength $B_\mathrm{arc}$ -- the field strength for which the time taken to traverse the Fermi arc due to the Lorentz force is equal to the mean inter-arc scattering time. For fields much larger than $B_\mathrm{arc}$, the magnetoconductance is unaffected by disorder. For fields much smaller than $B_\mathrm{arc}$, the slope is no longer determined by $N_\mathrm{ho}$ but by the simple fraction $N_\mathrm{L} N_\mathrm{R}/(N_\mathrm{L}+N_\mathrm{R})$, where $N_\mathrm{L}$ and $N_\mathrm{R}$ are the numbers of Weyl-node pairs in the left and right Weyl semimetal, respectively. We also consider the effect of spatially correlated disorder potentials, where we find that $B_\mathrm{arc}$ decreases exponentially with increasing correlation length. Our results provide a possible explanation for the recently observed robustness of the negative linear magnetoresistance in grained Weyl semimetals.

cond-mat.mes-hall↗

arXiv2024

On the band topology of the breathing kagome lattice

A two-dimensional second-order topological insulator exhibits topologically protected zero-energy states at its corners. In the literature, the breathing kagome lattice with nearest-neighbor hopping is often mentioned as an example of a two-dimensional second-order topological insulator. Here we show by explicit construction that the corner states of the breathing kagome lattice can be removed by a continuous change of the hopping parameters, without breaking any of the model's symmetries, without closing bulk and boundary gaps, and without introducing hopping terms not present in the original model. Furthermore, we topologically classify all three-band lattice models with the same crystalline symmetries as the breathing kagome lattice and show that though none of the phases have protected zero-energy corner states, some of the phases are obstructed atomic limits which exhibit a filling anomaly.

cond-mat.mes-hall↗

arXiv2023

Quantum Oscillation Signatures of Fermi Arcs in Tunnel Magnetoconductance

Fermi-arc surface states of Weyl semimetals exhibit a unique combination of localization to a surface and connectivity to the bulk Weyl fermions that can move along the localization direction. We predict anomalous quantum-oscillation signatures of Fermi arcs in the tunnel mangetoconductance across an interface between two Weyl semimetals. These oscillations stem from a momentum-space analog of Aharonov-Bohm interference of electrons moving along the interface Fermi arcs, driven by an external magnetic field normal to the interface. The Fermi arcs' connectivity to the bulk enables their characterization via transport normal to the interface, while their localization manifests in a strong field-angle anisotropy of the oscillations. This combination distinguishes these anomalous oscillations from conventional Shubnikov-de Haas oscillations and makes them identifiable even in complex oscillation spectra of real materials.

cond-mat.mes-hall↗

arXiv2023

Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology

The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied and unoccupied bands, while imposing restrictions on one or both leads to ``fragile'' and ``delicate'' topology, respectively. In this article, we describe a homotopic classification of band structures -- which captures the topology beyond the stable equivalence -- in the presence of additional lattice symmetries. As examples, we present complete homotopic classifications for spinless band structures with twofold rotation, fourfold rotation and fourfold dihedral symmetries, both in presence and absence of time-reversal symmetry. Whereas the rules of delicate and fragile topology do not admit a bulk-boundary correspondence, we identify a version of stable topology, which restricts the representations of bands, but not their numbers, which does allow for anomalous states at symmetry-preserving boundaries, which are associated with nontrivial bulk topology.

cond-mat.mes-hall↗

arXiv2023

Magnetic Breakdown and Chiral Magnetic Effect at Weyl-Semimetal Tunnel Junctions

We investigate magnetotransport across an interface between two Weyl semimetals whose Weyl nodes project onto different interface momenta. Such an interface generically hosts Fermi arcs that connect Weyl nodes of identical chirality in different Weyl semimetals (homochiral connectivity) -- in contrast to surface Fermi arcs that connect opposite-chirality Weyl nodes within the same Weyl semimetal (heterochiral connectivity). We show that electron transport along the arcs with homochiral connectivity, in the presence of a longitudinal magnetic field, leads to a universal longitudinal magnetoconductance of $e^2/h$ per magnetic flux quantum. Furthermore, a weak tunnel coupling can result in a close encounter of two homochiral-connectivity Fermi arcs, enabling magnetic breakdown. Above the breakdown field the interface Fermi arc connectivity is effectively heterochiral, leading to a saturation of the conductance.

cond-mat.mes-hall↗

arXiv2020

Partial flux ordering and thermal Majorana metals in (higher-order) spin liquids

In frustrated quantum magnetism, chiral spin liquids are a particularly intriguing subset of quantum spin liquids in which the fractionalized parton degrees of freedom form a Chern insulator. Here we study an exactly solvable spin-3/2 model which harbors not only chiral spin liquids but also spin liquids with higher-order parton band topology -- a trivial band insulator, a Chern insulator with gapless chiral edge modes, and a second-order topological insulator with gapless corner modes. With a focus on the thermodynamic precursors and thermal phase transitions associated with these distinct states, we employ numerically exact quantum Monte Carlo simulations to reveal a number of unconventional phenomena. This includes a heightened thermal stability of the ground state phases, the emergence of a partial flux ordering of the associated $\mathbb{Z}_2$ lattice gauge field, and the formation of a thermal Majorana metal regime extending over a broad temperature range.

cond-mat.str-el↗

arXiv2019

Geometric responses of the Pfaffian state

We define and study the Pfaffian state on Riemann surfaces with arbitrary metrics and an inhomogeneous magnetic field and derive its universal transport coefficients. Following a path integral approach, we compute the generating functional which encodes the linear response of the system to a variation of the background metric and the magnetic field and use it to compute the leading and sub-leading corrections to the charge density in a large-$N$ expansion. We also present the first derivation of gravitational anomaly contribution at O$(k^6)$ to the static structure factor for the Pfaffian state in the long wavelength limit.

cond-mat.str-el↗

arXiv2019

Non-Hermitian systems and topology: A transfer-matrix perspective

Topological phases of Hermitian systems are known to exhibit intriguing properties such as the presence of robust boundary states and the famed bulk-boundary correspondence. These features can change drastically for their non-Hermitian generalizations, as exemplified by a general breakdown of bulk-boundary correspondence and a localization of all states at the boundary, termed the non-Hermitian skin effect. In this article, we present a completely analytical unifying framework for studying these systems using generalized transfer matrices -- a real-space approach suitable for systems with periodic as well as open boundary conditions. We show that various qualitative properties of these systems can be easily deduced from the transfer matrix. For instance, the connection between the breakdown of the conventional bulk-boundary correspondence and the existence of a non-Hermitian skin effect, previously observed numerically, is traced back to the transfer matrix having a determinant not equal to unity. The vanishing of this determinant signals real-space exceptional points, whose order scales with the system size. We also derive previously proposed topological invariants such as the biorthogonal polarization and the Chern number computed on a complexified Brillouin zone. Finally, we define an invariant for and thereby clarify the meaning of topologically protected boundary modes for non-Hermitian systems.

cond-mat.mes-hall↗

arXiv2018

Matrix product state representation of quasielectron wave functions

Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.

cond-mat.str-el↗

arXiv2018

Majorana Corner Modes in a Second-Order Kitaev Spin Liquid

Higher-order topological insulators are distinguished by the existence of topologically protected modes with codimension two or higher. Here, we report the manifestation of a second-order topological insulator in a two dimensional frustrated quantum magnet, which exhibits topological corner modes. Our exactly-solvable model is a generalization of the Kitaev honeycomb model to the Shastry-Sutherland lattice that, besides a chiral spin liquid phase, exhibits a gapped spin liquid with Majorana corner modes, which are protected by two mirror symmetries. This second-order Kitaev spin liquid remains stable in the presence of thermal fluctuations and undergoes a finite-temperature phase transition evidenced in large-scale quantum Monte Carlo simulations.

cond-mat.str-el↗

arXiv2018

Phase Space Entanglement Spectrum

We generalize the position- and momentum-space entanglement cuts to a family of cuts corresponding to regions in the classical phase space. We explicitly compute the entanglement spectra of free fermionic many-body wavefunctions for a family of phase space entanglement cuts that continuously interpolates between position- and momentum-space cuts. For inversion symmetric wavefunctions, the phase space entanglement spectrum possess a chiral symmetry, to which a topological index can be associated.

math-ph↗

arXiv2018

Fermi arc reconstruction at junctions between Weyl semimetals

We analyze junctions between noninteracting fermionic topological phases. A closed-form condition for the existence of localized modes at the interface is derived using the transfer matrix approach. These analytical conditions as well as numerical exact diagonalization are used to study interfaces between Weyl semimetals. We observe a Fermi arc reconstruction at the interface, leading to curves of zero energy modes in the interface Brillouin zone. These are stable even in certain cases where the two Weyl semimetals differ only in their Fermi arc connectivities.

cond-mat.mes-hall↗

arXiv2017

Crystalline Kitaev spin liquids

Frustrated magnetic systems exhibit many fascinating phases. Prime among them are quantum spin liquids, where the magnetic moments do not order even at zero temperature. A subclass of quantum spin liquids called Kitaev spin liquids are particularly interesting, because they are exactly solvable, can be realized in certain materials, and show a large variety of gapless and gapped phases. Here, we show that non-symmorphic symmetries can enrich spin liquid phases, such that the low-energy spinon degrees of freedom form three-dimensional Dirac cones or nodal chains. In addition, we suggest how such Kitaev spin liquids may be realized in metal-organic-frameworks.

cond-mat.str-el↗

arXiv2016

Connecting the dots: Time-reversal symmetric Weyl Semimetals with tunable Fermi arcs

We propose a one-parameter family of noninteracting lattice models for Weyl semimetals with 4 Weyl nodes and tunable Fermi arcs. These 2-band model Hamiltonians are time-reversal symmetric with $\mathrm{T}^2 = + 1$, and tuning the parameter changes the connectivity of the Fermi arcs continuously without affecting the location and chiralities of the Weyl nodes in the bulk Brillouin zone. The bulk polarization and magnetization are shown to vary with this parameter, a dependence inaccessible to the low energy effective field theory.

cond-mat.mes-hall↗

arXiv2016

Chiral kinetic theory and anomalous hydrodynamics in even spacetime dimensions

We study the hydrodynamics of a gas of noninteracting Weyl fermions coupled to the electromagnetic field in $(2N + 1) + 1$ spacetime dimensions using the chiral kinetic theory, which encodes the gauge anomaly in the Chern character of the nonabelian Berry connection over the Fermi surface. We derive the anomalous contributions to the relativistic hydrodynamic currents in equilibrium and at a finite temperature, which agree with and provides an approach complementary to the results derived previously using thermodynamic constraints.

hep-th↗

arXiv2016

Of Bulk and Boundaries: Generalized Transfer Matrices for Tight-Binding Models

We construct a generalized transfer matrix corresponding to noninteracting tight-binding lattice models, which can subsequently be used to compute the bulk bands as well as the edge states. Crucially, our formalism works even in cases where the hopping matrix is non-invertible. Following Hatsugai [PRL 71, 3697 (1993)], we explicitly construct the energy Riemann surfaces associated with the band structure for a specific class of systems which includes systems like Chern insulator, Dirac semimetal and graphene. The edge states can then be interpreted as non-contractible loops, with the winding number equal to the bulk Chern number. For these systems, the transfer matrix is symplectic, and hence we also describe the windings associated with the edge states on $Sp(2, \mathbb{R})$ and interpret the corresponding winding number as a Maslov index.

cond-mat.other↗

arXiv2015

Wigner translations and the observer-dependence of the position of masslesss spinning particles

The Wigner little group for massless particles is isomorphic to the Euclidean group ${\rm SE}(2)$. Applied to momentum eigenstates, or to infinite plane waves, the Euclidean "Wigner translations" act as the identity. We show that when applied to finite wavepackets the translation generators move the packet trajectory parallel to itself through a distance proportional to the particle's helicity. We relate this effect to the Hall effect of light and to the Lorentz-frame dependence of the position of a massless spinning particle.

hep-th↗

arXiv2014

Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles

We consider the relation between spin and the Berry-phase contribution to the anomalous velocity of massive and massless Dirac particles. We extend the Berry connection that depends only on the spatial components of the particle momentum to one that depends on the the space and time components in a covariant manner. We show that this covariant Berry connection captures the Thomas-precession part of the Bargmann-Michel-Telegdi spin evolution, and contrast it with the traditional (unitary, but not naturally covariant) Berry connection that describes spin-orbit coupling. We then consider how the covariant connection enters the classical relativistic dynamics of spinning particles due to Mathisson, Papapetrou and Dixon. We discuss the problems that arise with Lorentz covariance in the massless case, and trace them mathematically to a failure of the Wigner-translation part of the massless-particle little group to be an exact gauge symmetry in the presence of interactions, and physically to the fact that the measured position of a massless spinning particle is necessarily observer dependent.

hep-th↗