arXiv subjects

Shubhayu Chatterjee

Publications and source records attributed to Shubhayu Chatterjee.

54 records · Page 3Linked to original sources

arXiv2020

A mechanism for anomalous Hall ferromagnetism in twisted bilayer graphene

We use a lowest Landau level model to study the recent observation of an anomalous Hall effect in twisted bilayer graphene. This effective model is rooted in the occurrence of Chern bands which arise due to the coupling between the graphene device and its encapsulating substrate. Our model exhibits a phase transition from a spin-valley polarized insulator to a partial or fully valley unpolarized metal as the bandwidth is increased relative to the interaction strength, consistent with experimental observations. In sharp contrast to standard quantum Hall ferromagnetism, the Chern number structure of the flat bands precludes an instability to an inter-valley coherent phase, but allows for an excitonic vortex lattice at large interaction anisotropy.

cond-mat.str-el↗

arXiv2019

From eigenstate thermalization to hydrodynamic transport in correlated metals

We present a new framework for computing low frequency transport properties of strongly correlated, ergodic systems. Our main assumption is that, when a thermalizing diffusive system is driven at frequency $ω$, domains of size $ξ\sim\sqrt{D/ω}$ can be considered as internally thermal, but weakly coupled with each other. We calculate the transport coefficients to lowest order in the coupling, assuming incoherent transport between such domains. Our framework naturally captures the sub-leading non analytic corrections to the transport coefficients, known as hydrodynamic long time tails. In addition, it allows us to obtain a generalized relation between charge and thermal transport coefficients, in the spirit of the Wiedemann-Franz law. We verify our results, which satisfy several non-trivial consistency checks, via exact diagonalization studies on the one-dimensional extended Fermi-Hubbard model.

cond-mat.str-el↗

arXiv2019

Enhanced thermal Hall effect in the square-lattice Néel state

Recent experiments on several cuprate compounds have identified an enhanced thermal Hall response in the pseudogap phase. Most strikingly, this enhancement persists even in the undoped system, which challenges our understanding of the insulating parent compounds. To explain these surprising observations, we study the quantum phase transition of a square-lattice antiferromagnet from a confining Néel state to a state with coexisting Néel and semion topological order. The transition is driven by an applied magnetic field and involves no change in the symmetry of the state. The critical point is described by a strongly-coupled conformal field theory with an emergent global $SO(3)$ symmetry. The field theory has four different formulations in terms of $SU(2)$ or $U(1)$ gauge theories, which are all related by dualities; we relate all four theories to the lattice degrees of freedom. We show how proximity of the confining Néel state to the critical point can explain the enhanced thermal Hall effect seen in experiment.

cond-mat.str-el↗

arXiv2019

Isometric Tensor Network representation of string-net liquids

Recently, a class of tensor networks called isometric tensor network states (isoTNS) was proposed which generalizes the canonical form of matrix product states to tensor networks in higher dimensions. While this ansatz allows for efficient numerical computations, it remained unclear which phases admit an isoTNS representation. In this work, we show that two-dimensional string-net liquids, which represent a wide variety of topological phases including discrete gauge theories, admit an exact isoTNS representation. We further show that the isometric form can be preserved after applying a finite depth local quantum circuit. Taken together, these results show that long-range entanglement by itself is not an obstruction to isoTNS representation and suggest that all two-dimensional gapped phases with gappable edges admit an isoTNS representation.

cond-mat.str-el↗

arXiv2019

Thermal Hall effect in square-lattice spin liquids: A Schwinger boson mean-field study

Motivated by recent transport measurements in high-$T_c$ cuprate superconductors in a magnetic field, we study the thermal Hall conductivity in materials with topological order, focusing on the contribution from neutral spinons. Specifically, different Schwinger boson mean-field ansätze for the Heisenberg antiferromagnet on the square lattice are analyzed. We allow for both Dzyaloshinskii-Moriya interactions, and additional terms associated with scalar spin chiralities that break time-reversal and reflection symmetries, but preserve their product. It is shown that these scalar spin chiralities, which can either arise spontaneously or are induced by the orbital coupling of the magnetic field, can lead to spinon bands with nontrivial Chern numbers and significantly enhanced thermal Hall conductivity. Associated states with zero-temperature magnetic order, which is thermally fluctuating at any $T>0$, also show a similarly enhanced thermal Hall conductivity.

cond-mat.str-el↗

arXiv2019

Diagnosing phases of magnetic insulators via noise magnetometry with spin qubits

Two-dimensional magnetic insulators exhibit a plethora of competing ground states, such as ordered (anti)ferromagnets, exotic quantum spin liquid states with topological order and anyonic excitations, and random singlet phases emerging in highly disordered frustrated magnets. Here we show how single spin qubits, which interact directly with the low-energy excitations of magnetic insulators, can be used as a diagnostic of magnetic ground states. Experimentally tunable parameters, such as qubit level splitting, sample temperature, and qubit-sample distance, can be used to measure spin correlations with energy and wavevector resolution. Such resolution can be exploited, for instance, to distinguish between fractionalized excitations in spin liquids and spin waves in magnetically ordered states, or to detect anyonic statistics in gapped systems.

cond-mat.str-el↗

arXiv2018

Signatures of fractionalization in spin liquids from interlayer thermal transport

Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations. Several quasi-two dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacking. In this paper, we show that the inter-plane thermal conductivity in layered QSLs carries a unique signature of fractionalization. We examine several types of gapless QSL phases - a $Z_2$ QSL with either a Dirac spectrum or a spinon Fermi surface, and a $U(1)$ QSL with a Fermi surface. In all cases, the in-plane and $c-$axis thermal conductivities have a different power law dependence on temperature, due to the different mechanisms of transport in the two directions: in the planes, the thermal current is carried by fractionalized excitations, whereas the inter-plane current is carried by integer (non-fractional) excitations. In layered $Z_2$ and $U(1)$ QSLs with a Fermi surface, the $c-$axis thermal conductivity is parametrically smaller than the in-plane one, but parametrically larger than the phonon contribution at low temperatures.

cond-mat.str-el↗

arXiv2018

Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene

We present the electronic band structures of states with the same symmetry as the three-sublattice planar antiferromagnetic order of the triangular lattice. Such states can also be defined on the honeycomb lattice provided the spin density waves lie on the bonds. We identify cases which are consistent with observations on twisted bilayer graphene: a correlated insulator with an energy gap, yielding a single doubly-degenerate Fermi surface upon hole doping. We also discuss extensions to metallic states which preserve spin rotation invariance, with fluctuating spin density waves and bulk $\mathbb{Z}_2$ topological order.

cond-mat.str-el↗

arXiv2018

Topological order in the pseudogap metal

We compute the electronic Green's function of the topologically ordered Higgs phase of a SU(2) gauge theory of fluctuating antiferromagnetism on the square lattice. The results are compared with cluster extensions of dynamical mean field theory, and quantum Monte Carlo calculations, on the pseudogap phase of the strongly interacting hole-doped Hubbard model. Good agreement is found in the momentum, frequency, hopping, and doping dependencies of the spectral function and electronic self-energy. We show that lines of (approximate) zeros of the zero-frequency electronic Green's function are signs of the underlying topological order of the gauge theory, and describe how these lines of zeros appear in our theory of the Hubbard model. We also derive a modified, non-perturbative version of the Luttinger theorem that holds in the Higgs phase.

cond-mat.str-el↗

arXiv2018

Pseudogap and Fermi surface topology in the two-dimensional Hubbard model

One of the distinctive features of hole-doped cuprate superconductors is the onset of a `pseudogap' below a temperature $T^*$. Recent experiments suggest that there may be a connection between the existence of the pseudogap and the topology of the Fermi surface. Here, we address this issue by studying the two-dimensional Hubbard model with two distinct numerical methods. We find that the pseudogap only exists when the Fermi surface is hole-like and that, for a broad range of parameters, its opening is concomitant with a Fermi surface topology change from electron- to hole-like. We identify a common link between these observations: the pole-like feature of the electronic self-energy associated with the formation of the pseudogap is found to also control the degree of particle-hole asymmetry, and hence the Fermi surface topology transition. We interpret our results in the framework of an SU(2) gauge theory of fluctuating antiferromagnetism. We show that a mean-field treatment of this theory in a metallic state with U(1) topological order provides an explanation of this pole-like feature, and a good description of our numerical results. We discuss the relevance of our results to experiments on cuprates.

cond-mat.str-el↗

arXiv2017

Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves

The pseudogap metal phase of the hole-doped cuprate superconductors has two seemingly unrelated characteristics: a gap in the electronic spectrum in the `anti-nodal' region of the square lattice Brillouin zone, and discrete broken symmetries. We present a SU(2) gauge theory of quantum fluctuations of magnetically ordered states which appear in a classical theory of square lattice antiferromagnets, in a spin density wave mean field theory of the square lattice Hubbard model, and in a CP$^1$ theory of spinons. This theory leads to metals with an antinodal gap, and topological order which intertwines with precisely the observed broken symmetries.

cond-mat.str-el↗

arXiv2017

Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions

We study thermal and electrical transport in metals and superconductors near a quantum phase transition where antiferromagnetic order disappears. The same theory can also be applied to quantum phase transitions involving the loss of certain classes of intrinsic topological order. For a clean superconductor, we recover and extend the well-known universal results. The heat conductivity for commensurate and incommensurate antiferromagnetism coexisting with superconductivity shows a markedly different doping dependence near the quantum critical point, thus allowing to distinguish the states. In the dirty limit, the results for the conductivities are qualitatively similar for the metal and the superconductor. In this regime, the geometric properties of the Fermi surface allow for a very good phenomenological understanding of the numerical results on the conductivities. In the simplest model, we find that the conductivities do not track the doping evolution of the Hall coefficient, in contrast to recent experimental findings. We propose a doping dependent scattering rate, possibly due to quenched short-range charge fluctuations below optimal doping, to consistently describe both the Hall data and the longitudinal conductivities.

cond-mat.str-el↗

arXiv2017

Insulators and metals with topological order and discrete symmetry breaking

Numerous experiments have reported discrete symmetry breaking in the high temperature pseudogap phase of the hole-doped cuprates, including breaking of one or more of lattice rotation, inversion, or time-reversal symmetries. In the absence of translational symmetry breaking or topological order, these conventional order parameters cannot explain the gap in the charged fermion excitation spectrum in the anti-nodal region. Zhao et al. (1601.01688) and Jeong et al. (arXiv:1701.06485) have also reported inversion and time-reversal symmetry breaking in insulating Sr2IrO4 similar to that in the metallic cuprates, but co-existing with Neel order. We extend an earlier theory of topological order in insulators and metals, in which the topological order combines naturally with the breaking of these conventional discrete symmetries. We find translationally-invariant states with topological order co-existing with both Ising-nematic order and spontaneous charge currents. The link between the discrete broken symmetries and the topological-order-induced pseudogap explains why the broken symmetries do not survive in the confining phases without a pseudogap at large doping. Our theory also connects to the O(3) non-linear sigma model and CP1 descriptions of quantum fluctuations of the Neel order. In this framework, the optimal doping criticality of the cuprates is primarily associated with the loss of topological order.

cond-mat.str-el↗

arXiv2016

Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal

Doping a Mott-insulating $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*). Such a phase has several favorable features that make it a candidate for the pseudogap metal for the underdoped cuprates. We focus on a particular, simple $\mathbb{Z}_2$-FL* state which can undergo a confinement transition to a spatially uniform superconductor which is smoothly connected to the `plain vanilla' BCS superconductor with $d$-wave pairing. Such a transition occurs by the condensation of bosonic particles carrying $+e$ charge but no spin (`chargons'). We show that modifying the dispersion of the bosonic chargons can lead to confinement transitions with charge density waves and pair density waves at the same wave-vector $\mathbf{K}$, co-existing with $d$-wave superconductivity. We also compute the evolution of the Hall number in the normal state during the transition from the plain vanilla FL* state to a Fermi liquid, and argue, following Coleman, Marston, and Schofield [Phys. Rev. B 72, 245111 (2005)], that it exhibits a discontinuous jump near optimal doping. We note the distinction between these results and those obtained from models of the pseudogap with fermionic chargons.

cond-mat.str-el↗

arXiv2016

Spin density wave order, topological order, and Fermi surface reconstruction

In the conventional theory of density wave ordering in metals, the onset of spin density wave (SDW) order co-incides with the reconstruction of the Fermi surfaces into small 'pockets'. We present models which display this transition, while also displaying an alternative route between these phases via an intermediate phase with topological order, no broken symmetry, and pocket Fermi surfaces. The models involve coupling emergent gauge fields to a fractionalized SDW order, but retain the canonical electron operator in the underlying Hamiltonian. We establish an intimate connection between the suppression of certain defects in the SDW order, and the presence of Fermi surface sizes distinct from the Luttinger value in Fermi liquids. We discuss the relevance of such models to the physics of the hole-doped cuprates near optimal doping.

cond-mat.str-el↗

arXiv2016

Superconductivity from a confinement transition out of a fractionalized Fermi liquid with $\mathbb{Z}_2$ topological and Ising-nematic orders

The Schwinger-boson theory of the frustrated square lattice antiferromagnet yields a stable, gapped $\mathbb{Z}_2$ spin liquid ground state with time-reversal symmetry, incommensurate spin correlations and long-range Ising-nematic order. We obtain an equivalent description of this state using fermionic spinons (the fermionic spinons can be considered to be bound states of the bosonic spinons and the visons). Upon doping, the $\mathbb{Z}_2$ spin liquid can lead to a fractionalized Fermi liquid (FL*) with small Fermi pockets of electron-like quasiparticles, while preserving the $\mathbb{Z}_2$ topological and Ising-nematic orders. We describe a Higgs transition out of this deconfined metallic state into a confining superconducting state which is usually of the Fulde-Ferrell-Larkin-Ovchinnikov type, with spatial modulation of the superconducting order.

cond-mat.str-el↗

arXiv2015

Probing excitations in insulators via injection of spin-currents

We propose a spin transport experiment to measure the low-energy excitations in insulators with spin degrees of freedom, with a focus on detecting ground states that lack magnetic order. A general formalism to compute the spin-current from a metal with a non-equilibrium distribution of spins to an insulator is developed. It is applied to insulating states with and without long range magnetic order, and salient features in the spin-conductance are noted.

cond-mat.str-el↗

arXiv2013

Modified Ricci flow and asymptotically non-flat spaces

The present work extends the application of a modified Ricci flow equation to an asymptotically non flat space, namely Marder's cylindrially symmetric space. It is found that the flow equation has a solution at least in a particular case.

gr-qc↗