Resonating Valence Bond States in an Electron-Phonon System

We study a simple electron-phonon model on square and triangular versions of the Lieb lattice using an asymptotically exact strong coupling analysis. At zero temperature and electron density n=1 (one electron per unit cell), for various ranges of parameters in the model, we exploit a mapping to the quantum dimer model to establish the existence of a spin-liquid phase with Z_{2} topological order (on the triangular lattice) and a multicritical line corresponding to a quantum critical spin liquid (on the square lattice). In the remaining part of the phase diagram, we find a host of charge-density-wave phases (valence-bond solids), a conventional s-wave superconducting phase, and with the addition of a small Hubbard U to tip the balance, a phonon-induced d-wave superconducting phase. Under a special condition, we find a hidden pseudospin SU(2) symmetry that implies an exact constraint on the superconducting order parameters.

A stability bound on the [Formula: see text]-linear resistivity of conventional metals

Perturbative considerations account for the properties of conventional metals, including the range of temperatures where the transport scattering rate is 1/τtr = 2πλT, where λ is a dimensionless strength of the electron-phonon coupling. The fact that measured values satisfy λ ≲ 1 has been noted in the context of a possible "Planckian" bound on transport. However, since the electron-phonon scattering is quasielastic in this regime, no such Planckian considerations can be relevant. We present and analyze Monte Carlo results on the Holstein model which show that a different sort of bound is at play: a "stability" bound on λ consistent with metallic transport. We conjecture that a qualitatively similar bound on the strength of residual interactions, which is often stronger than Planckian, may apply to metals more generally.

Interstitial-Induced Ferromagnetism in a Two-Dimensional Wigner Crystal

The two-dimensional Wigner crystal (WC) occurs in the strongly interacting regime (r_{s}≫1) of the two-dimensional electron gas (2DEG). The magnetism of a pure WC is determined by tunneling processes that induce multispin ring-exchange interactions, resulting in fully polarized ferromagnetism for large enough r_{s}. Recently, Hossain et al. [Proc. Natl. Acad. Sci. U.S.A. 117, 32244 (2020)PNASA60027-842410.1073/pnas.2018248117] reported the occurrence of a fully polarized ferromagnetic insulator at r_{s}≳35 in an AlAs quantum well, but at temperatures orders of magnitude larger than the predicted exchange energies for the pure WC. Here, we analyze the large r_{s} dynamics of an interstitial defect in the WC, and show that it produces local ferromagnetism with much higher energy scales. Three hopping processes are dominant, which favor a large, fully polarized ferromagnetic polaron. Based on the above results, we speculate concerning the phenomenology of the magnetism near the metal-insulator transition of the 2DEG.

High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid

We have performed density-matrix renormalization group studies of a square lattice t-J model with small hole doping, δ≪1, on long four and six-leg cylinders. We include frustration in the form of a second-neighbor exchange coupling, J_{2}=J_{1}/2, such that the undoped (δ=0) "parent" state is a quantum spin liquid. In contrast to the relatively short range superconducting (SC) correlations that have been observed in recent studies of the six-leg cylinder in the absence of frustration, we find power-law SC correlations with a Luttinger exponent, K_{SC}≈1, consistent with a strongly diverging SC susceptibility, χ∼T^{-(2-K_{SC})} as the temperature T→0. The spin-spin correlations-as in the undoped state-fall exponentially suggesting that the SC "pairing" correlations evolve smoothly from the insulating parent state.

Nematic quantum criticality in an Fe-based superconductor revealed by strain-tuning

Quantum criticality may be essential to understanding a wide range of exotic electronic behavior; however, conclusive evidence of quantum critical fluctuations has been elusive in many materials of current interest. An expected characteristic feature of quantum criticality is power-law behavior of thermodynamic quantities as a function of a nonthermal tuning parameter close to the quantum critical point (QCP). Here, we observed power-law behavior of the critical temperature of the coupled nematic/structural phase transition as a function of uniaxial stress in a representative family of iron-based superconductors, providing direct evidence of quantum critical nematic fluctuations in this material. These quantum critical fluctuations are not confined within a narrow regime around the QCP but rather extend over a wide range of temperatures and compositions.

Strong Coupling Limit of the Holstein-Hubbard Model

We analyze the quantum phase diagram of the Holstein-Hubbard model using an asymptotically exact strong coupling expansion. We find all sorts of interesting phases including a pair-density wave, a charge 4e (and even a charge 6e) superconductor, regimes of phase separation, and a variety of distinct charge-density-wave, spin-density-wave, and superconducting regimes. We chart the crossovers that occur as a function of the degree of retardation, i.e., the ratio of characteristic phonon frequency to the strength of interactions.

Enhanced Thermal Hall Effect in Nearly Ferroelectric Insulators

In the context of recent experimental observations of an unexpectedly large thermal Hall conductivity, κ_{H}, in insulating La_{2}CuO_{4} (LCO) and SrTiO_{3} (STO), we theoretically explore conditions under which acoustic phonons can give rise to such a large κ_{H}. Both the intrinsic and extrinsic contributions to κ_{H} are large in proportion to the dielectric constant, ε, and the "flexoelectric" coupling, F. While the intrinsic contribution is still orders of magnitude smaller than the observed effect, an extrinsic contribution proportional to the phonon mean-free path appears likely to account for the observations, at least in STO. We predict a larger intrinsic κ_{H} in certain insulating perovskites.

Observation of two types of charge-density-wave orders in superconducting La2-xSrxCuO4

The discovery of charge- and spin-density-wave (CDW/SDW) orders in superconducting cuprates has altered our perspective on the nature of high-temperature superconductivity (SC). However, it has proven difficult to fully elucidate the relationship between the density wave orders and SC. Here, using resonant soft X-ray scattering, we study the archetypal cuprate La_2-xSr_xCuO₄ (LSCO) over a broad doping range. We reveal the existence of two types of CDW orders in LSCO, namely CDW stripe order and CDW short-range order (SRO). While the CDW-SRO is suppressed by SC, it is partially transformed into the CDW stripe order with developing SDW stripe order near the superconducting T_c. These findings indicate that the stripe orders and SC are inhomogeneously distributed in the superconducting CuO₂ planes of LSCO. This further suggests a new perspective on the putative pair-density-wave order that coexists with SC, SDW, and CDW orders.

To fully elucidate the relationship between density wave orders and superconductivity in high-T_c cuprates remains difficult. Here, the authors reveal two types of charge-density-wave orders and their intertwined relationship with spin-density-wave order and superconductivity in La_2-xSr_xCuO_4.

Holon Wigner Crystal in a Lightly Doped Kagome Quantum Spin Liquid

We address the problem of a lightly doped spin liquid through a large-scale density-matrix renormalization group study of the t-J model on a kagome lattice with a small but nonzero concentration δ of doped holes. It is now widely accepted that the undoped (δ=0) spin-1/2 Heisenberg antiferromagnet has a spin-liquid ground state. Theoretical arguments have been presented that light doping of such a spin liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal. Instead, we infer that the doped holes form an insulating charge-density wave state with one doped hole per unit cell, i.e., a Wigner crystal. Spin correlations remain short ranged, as in the spin-liquid parent state, from which we infer that the state is a crystal of spinless holons, rather than of holes. Our results may be relevant to kagome lattice herbertsmithite upon doping.

Necessity of Time-Reversal Symmetry Breaking for the Polar Kerr Effect in Linear Response

We show that, measured in a backscattering geometry, the polar Kerr effect is absent if the nonlocal electromagnetic response function respects Onsager symmetry, characteristic of thermodynamic states that preserve time-reversal symmetry. A key element is an expression for the reflectivity tensor in terms of the retarded Green's function.

Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields

Charge density wave (CDW) correlations have been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured with x-ray scattering at zero and low fields. We combined a pulsed magnet with an x-ray free-electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields of up to 28 tesla. While the zero-field CDW order, which develops at temperatures below ~150 kelvin, is essentially two dimensional, at lower temperature and beyond 15 tesla, another three-dimensionally ordered CDW emerges. The field-induced CDW appears around the zero-field superconducting transition temperature; in contrast, the incommensurate in-plane ordering vector is field-independent. This implies that the two forms of CDW and high-temperature superconductivity are intimately linked.

One Hole in the Two-Leg t-J Ladder and Adiabatic Continuity to the Noninteracting Limit

We carry out density-matrix-renormalization group (DMRG) calculations for the problem of one doped hole in a two-leg t-J ladder. Recent studies have concluded that exotic "Mott" physics-arising from the projection onto the space of no double-occupied sites-is manifest in this model system, leading to charge localization and a new mechanism for charge modulation. In contrast, we show that there is no localization and that the charge-density modulation arises when the minimum in the quasiparticle dispersion moves away from π. Although singular changes in the quasiparticle dispersion do occur as a function of model parameters, all of the DMRG results can be qualitatively understood from a noninteracting "band-structure" perspective.

Enhancement of superconductivity near a nematic quantum critical point

We consider a low T_{c} metallic superconductor weakly coupled to the soft fluctuations associated with proximity to a nematic quantum critical point (NQCP). We show that (1) a BCS-Eliashberg treatment remains valid outside of a parametrically narrow interval about the NQCP, (2) the symmetry of the superconducting state (d wave, s wave, p wave) is typically determined by the noncritical interactions, but T_{c} is enhanced by the nematic fluctuations in all channels, and (3) in 2D, this enhancement grows upon approach to criticality up to the point at which the weak coupling approach breaks down, but in 3D, the enhancement is much weaker.

Microscopic model of quasiparticle wave packets in superfluids, superconductors, and paired Hall states

We study the structure of Bogoliubov quasiparticles, bogolons, the fermionic excitations of paired superfluids that arise from fermion (BCS) pairing, including neutral superfluids, superconductors, and paired quantum Hall states. The naive construction of a stationary quasiparticle in which the deformation of the pair field is neglected leads to a contradiction: it carries a net electrical current even though it does not move. However, treating the pair field self-consistently resolves this problem: in a neutral superfluid, a dipolar current pattern is associated with the quasiparticle for which the total current vanishes. When Maxwell electrodynamics is included, as appropriate to a superconductor, this pattern is confined over a penetration depth. For paired quantum Hall states of composite fermions, the Maxwell term is replaced by a Chern-Simons term, which leads to a dipolar charge distribution and consequently to a dipolar current pattern.

Exact spin liquid ground states of the quantum dimer model on the square and honeycomb lattices

We study a generalized quantum hard-core dimer model on the square and honeycomb lattices, allowing for first and second neighbor dimers. At generalized Rokhsar-Kivelson points, the exact ground states can be constructed, and ground-state correlation functions can be equated to those of interacting (1+1)-dimensional Grassmann fields. When the concentration of second neighbor dimers is small, the ground-state correlations are shown to be short ranged corresponding to a (gaped) spin liquid phase. On a 2-torus, the ground states exhibit fourfold topological degeneracy. On a finite cylinder we have found a dramatic even-odd effect depending on the circumference and propose that this can be used as a numerical diagnostic of gapped spin-liquid phases, more generally.

Phases of the infinite U Hubbard model on square lattices

We apply the density matrix renormalization group to study the phase diagram of the infinite U Hubbard model on 2- to 6-leg ladders. Where the results are largely insensitive to the ladder width, we consider the results representative of the 2D square lattice. We find a fully polarized ferromagnetic Fermi liquid phase when n, the density of electrons per site, is in the range 1>n≳0.800. For n=3/4 we find an unexpected insulating checkerboard phase with coexisting bond-density order with 4 sites per unit cell and block-spin antiferromagnetic order with 8 sites per unit cell. For 3/4>n, all ladders with width >2 have unpolarized ground states.

Hydrodynamic description of transport in strongly correlated electron systems

We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, κ. This is in striking contrast to the Stokes flow, in which the resistance is independent of κ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magnetoresistance.

Weakly coupled Pfaffian as a type I quantum Hall liquid

The Pfaffian phase in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing energy is small, i.e., in the weak-coupling, BCS limit, where the coherence length is much larger than the charge screening length. We find that, as in a type I superconductor, vortices attract so that, upon varying the magnetic field from its magic value at ν=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffians exemplify a general dichotomy between type I and type II quantum Hall fluids.

From a single-band metal to a high-temperature superconductor via two thermal phase transitions

The nature of the pseudogap phase of cuprate high-temperature superconductors is a major unsolved problem in condensed matter physics. We studied the commencement of the pseudogap state at temperature T* using three different techniques (angle-resolved photoemission spectroscopy, polar Kerr effect, and time-resolved reflectivity) on the same optimally doped Bi2201 crystals. We observed the coincident, abrupt onset at T* of a particle-hole asymmetric antinodal gap in the electronic spectrum, a Kerr rotation in the reflected light polarization, and a change in the ultrafast relaxational dynamics, consistent with a phase transition. Upon further cooling, spectroscopic signatures of superconductivity begin to grow close to the superconducting transition temperature (T(c)), entangled in an energy-momentum-dependent manner with the preexisting pseudogap features, ushering in a ground state with coexisting orders.

Fragile Mott insulators

We prove that there exists a class of crystalline insulators, which we call "fragile Mott insulators," which are not adiabatically connected to any sort of band insulator provided time-reversal and certain point-group symmetries are respected, but which are otherwise unspectacular in that they exhibit no topological order nor any form of fractionalized quasiparticles. Different fragile Mott insulators are characterized by different nontrivial one-dimensional representations of the crystal point group. We illustrate this new type of insulators with two examples: the d Mott insulator discovered in the checkerboard Hubbard model at half-filling and the Affleck-Kennedy-Lieb-Tasaki insulator on the square lattice.

Pair-density-wave correlations in the Kondo-Heisenberg model

We show, using density-matrix renormalization-group calculations complemented by field-theoretic arguments, that the spin-gapped phase of the one dimensional Kondo-Heisenberg model exhibits quasi-long-range superconducting correlations only at a nonzero momentum. The local correlations in this phase resemble those of the pair-density-wave state which was recently proposed to describe the phenomenology of the striped ordered high-temperature superconductor La(2-x)Ba(x)CuO₄, in which the spin, charge, and superconducting orders are strongly intertwined.

Hidden quasi-one-dimensional superconductivity in Sr₂RuO₄

We show that the interplay between spin and charge fluctuations in Sr₂RuO₄ leads unequivocally to triplet pairing which has a hidden quasi-one-dimensional character. The resulting superconducting state spontaneously breaks time-reversal symmetry and is of the form Δ ~(p(x)+ip(y))z(^) with sharp gap minima and a d vector that is only weakly pinned. The superconductor lacks robust chiral Majorana fermion modes along the boundary. The absence of topologically protected edge modes could explain the surprising absence of experimentally detectable edge currents in this system.

Topological insulators and nematic phases from spontaneous symmetry breaking in 2D fermi systems with a quadratic band crossing

We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the noninteracting level, we show that a QBCP exists and is topologically stable for a Berry flux +/-2pi if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to arbitrarily weak short-range repulsive interactions. We consider both spinless and spin-1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematic-spin-nematic phase.

Algebraic spin liquid in an exactly solvable spin model

We have proposed an exactly solvable quantum spin-3/2 model on a square lattice. Its ground state is a quantum spin liquid with a half-integer spin per unit cell. The fermionic excitations, dubbed as "spinons", are gapless with a linear dispersion, while the topological "vison" excitations are gapped. Moreover, these massless fermionic spinon excitations are topologically stable. Thus, this model is, to the best of our knowledge, the first exactly solvable model of half-integer spins whose ground state is an "algebraic spin liquid."

In search of a theory of supercooled liquids

Despite the absence of consensus on a theory of the transition from supercooled liquids to glasses, the experimental observations suggest that a detail-independent theory should exist.

Polar Kerr-effect measurements of the high-temperature YBa2Cu3O6+x superconductor: evidence for broken symmetry near the pseudogap temperature

The polar Kerr effect in the high-T_(c) superconductor YBa2Cu3O6+x was measured at zero magnetic field with high precision using a cyogenic Sagnac fiber interferometer. We observed nonzero Kerr rotations of order approximately 1 microrad appearing near the pseudogap temperature T(*) and marking what appears to be a true phase transition. Anomalous magnetic behavior in magnetic-field training of the effect suggests that time reversal symmetry is already broken above room temperature.

Stability of nodal quasiparticles in superconductors with coexisting orders

We establish a condition for the perturbative stability of zero energy nodal points in the quasiparticle spectrum of superconductors in the presence of coexisting commensurate orders. The nodes are found to be stable if the Hamiltonian is invariant under time reversal followed by a lattice translation. The principle is demonstrated with a few examples. Some experimental implications of various types of assumed order are discussed in the context of the cuprate superconductors.

Exact chiral spin liquid with non-Abelian anyons

We establish the existence of a chiral spin liquid (CSL) as the exact ground state of the Kitaev model on a decorated honeycomb lattice, which is obtained by replacing each site in the familiar honeycomb lattice with a triangle. This CSL state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSL's separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial (Chern number +/-1) CSL obey non-Abelian statistics.

Dynamical layer decoupling in a stripe-ordered high-T(c) superconductor

In the stripe-ordered state of a strongly correlated two-dimensional electronic system, under a set of special circumstances, the superconducting condensate, like the magnetic order, can occur at a nonzero wave vector corresponding to a spatial period double that of the charge order. In this case, the Josephson coupling between near neighbor planes, especially in a crystal with the special structure of La(2-x)Ba(x)CuO(4), vanishes identically. We propose that this is the underlying cause of the dynamical decoupling of the layers recently observed in transport measurements at x = 1/8.

Hysteresis and noise from electronic nematicity in high-temperature superconductors

An electron nematic is a translationally invariant state which spontaneously breaks the discrete rotational symmetry of a host crystal. In a clean square lattice, the electron nematic has two preferred orientations, while dopant disorder favors one or the other orientations locally. In this way, the electron nematic in a host crystal maps to the random field Ising model. Since the electron nematic has anisotropic conductivity, we associate each Ising configuration with a resistor network and use what is known about the random field Ising model to predict new ways to test for local electronic nematic order (nematicity) using noise and hysteresis. In particular, we have uncovered a remarkably robust linear relation between the orientational order and the resistance anisotropy which holds over a wide range of circumstances.

Gap-inhomogeneity-induced electronic states in superconducting Bi2Sr2CaCu2O(8+delta)

In this Letter, we analyze, using scanning tunneling spectroscopy, the density of electronic states in nearly optimally doped Bi2Sr2CaCu2O(8+delta) in zero magnetic field. Focusing on the superconducting gap, we find patches of what appear to be two different phases in a background of some average gap, one with a relatively small gap and sharp large coherence peaks and one characterized by a large gap with broad weak coherence peaks. We compare these spectra with calculations of the local density of states for a simple phenomenological model in which a 2xi0 x 2xi0 patch with an enhanced or suppressed d-wave gap amplitude is embedded in a region with a uniform average d-wave gap.

Incipient order in the t-J model at high temperatures

We analyze the high-temperature behavior of the susceptibilities towards a number of possible ordered states in the t-J-V model using the high-temperature series expansion. From all diagrams with up to ten edges, reliable results are obtained down to temperatures of order J, or (with some optimism) to J/2. In the unphysical regime, t<J, large superconducting susceptibilities are found which, moreover, increase with decreasing temperatures, but for t>J, these susceptibilities are small and decreasing with decreasing temperature; this suggests that the t-J model does not support high-temperature superconductivity. We also find modest evidence of a tendency toward nematic and d-density wave orders.

Spin-1 neutron resonance peak cannot account for electronic anomalies in the cuprate superconductors

In certain cuprates, a spin-1 resonance mode is prominent in the magnetic structure measured by neutron scattering. It has been proposed that this mode is responsible for significant features seen in other spectroscopies, such as photoemission and optical absorption, which are sensitive to the charge dynamics, and even that this mode is the boson responsible for "mediating" the superconducting pairing. We show that its small (measured) intensity and weak coupling to electron-hole pairs (as deduced from the measured lifetime) disqualifies the resonant mode from either proposed role.

Nodal quasiparticles in stripe ordered superconductors

We study the properties of a quasi-one-dimensional superconductor which consists of an alternating array of two inequivalent chains. This model is a simple caricature of a striped high temperature superconductor, and is more generally a theoretically controllable system in which the superconducting state emerges from a non-Fermi-liquid normal state. Even in this limit, " d-wave-like" order parameter symmetry is natural, but the superconducting state can either have a complete gap in the quasiparticle spectrum, or gapless "nodal" quasiparticles. We also find circumstances in which antiferromagnetic order (typically incommensurate) coexists with superconductivity.

Thermodynamics of the interplay between magnetism and high-temperature superconductivity

Copper-oxide-based high-temperature superconductors have complex phase diagrams with multiple ordered phases. It even appears that the highest superconducting transition temperatures for certain cuprates are found in samples that display simultaneous onset of magnetism and superconductivity. We show here how the thermodynamics of fluid mixtures-a touchstone for chemistry as well as hard and soft condensed matter physics-accounts for this startling observation, as well as many other properties of the cuprates in the vicinity of the instability toward "striped" magnetism.

Evidence of electron fractionalization from photoemission spectra in the high temperature superconductors

In the normal state of the high temperature superconductors Bi(2)Sr(2)CaCu(2)O(8+delta) and La2(-x)Sr(x)CuO4, and in the related "stripe ordered" material, La(1.25)Nd(0.6)Sr(0.15)CuO4, there is sharp structure in the measured single hole spectral function, A<(k-->,omega), considered as a function of k--> at fixed small binding energy omega. At the same time, as a function of omega at fixed k--> on much of the putative Fermi surface, any structure in A<(k-->,omega), other than the Fermi cutoff, is very broad. This is characteristic of the situation in which there are no stable excitations with the quantum numbers of the electron, as is the case in the one-dimensional electron gas.

Quantum theory of the smectic metal state in stripe phases

We present a theory of the electron smectic fixed point of the stripe phases of doped layered Mott insulators. We show that in the presence of a spin gap three phases generally arise: (a) a smectic superconductor, (b) an insulating stripe crystal, and (c) a smectic metal. The latter phase is a stable two-dimensional anisotropic non-Fermi liquid. In the absence of a spin gap there is also a more conventional Fermi-liquid-like phase. The smectic superconductor and smectic metal phases (or glassy versions thereof) may have already been seen in Nd-doped La2-xSrxCuO4.

Nematic phase of the two-dimensional electron gas in a magnetic field

The two-dimensional electron gas (2DEG) in moderate magnetic fields in ultraclean AlAs-GaAs heterojunctions exhibits transport anomalies suggestive of a compressible anisotropic metallic state. Using scaling arguments and Monte Carlo simulations, we develop an order parameter theory of an electron nematic phase. The observed temperature dependence of the resistivity anisotropy behaves like the orientational order parameter if the transition to the nematic state occurs at a finite temperature T(c) approximately 65 mK, and is slightly rounded by a small background microscopic anisotropy. We propose a light scattering experiment to measure the critical susceptibility.

Stripe phases in high-temperature superconductors

Stripe phases are predicted and observed to occur in a class of strongly correlated materials describable as doped antiferromagnets, of which the copper-oxide superconductors are the most prominent representatives. The existence of stripe correlations necessitates the development of new principles for describing charge transport and especially superconductivity in these materials.