arXiv subjects

S. A. Kivelson

Publications and source records attributed to S. A. Kivelson.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Hall Liquids Coupled to Dynamical Electromagnetism

We investigate the effect on a Quantum Hall (QH) liquid of its coupling to 3+1 dimensional dynamical electromagnetism, which renders the system gapless. We calculate both the Hall and longitudinal resistances, $ρ_H$ and $ρ_L$, in the context of a minimal model of the electromagnetic environment, with a small three dimensional conductivity ${\tildeσ}$, that allows for a counter-flow current. In the thermodynamic limit, we show that $ρ_H$ is quantized, while $ρ_L$ approaches a non-zero limit, $ρ_L \sim α\, R_K$, where $α$ and $R_K=2π/e^2$ are the fine structure and the Klitzing constant. In contrast, the QH conductance, $σ_H$, is smaller than the expected quantized value by a correction $\sim α^2/R_K$. The electromagnetic interaction also generates corrections of order $α^2$ to the quasiparticle charges and statistics, in a way that is consistent with general arguments based on gauge invariance. In addition, we present an intuitive argument that relates the flux attachment associated with the composite boson representation of the electron liquid to the empirically observed %persistence of approximate quantization of $ρ_H$, even in circumstances in which $ρ_L$, and the deviation of $σ_H$ from its quantized value, are substantial.

cond-mat.mes-hall↗

arXiv2021

Mean Field Theories of Quantum Hall Liquids Justified: Variations on the Greiter Wilczek Theme

We present a field theoretic variant of the Wilczek - Greiter adiabatic approach to Quantum Hall liquids. Specifically, we define a Chern-Simons-Maxwell theory such that the flux-attachment mean field theory is exact in a certain limit. This permits a systematic way to justify a variety of useful approximate approaches to these problems as constituting the first term in a (still to be developed) systematic expansion about a solvable limit.

cond-mat.str-el↗

arXiv2021

Superconductivity, Charge-Density-Waves, and Bipolarons in the Holstein model

The electron-phonon (e-ph) interaction remains of great interest in condensed matter physics and plays a vital role in realizing superconductors, charge-density-waves (CDW), and polarons. We study the two-dimensional Holstein model for e-ph coupling using determinant quantum Monte Carlo across a wide range of its phase diagram as a function of temperature, electron density, dimensionless e-ph coupling strength, and the adiabatic ratio of the phonon frequency to the Fermi energy. We describe the behavior of the CDW correlations, the competition between superconducting and CDW orders and polaron formation, the optimal conditions for superconductivity, and the transition from the weak-coupling regime to the strong-coupling regime. Superconductivity is optimized at intermediate e-ph coupling strength and intermediate electron density, and the superconducting correlations increase monotonically with phonon frequency. The global maximum for superconductivity in the Holstein model occurs at large phonon frequency, the limit where an attractive Hubbard model effectively describes the physics.

cond-mat.str-el↗

arXiv2020

Floating topological phases

While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered quantum phases with an emergent 2+1 dimensional gauge symmetry can be asymptotically impervious to interplane couplings. We discuss the stability of such "floating topological phases", as well as their diagnosis by means of a non-local order parameter. Such a phase can produce a divergent ratio $ρ_{\perp}/ρ_{\parallel}$ of the inter-layer to intra-layer resistivity as $T\to 0$, even in an insulator where both $ρ_{\perp}$ and $ρ_\parallel$ individually diverge. Experimental observation of such a divergence would constitute proof of the existence of a topological (e.g. spin liquid) phase.

cond-mat.str-el↗

arXiv2019

Observation of two types of charge density wave orders in superconducting La$_{2-x}$Sr$_x$CuO$_4$

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$_{2-x}$Sr$_x$CuO$_4$ (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 $T_{\rm c}$. These findings indicate that the stripe orders and SC are inhomogeneously distributed in the superconducting CuO$_2$ planes of LSCO. This further suggests a new perspective on the putative pair-density-wave order that coexists with SC, SDW, and CDW orders.

cond-mat.supr-con↗

arXiv2019

Quantum Spin Liquids

Spin liquids are quantum phases of matter that exhibit a variety of novel features associated with their topological character. These include various forms of fractionalization - elementary excitations that behave as fractions of an electron. While there is not yet entirely convincing experimental evidence that any particular material has a spin liquid ground state, in the past few years, increasing evidence has accumulated for a number of materials suggesting that they have characteristics strongly reminiscent of those expected for a quantum spin liquid.

cond-mat.str-el↗

arXiv2019

Quenched disorder and vestigial nematicity in the pseudo-gap regime of the cuprates

We have carried out a theoretical analysis of the Landau-Ginzburg-Wilson effective field theory of a classical incommensurate CDW in the presence of weak quenched disorder. While the possibility a sharp phase transition and long-range CDW order are precluded in such systems, we show that any discrete symmetry breaking aspect of the charge order -- nematicity in the case of the unidirectional (stripe) CDW we consider explicitly -- generically survives up to a non-zero critical disorder strength. Such "vestigial order", which is subject to unambiguous macroscopic detection, can serve as an avatar of what would be CDW order in the ideal, zero disorder limit. Various recent experiments in the pseudo-gap regime of the hole-doped cuprate high-temperature superconductors are readily interpreted in light of these results.

cond-mat.str-el↗

arXiv2019

Fragile superconductivity in the presence of weakly disordered charge density waves

When superconducting (SC) and charge-density wave (CDW) orders compete, novel low temperature behaviors can result. From an analysis of the Landau-Ginzberg-Wilson theory of competing orders, we demonstrate the generic occurrence of a `fragile' SC phase at low temperatures and high fields in the presence of weak disorder. Here, the SC order is largely concentrated in the vicinity of dilute dislocations in the CDW order, leading to transition temperatures and critical currents that are parametrically smaller than those characterizing the zero field SC phase. This may provide the outline of an explanation of the recently discovered `resilient' superconducting phase at high fields in underdoped YBa$_2$Cu$_3$O$_{6+δ}$.

cond-mat.supr-con↗

arXiv2018

A bound on superconducting $T_c$'s

It is notoriously difficult to make quantitative theoretical predictions of the superconducting $T_c$, either from first-principles or even from a knowledge of normal state properties. Ultimately, this reflects the fact that the energy scales involved in the superconducting state are extremely small in natural units, and that $T_c$ depends exponentially on a subtle interplay between different interactions so that small uncertainties in microscopic processes can lead to order 1 effects on $T_c$. However, in some circumstances, it may be possible to determine (approximate) bounds on $T_c$. Here, we propose such a bound for the conventional phonon-mediated mechanism of pairing with strongly retarded interactions, i.e. in the case in which $\hbar\bar ω\ll E_F$ where $\bar ω$ is an appropriate characteristic phonon frequency and $E_F$ is the Fermi energy. Specifically, drawing on both empirical results (shown in Figure 2 below) and recent results[1] of determinant quantum Monte Carlo (DQMC) studies of the paradigmatic Holstein model, we propose that \begin{equation} k_B T_c \leq A_{max} \ \hbar \bar ω\end{equation} where $A_{max}$ is a dimensionless number of order one that we estimate to be \begin{equation} A_{max} \approx 1/10. \end{equation}

cond-mat.supr-con↗

arXiv2017

Evidence of a fractional quantum Hall nematic phase in a microscopic model

At small momenta, the Girvin-MacDonald-Platzman (GMP) mode in the fractional quantum Hall (FQH) effect can be identified with gapped nematic fluctuations in the isotropic FQH liquid. This correspondence would be exact as the GMP mode softens upon approach to the putative point of a quantum phase transition to a FQH nematic. Motivated by these considerations as well as by suggestive evidence of an FQH nematic in tilted field experiments, we have sought evidence of such a nematic FQHE in a microscopic model of interacting electrons in the lowest Landau level at filling factor 1/3. Using a family of anisotropic Laughlin states as trial wave functions, we find a continuous quantum phase transition between the isotropic Laughlin liquid and the FQH nematic. Results of numerical exact diagonalization also suggest that rotational symmetry is spontaneously broken, and that the phase diagram of the model contains both a nematic and a stripe phase.

cond-mat.str-el↗

arXiv2017

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 (DMRG) study of the $t$-$J$ model on a Kagome lattice with a small but non-zero concentration, $δ$, of doped holes. It is now widely accepted that the undoped ($δ=0$) spin 1/2 Heisenberg antiferromagnet has a spin-liquid groundstate. 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 (FL$^\ast$). 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 (WC). 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 (WC$^\ast$), rather than of holes. Our results may be relevant to Kagome lattice Herbertsmithite $\rm ZnCu_3(OH)_6Cl_2$ upon doping.

cond-mat.str-el↗

arXiv2017

The Hall number across a van Hove singularity

In the context of the relaxation time approximation to Boltzmann transport theory, we examine the behavior of the Hall number, $n_H$, of a metal in the neighborhood of a Lifshitz transition from a closed Fermi surface to open sheets. We find a universal non-analytic dependence of $n_H$ on the electron density in the high field limit, but a non-singular dependence at low fields. The existence of an assumed nematic transition produces a doping dependent $n_H$ similar to that observed in recent experiments in the high temperature superconductor YBa$_2$Cu$_3$O$_{7-x}$.

cond-mat.str-el↗

arXiv2016

Ideal charge density wave order in the high-field state of superconducting YBCO

The existence of charge density wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the ground state order has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to a dozen unit cells or less. Here we explore the CDW correlations in YBa2Cu3Ox (YBCO) ortho-II and ortho-VIII crystals, which belong to the cleanest available cuprate family, at magnetic fields in excess of the resistive upper critical field (Hc2) where the superconductivity is heavily suppressed. We find an incommensurate, unidirectional CDW with a well-defined onset at a critical field strength that is proportional to Hc2. It is related to but distinct from the short-range bidirectional CDW that exists at zero magnetic field. The unidirectional CDW possesses a long inplane correlation length as well as significant correlations between neighboring CuO2 planes, yielding a correlation volume that is at least 2 - 3 orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground-state of an "ideal" disorder-free cuprate.

cond-mat.str-el↗

arXiv2016

Vestigial chiral and charge orders from bidirectional spin-density waves: Application to the iron-based superconductors

Recent experiments in optimally hole-doped iron arsenides have revealed a novel magnetically ordered ground state that preserves tetragonal symmetry, consistent with either a charge-spin density wave (CSDW), which displays a non-uniform magnetization, or a spin-vortex crystal (SVC), which displays a non-collinear magnetization. Here we show that, similarly to the partial melting of the usual stripe antiferromagnet into a nematic phase, either of these phases can also melt in two stages. As a result, intermediate paramagnetic phases with vestigial order appears: a checkerboard charge density-wave for the CSDW ground state, characterized by an Ising-like order parameter, and a remarkable spin-vorticity density-wave for the SVC ground state -- a triplet d-density wave characterized by a vector chiral order parameter. We propose experimentally detectable signatures of these phases, show that their fluctuations can enhance the superconducting transition temperature, and discuss their relevance to other correlated materials.

cond-mat.supr-con↗

arXiv2015

Quantum oscillations in a bilayer with broken mirror symmetry: a minimal model for YBa$_2$Cu$_3$O$_{6 + δ}$

Using an exact numerical solution and semiclassical analysis, we investigate quantum oscillations (QOs) in a model of a bilayer system with an anisotropic (elliptical) electron pocket in each plane. Key features of QO experiments in the high temperature superconducting cuprate YBCO can be reproduced by such a model, in particular the pattern of oscillation frequencies (which reflect "magnetic breakdown" between the two pockets) and the polar and azimuthal angular dependence of the oscillation amplitudes. However, the requisite magnetic breakdown is possible only under the assumption that the horizontal mirror plane symmetry is spontaneously broken and that the bilayer tunneling, $t_\perp$, is substantially renormalized from its `bare' value. Under the assumption that $t_\perp= \tilde{Z}t_\perp^{(0)}$, where $\tilde{Z}$ is a measure of the quasiparticle weight, this suggests that $\tilde{Z} \lesssim 1/20$. Detailed comparisons with new YBa$_2$Cu$_3$O$_{6.58}$ QO data, taken over a very broad range of magnetic field, confirm specific predictions made by the breakdown scenario.

cond-mat.str-el↗

arXiv2015

Macroscopic character of composite high temperature superconducting wires

The "d-wave" symmetry of the superconducting order in the cuprate high temperature superconductors is a well established fact, and one which identifies them as "unconventional." However, in macroscopic contexts -- including many potential applications ({\it i.e.} superconducting "wires") -- the material is a composite of randomly oriented superconducting grains in a metallic matrix, in which Josephson coupling between grains mediates the onset of long-range phase coherence. Here, we analyze the physics at length scales large compared to the size of such grains, and in particular the macroscopic character of the long-range order that emerges. While XY-glass order and macroscopic d-wave superconductivity may be possible, we show that under many circumstances -- especially when the d-wave superconducting grains are embedded in a metallic matrix -- the most likely order has global s-wave symmetry.

cond-mat.supr-con↗

arXiv2015

Three-Dimensional Charge Density Wave Order in YBa2Cu3O6.67 at High Magnetic Fields

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

cond-mat.str-el↗

arXiv2015

One hole in the two-leg t-J ladder and adiabatic continuity to the non-interacting limit

We have carried 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 the DMRG results can be qualitatively understood from a non-interacting "band-structure" perspective.

cond-mat.str-el↗