arXiv subjects

Steven A. Kivelson

Publications and source records attributed to Steven A. Kivelson.

At least 145 records · Page 8Linked to original sources

arXiv2009

Striped superconductors: How the cuprates intertwine spin, charge and superconducting orders

Recent transport experiments in the original cuprate high temperature superconductor, {La$_{2-x}$Ba$_x$CuO$_4$}, have revealed a remarkable sequence of transitions and crossovers which give rise to a form of dynamical dimensional reduction, in which a bulk crystal becomes essentially superconducting in two directions while it remains poorly metallic in the third. We identify these phenomena as arising from a distinct new superconducting state, the "striped superconductor," in which the superconducting order is spatially modulated, so that its volume average value is zero. Here, in addition to outlining the salient experimental findings, we sketch the order parameter theory of the state, stressing some of the ways in which a striped superconductor differs fundamentally from an ordinary (uniform) superconductor, especially concerning its response to quenched randomness. We also present the results of DMRG calculations on a model of interacting electrons in which sign oscillations of the superconducting order are established. Finally, we speculate concerning the relevance of this state to experiments in other cuprates, including recent optical studies of {La$_{2-x}$Sr$_x$CuO$_4$} in a magnetic field, neutron scattering experiments in underdoped {YBa$_2$Cu$_3$O$_{6+x}$}, and a host of anomalies seen in STM and ARPES studies of {Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ} $}.

cond-mat.supr-con↗

arXiv2009

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 non-interacting level, we show that a QBCP exists and is topologically stable for a Berry flux $\pm 2π$, if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to {\em 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.

cond-mat.str-el↗

arXiv2009

Theory of the striped superconductor

We define a distinct phase of matter, a "pair density wave" (PDW), in which the superconducting order parameter $ϕ$ varies periodically as a function of position such that when averaged over the center of mass position, all components of $ϕ$ vanish identically. Specifically, we study the simplest, unidirectional PDW, the "striped superconductor," which we argue may be at the heart of a number of spectacular experimental anomalies that have been observed in the failed high temperature superconductor, La$_{2-x}$ Ba$_x$CuO$_4$. We present a solvable microscopic model with strong electron-electron interactions which supports a PDW groundstate. We also discuss, at the level of Landau theory, the nature of the coupling between the PDW and other order parameters, and the origins and some consequences of the unusual sensitivity of this state to quenched disorder.

cond-mat.supr-con↗

arXiv2008

Fe-based superconductors: unity or diversity?

Does the high temperature superconductivity observed in the newly discovered iron-pnictide materials represent another example of the same essential physics responsible for superconductivity in the cuprates, or does it embody a new mechanism?

cond-mat.str-el↗

arXiv2008

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 are gapless with a linear dispersion, while the topological "vison" excitations are gapped. Moreover, the massless Dirac fermions are 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."

cond-mat.str-el↗

arXiv2008

The Optimal Inhomogeneity for Superconductivity: Finite Size Studies

We report the results of exact diagonalization studies of Hubbard models on a $4\times 4$ square lattice with periodic boundary conditions and various degrees and patterns of inhomogeneity, which are represented by inequivalent hopping integrals $t$ and $t^{\prime}$. We focus primarily on two patterns, the checkerboard and the striped cases, for a large range of values of the on-site repulsion $U$ and doped hole concentration, $x$. We present evidence that superconductivity is strongest for $U$ of order the bandwidth, and intermediate inhomogeneity, $0 <t^\prime< t$. The maximum value of the ``pair-binding energy'' we have found with purely repulsive interactions is $Δ_{pb} = 0.32t$ for the checkerboard Hubbard model with $U=8t$ and $t^\prime = 0.5t$. Moreover, for near optimal values, our results are insensitive to changes in boundary conditions, suggesting that the correlation length is sufficiently short that finite size effects are already unimportant.

cond-mat.supr-con↗

arXiv2008

Theory of the nodal nematic quantum phase transition in superconductors

We study the character of an Ising nematic quantum phase transition (QPT) deep inside a d-wave superconducting state with nodal quasiparticles in a two-dimensional tetragonal crystal. We find that, within a 1/N expansion, the transition is continuous. To leading order in 1/N, quantum fluctuations enhance the dispersion anisotropy of the nodal excitations, and cause strong scattering which critically broadens the quasiparticle (qp) peaks in the spectral function, except in a narrow wedge in momentum space near the Fermi surface where the qp's remain sharp. We also consider the possible existence of a nematic glass phase in the presence of weak disorder. Some possible implications for cuprate physics are also discussed.

cond-mat.supr-con↗

arXiv2008

Theory of Electron Nematic Order in LaOFeAs

We study a spin $S$ quantum Heisenberg model on the Fe lattice of the rare-earth oxypnictide superconductors. Using both large $S$ and large $N$ methods, we show that this model exhibits a sequence of two phase transitions: from a high temperature symmetric phase to a narrow region of intermediate ``nematic'' phase, and then to a low temperature spin ordered phase. Identifying phases by their broken symmetries, these phases correspond precisely to the sequence of structural (tetragonal to monoclinic) and magnetic transitions that have been recently revealed in neutron scattering studies of LaOFeAs. The structural transition can thus be identified with the existence of incipient (``fluctuating'') magnetic order.

cond-mat.str-el↗

arXiv2008

Superconductivity in zigzag CuO chains

Superconductivity has recently been discovered in Pr$_{2}$Ba$_{4}$Cu$_{7}$O$_{15-δ}$ with a maximum $T_c$ of about 15K. Since the CuO planes in this material are believed to be insulating, it has been proposed that the superconductivity occurs in the double (or zigzag) CuO chain layer. On phenomenological grounds, we propose a theoretical interpretation of the experimental results in terms of a new phase for the zigzag chain, labelled by C$_1$S$_{3/2}$. This phase has a gap for some of the relative spin and charge modes but no total spin gap, and can have a divergent superconducting susceptibility for repulsive interactions. A microscopic model for the zigzag CuO chain is proposed, and on the basis of density matrix renormalization group (DMRG) and bosonization studies of this model, we adduce evidence that supports our proposal.

cond-mat.supr-con↗

arXiv2007

An 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. The CSL state spontaneously breaks time reversal symmetry but preserves other symmetries. There are two topologically distinct CSLs separated by a quantum critical point. Interestingly, vortex excitations in the topologically nontrivial (Chern number $\pm 1$) CSL obey non-Abelian statistics.

cond-mat.str-el↗

arXiv2007

Myriad phases of the Checkerboard Hubbard Model

The zero temperature phase diagram of the checkerboard Hubbard model is obtained in the solvable limit in which it consists of weakly coupled square plaquettes. As a function of the on-site Coulomb repulsion U and the density of holes per site, x, we demonstrate the existence of at least 16 distinct phases. For instance, at zero doping, the ground state is a novel d-wave Mott insulator (d-Mott), which is not adiabatically continuable to a band insulator; by doping the d-Mott state with holes, depending on the magnitude of U, it gives way to a d-wave superconducting state, a two-flavor spin-1/2 Fermi liquid (FL), or a spin-3/2 FL.

cond-mat.str-el↗

arXiv2007

Superconductivity in Inhomogeneous Hubbard Models

We present a controlled perturbative approach to the low temperature phase diagram of highly inhomogeneous Hubbard models in the limit of small coupling, $t'$, between clusters. We apply this to the dimerized and checkerboard models. The dimerized model is found to behave like a doped semiconductor, with a Fermi-liquid groundstate with parameters ({\it e.g.} the effective mass) which are smooth functions of the Hubbard interaction, $U$. By contrast, the checkerboard model has a nodeless d-wave superconducting state (preformed pair condensate, $d$-BEC) for $0 < U < U_c$, which smoothly crosses over to an intermediate BCS-like superconducting phase ($d$-BCS), also with no nodal quasi-particles, for $|U - U_c| < {\cal O}(t^\prime)$, which gives way to a Fermi liquid phase at large $U > U_c = 4.58$.

cond-mat.str-el↗

arXiv2007

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 non-zero 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_xCuO_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.

cond-mat.str-el↗

arXiv2007

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, 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. ERRATUM: Due to an error in the calculation, the series for d-wave supeconducting and extended s-wave superconducting orders were incorrect. We recalculate the series and give the replacement figures. In agreement with our earlier findings, we still find no evidence of any strong enhancement of the superconducting susceptibility with decreasing temperature. However, because different Pade approximants diverge from each other at somewhat higher temperatures than we originally found, it is less clear what this implies concerning the presence or absence of high-temperature superconductivity in the t-J model.

cond-mat.str-el↗

arXiv2006

On the absence of ferromagnetism in typical 2D ferromagnets

We consider the Ising systems in $d$ dimensions with nearest-neighbor ferromagnetic interactions and long-range repulsive (antiferromagnetic) interactions which decay with a power, $s$, of the distance. The physical context of such models is discussed; primarily this is $d=2$ and $s=3$ where, at long distances, genuine magnetic interactions between genuine magnetic dipoles are of this form. We prove that when the power of decay lies above $d$ and does not exceed $d+1$, then for all temperatures, the spontaneous magnetization is zero. In contrast, we also show that for powers exceeding $d+1$ (with $d\ge2$) magnetic order can occur.

math-ph↗

arXiv2006

Theory of stripes in quasi two dimensional rare-earth tritellurides

Even though the rare-earth tritellurides are tetragonal materials with a quasi two dimensional (2D) band structure, they have a "hidden" 1D character. The resultant near-perfect nesting of the Fermi surface leads to the formation of a charge density wave (CDW) state. We show that for this band structure, there are two possible ordered phases: A bidirectional "checkerboard" state would occur if the CDW transition temperature were sufficiently low, whereas a unidirectional "striped" state, consistent with what is observed in experiment, is favored when the transition temperature is higher. This result may also give some insight into why, in more strongly correlated systems, such as the cuprates and nickelates, the observed charge ordered states are generally stripes as opposed to checkerboards.

cond-mat.str-el↗

arXiv2006

Distinguishing Patterns of Charge Order: Stripes or Checkerboards

In two dimensions, quenched disorder always rounds transitions involving the breaking of spatial symmetries so, in practice, it can often be difficult to infer what form the symmetry breaking would take in the ``ideal,'' zero disorder limit. We discuss methods of data analysis which can be useful for making such inferences, and apply them to the problem of determining whether the preferred order in the cuprates is ``stripes'' or ``checkerboards.'' In many cases we show that the experiments clearly indicate stripe order, while in others (where the observed correlation length is short), the answer is presently uncertain.

cond-mat.str-el↗

arXiv2005

How optimal inhomogeneity produces high temperature superconductivity

Before Vic Emery's untimely death, we had the privilege of working closely with him on the role of Coulomb frustrated phase separation in doped Mott insulators, and on the consequences of the resulting local electronic structures on the "mechanism" of high temperature superconductivity. In the present article, we discuss the resulting perspective on superconductivity in the cuprates, and on the more general theoretical issue of what sorts of systems can support high temperature superconductivity. We discuss some of the general, qualitative aspects of the experimental lore which we think should constrain any theory of the mechanism, and show how they are accounted for within the context of our theory.

cond-mat.supr-con↗