arXiv subjects

Steven Kivelson

Publications and source records attributed to Steven Kivelson.

14 recordsLinked to original sources

arXiv2024

Emergent Gauge Fields in Band Insulators

By explicit microscopic construction involving a mapping to a quantum vertex model subject to the `ice rule,' we show that an electronically `trivial' band insulator with suitable vibrational (phonon) degrees of freedom can host a ``resonating valence-bond'' state - a quantum phase with emergent gauge fields. This novel type of band insulator is identifiable by the existence of emergent gapless `photon' modes and deconfined excitations, the latter of which carry non-quantized mobile charges. We suggest that such phases may exist in the quantum regimes of various nearly ferroelectric materials.

cond-mat.str-el↗

arXiv2022

To See a World in a Grain of Sand -- The Scientific Life of Shoucheng Zhang

Our friend and colleague, Prof. Shoucheng Zhang, passed away in 2018, which was a great loss for the entire physics community. For all of us who knew Shoucheng, it is difficult to overcome the sadness and shock of his early departure. However, we are very fortunate that Shoucheng has left us such a rich legacy and so many memories in his 55 years of life as a valuable friend, a world-leading physicist, a remarkable advisor, and a great thinker. On May 2-4, 2019, a memorial workshop for Shoucheng was organized at Stanford University, where we displayed a small exhibition of 12 posters, as a brief overview of Shoucheng's wonderful scientific life. This article is prepared based on those posters.

physics.hist-ph↗

arXiv2021

The Hubbard Model

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems, and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology which is reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model, based on exact results or controlled approximate solutions in various limits, for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions, although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions.

cond-mat.str-el↗

arXiv2018

Pseudogap crossover in the electron-phonon system

Thermodynamic properties of the square-lattice Holstein model of the electron-phonon problem with phonon frequencies small compared to the bare Fermi energy are obtained using Monte Carlo methods, a strong-coupling (bipolaronic) expansion, and a weak coupling Migdal-Eliashberg approach. Already at elevated temperatures where the charge-density wave (CDW) and superconducting (SC) correlations are very short-range, a crossover occurs as a function of increasing electron-phonon coupling, $\lambda_0$, from a normal metallic regime to a pseudogap regime. At sufficiently low $T$, a SC phase is found for small $\lambda_0$ and a commensurate insulating CDW phase for large $\lambda_0$.

cond-mat.str-el↗

arXiv2015

Electronic Pair-Binding and Hund's Rule Violations in Doped $C_{60}$

We calculate the electronic properties of the $t$-$J$ model on a $C_{60}$ molecule using the density-matrix renormalization group and show that Hund's first rule is violated and that for an average of three added electron per molecule, an effective attraction (pair-binding) arises for intermediate values of $t/J$. Specifically, it is energetically favorable to put four electrons on one $C_{60}$ and two on a second rather than putting three on each. Our results show that a dominantly electronic mechanism of superconductivity is possible in doped $C_{60}$.

cond-mat.str-el↗

arXiv2014

Coherent Transmutation of Electrons into Fractionalized Anyons

Electrons have three quantized properties -- charge, spin, and Fermi statistics -- that are directly responsible for a vast array of phenomena. Here we show how these properties can be coherently and dynamically stripped from the electron as it enters certain exotic states of matter known as a quantum spin liquid (QSL). In a QSL, electron spins collectively form a highly entangled quantum state that gives rise to emergent gauge forces and fractionalization of spin, charge, and statistics. We show that certain QSLs host distinct, topologically robust boundary types, some of which allow the electron to coherently enter the QSL as a fractionalized quasiparticle, leaving its spin, charge, or statistics behind. We use these ideas to propose a number of universal, conclusive experimental signatures that would establish fractionalization in QSLs.

cond-mat.str-el↗

arXiv2006

A Magnetic Model of the Tetragonal-Orthorhombic Transition in the Cuprates

It is shown that a quasi two dimensional (layered) Heisenberg antiferromagnet with fully frustrated interplane couplings ({\it e.g.} on a body-centered tetragonal lattice) generically exhibits two thermal phase transitions with lowering temperature -- an upper transition at $T_{TO}$ (``order from disorder without order'') in which the lattice point-group symmetry is spontaneously broken, and a lower Néel transition at $T_{N}$ at which spin-rotation symmetry is broken. Although this is the same sequence of transitions observed in La$_2$CuO$_4$, in the Heisenberg model (without additional lattice degrees of freedom) $(T_{TO}-T_N) /T_N$ is much smaller than is observed. The model may apply to the bilayer cuprate La$_2$CaCuO$_6$, in which the transitions are nearly coincident.

cond-mat.str-el↗

arXiv2004

Universal Aspects of Coulomb Frustrated Phase Separation

We study the consequences of Coulomb interactions on a system undergoing a putative first order phase transition. In two dimensions (2D), near the critical density, the system is universally unstable to the formation of new intermediate phases, which we call ``electronic microemulsion phases,'' which consist of an intermediate scale mixture of regions of the two competing phases. A correlary is that there can be no direct transition as a function of density from a 2D Wigner crystal to a uniform electron liquid. In 3D, %we find that if the strength of the Coulomb interactions exceeds a critical value, no phase separation occurs, while for weaker Coulomb strength, electronic microemulsions are inevitable. This tendency is considerably more pronounced in anisotropic (quasi 2D or quasi 1D) systems, where a devil's staircase of transitions is possible.

cond-mat.mes-hall↗

arXiv2001

Making High T$_c$ Higher: A Theoretical Proposal

There is considerable evidence that the highest $T_c$ obtainable in a copper-oxide plane is limitted by the competition between two effects: On the one hand, as the concentration of doped-holes, $ x$, is increased, the pairing scale, which is related to the properties of a doped Mott insulator, decreases. On the otherhand, the superfluid density, which controls the stiffness of the system to phase fluctuations, vanishes as $x \to 0$, and increases with increasing $x$. Optimal $T_c$ is obtained at a crossover from a phase ordering dominated regime at small $x$ to a pairing dominated regime at large $x$. If this description is valid, then higher $T_c$'s can be obtained in an array of coupled planes with different doped hole concentrations, such that a high pairing scale is derived from the underdoped planes and a large phase stiffness from the optimally or overdoped ones.

cond-mat.str-el↗

arXiv2001

Josephson tunnelling spectroscopy of negative U centers

We consider a superconductor-insulator-superconductor (SIS) junction in which the tunnelling through the insulating barrier is dominated by a localized ``negative U'' center. We show that the $I_{c}R$ product of the junction depends sensitively on the spectrum of impurity states, and in near resonant condiditions exhibits an anomalously large I$_c$R product which can exceed the famous Ambegoakar-Baratoff limit by an arbitrarily large factor. The analysis is extended to problems in which there is an array of negative U centers in the junction. We also discuss general reasons to expect significant violations of the optical conductivity sum rule in most SIS junctions and of the Ambegoakar-Baratoff result when the superconductors emerge from a non-Fermi liquid normal state.

cond-mat.supr-con↗

arXiv2001

Quantum Theory of a Nematic Fermi Fluid

We develop a microscopic theory of the electronic nematic phase proximate to an isotropic Fermi liquid in both two and three dimensions. Explicit expressions are obtained for the small amplitude collective excitations in the ordered state; remarkably, the nematic Goldstone mode (the directorwave) is overdamped except along special directions dictated by symmetry. At the quantum critical point we find a dynamical exponent of $z=3$, implying stability of the gaussian fixed point. The leading perturbative effect of the overdamped Goldstone modes leads to a breakdown of Fermi liquid theory in the nematic phase and to strongly angle dependent electronic self energies around the Fermi surface. Other metallic liquid crystal phases, {\it e. g.} a quantum hexatic, behave analogously.

cond-mat.str-el↗

arXiv1998

Wigner Glass, Spin-liquids, and the Metal-Insulator Transition

Recent experiments on the two dimensional electron gas in various semiconductor devices have revealed an unexpected metal-insulator transition and have challenged the previously held assumption that there is no such transition in two dimensions. While the experiments are still at the stage of rapid development, it is becoming evident that they cannot be understood from the conventional perspective of weak interactions. In the present paper, we propose the following. (1) The low-density insulating state is the Wigner Glass, a phase with quasi-long-range translational order and competing ferromagnetic and antiferromagnetic spin-exchange interactions. (2) The transition is the melting of this Wigner Glass, disorder being the agent allowing the transition to be second order. (3) Within the Wigner Glass phase, there are at least two, distinct magnetic ground-states, a ferromagnetic state at very low electron density and a spin-liquid state with a spin pseudo-gap at higher densities. (4) The metallic side of the transition is a non-Fermi liquid. These conclusions are encapsulated in Figure 1 which presents the proposed phase diagram as a function of disorder strength and density; we also suggest experimental signatures of the various phases and transitions.

cond-mat.str-el↗

arXiv1998

Instability of charge ordered states in doped antiferromagnets

We analyze the induced interactions between localized holes in weakly-doped Heisenberg antiferromagnets due to the modification of the quantum zero point spin wave energy; i.e. the analogue of the Casimir effect. We show that this interaction is uniformly attractive and falls off as r^{-2 d+1} in d dimensions. For ``stripes'', i.e parallel (d-1)-dimensional hypersurfaces of localized holes, the interaction energy per unit hyperarea is attractive and falls, generically, like r^{-d}. We argue that, in the absence of a long-range Coulomb repulsion between holes, this interaction leads to an instability of any charge-ordered state in the dilute doping limit.

cond-mat↗

arXiv1996

Modular Invariance, Self-Duality and The Phase Transition Between Quantum Hall Plateaus

We investigate the problem of the superuniversality of the phase transition between different quantum Hall plateaus. We construct a set of models which give a qualitative description of this transition in a pure system of interacting charged particles. One of the models is manifestly invariant under both Duality and Periodic shifts of the statistical angle and, hence, it has a full Modular Invariance. We derive the transformation laws for the correlation functions under the modular group and use them to derive symmetry constraints for the conductances. These allow us to calculate exactly the conductivities at the modular fixed points. We show that, at least at the modular fixed points, the system is critical. Away from the fixed points, the behavior of the model is determined by extra symmetries such as Time Reversal. We speculate that if the natural connection between spin and statistics holds, the model may exhibit an effective analyticity at low energies. In this case, the conductance is completely determined by its behavior under modular transformations.

cond-mat↗