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Steven A. Kivelson

Publications and source records attributed to Steven A. Kivelson.

At least 109 records · Page 6Linked to original sources
arXiv2017

Superconductivity and non-Fermi liquid behavior near a nematic quantum critical point

Using determinantal quantum Monte Carlo, we compute the properties of a lattice model with spin $\frac 1 2$ itinerant electrons tuned through a quantum phase transition to an Ising nematic phase. The nematic fluctuations induce superconductivity with a broad dome in the superconducting $T_c$ enclosing the nematic quantum critical point. For temperatures above $T_c$, we see strikingly non-Fermi liquid behavior, including a "nodal - anti nodal dichotomy" reminiscent of that seen in several transition metal oxides. In addition, the critical fluctuations have a strong effect on the low frequency optical conductivity, resulting in behavior consistent with "bad metal" phenomenology.

cond-mat.str-el↗
arXiv2017

Vestigial nematicity from spin and/or charge order in the cuprates

Nematic order has manifested itself in a variety of materials in the cuprate family. We propose an effective field theory of a layered system with incommensurate, intertwined spin- and charge-density wave (SDW and CDW) orders, each of which consists of two components related by $C_4$ rotations. Using a variational method (which is exact in a large $N$ limit), we study the development of nematicity from partially melting those density waves by either increasing temperature or adding quenched disorder. As temperature decreases we first find a transition to a nematic phase, but depending on the range of parameters (e.g. doping concentration) the strongest fluctuations associated with this phase reflect either proximate SDW or CDW order. We also discuss the changes in parameters that can account for the differences in the SDW-CDW interplay between the (214) family and the other hole-doped cuprates.

cond-mat.str-el↗
arXiv2016

Intertwined Order in a Frustrated 4-leg $t - J$ Cylinder

We report a density-matrix renormalization group study of the $t$-$J$ model with nearest ($t_1$ & $J_1$) and next-nearest ($t_2$ & $J_2$) interactions on a 4-leg cylinder with concentration $δ=1/8$ of doped holes. We observe an astonishingly complex interplay between uniform $d$-wave superconductivity (SC) and strong spin and charge density wave ordering tendencies (SDW and CDW). Depending on parameters, the CDWs can be commensurate with period 4 or 8. By comparing the charge ordering vectors with $2 k_F$, we rule out Fermi surface nesting-induced density wave order in our model. Magnetic frustration (i.e. $J_2/J_1 \sim 1/2$) significantly quenches SDW correlations with little effect on the CDW. Typically, the SC order is strongly modulated at the CDW ordering vector and exhibits $d$-wave symmetry around the cylinder. There is no evidence of a near-degenerate tendency to pair-density wave (PDW) ordering, charge 4e SC, or orbital current order.

cond-mat.str-el↗
arXiv2016

Fractional charge and emergent mass hierarchy in diagonal two-leg t-J cylinders

We define a new class of "diagonal" t-J ladders rotated by $π$/4 relative to the canonical lattice directions of the square lattice, and study it using density matrix renormalization group (DMRG). Here, we focus on the two-leg cylinder with a doped hole concentration near x = 1/4. At exactly x = 1/4, the system forms a period 4 charge density wave (CDW) and exhibits spin-charge separation. Slightly away from 1/4 doping we observe several topologically distinct types of solitons with well defined fractionalized quantum numbers. Remarkably, given the absence of any obvious small parameter, the effective masses of the emergent solitons differ by several orders of magnitude.

cond-mat.str-el↗
arXiv2016

Cold-spots and glassy nematicity in underdoped cuprates

There is now copious direct experimental evidence of various forms of (short-range) charge order in underdoped cuprate high temperature superconductors, and spectroscopic signatures of a nodal-antinodal dichotomy in the structure of the single-particle spectral functions. In this context, we analyze the Bogoliubov quasiparticle spectrum in a superconducting nematic glass. The coincidence of the superconducting "nodal points" and the nematic "cold-spots" on the Fermi surface naturally accounts for many of the most salient features of the measured spectral functions (from angle-resolved photoemission) and the local density of states (from scanning tunneling microscopy).

cond-mat.supr-con↗
arXiv2016

Non-quasiparticle transport and resistivity saturation: A view from the large-N limit

The electron dynamics in metals are usually well described by the semiclassical approximation for long-lived quasiparticles. However, in some metals, the scattering rate of the electrons at elevated temperatures becomes comparable to the Fermi energy; then, this approximation breaks down, and the full quantum-mechanical nature of the electrons must be considered. In this work, we study a solvable, large-$N$ electron-phonon model, which at high temperatures enters the non-quasiparticle regime. In this regime, the model exhibits "resistivity saturation" to a temperature-independent value of the order of the quantum of resistivity - the first analytically tractable model to do so. The saturation is not due to a fundamental limit on the electron lifetime, but rather to the appearance of a second conductivity channel. This is suggestive of the phenomenological "parallel resistor formula", known to describe the resistivity of a variety of saturating metals.

cond-mat.str-el↗
arXiv2016

Ising nematic quantum critical point in a metal: a Monte Carlo study

The Ising nematic quantum critical point (QCP) associated with the zero temperature transition from a symmetric to a nematic {\it metal} is an exemplar of metallic quantum criticality. We have carried out a minus sign-free quantum Monte Carlo study of this QCP for a two dimensional lattice model with sizes up to $24\times 24$ sites. The system remains non-superconducting down to the lowest accessible temperatures. The results exhibit critical scaling behavior over the accessible ranges of temperature, (imaginary) time, and distance. This scaling behavior has remarkable similarities with recently measured properties of the Fe-based superconductors proximate to their putative nematic QCP.

cond-mat.supr-con↗
arXiv2016

Charge-4e superconductors: a Majorana quantum Monte Carlo study

Many features of charge-4e superconductors remain unknown because even the "mean-field Hamiltonian" describing them is an interacting model. Here we introduce an interacting model to describe a charge-4e superconductor (SC) deep in the superconducting phase, and explore its properties using quantum Monte Carlo (QMC) simulations. The QMC is sign-problem-free, but only when a Majorana representation is employed. As a function of the chemical potential we observe two sharply-distinct behaviors: a "strong" quarteting phase in which charge-4e quartets are tightly bound (like molecules) so that charge-2e pairing does not occur even in the temperature $T \to 0$ limit, and a "weak" quarteting phase in which a further transition to a charge-2e superconducting phase occurs at a lower critical temperature. Analogous issues arise in a putative Z4 spin-liquid with a pseudo-Fermi surface and in characterizing charge-2e SCs with "odd frequency pairing" (or equivalently with a "composite order parameter") and metallic spin-nematics. Under certain circumstances, we also identified a stable T=0 charge-4e SC phase with gapless nodal quasiparticles. We further discuss possible relevance of our results to various experimental observations in 1/8-doped LBCO.

cond-mat.supr-con↗
arXiv2016

Ubiquitous signatures of nematic quantum criticality in optimally doped Fe-based superconductors

A key actor in the conventional theory of superconductivity is the induced interaction between electrons mediated by the exchange of virtual collective fluctuations, originally phonons. Other collective modes that can play the same role, especially spin-fluctuations, have been widely discussed in the context of high-temperature and heavy Fermion superconductors. The strength of such collective fluctuations is measured by the associated susceptibility. Here we use differential elastoresistance measurements on five optimally doped Fe-based superconductors to reveal that a diverging \emph{nematic} susceptibility appears to be a generic feature in the optimal doping regime of these materials. The observation motivates consideration of the effects of nematic fluctuations on the superconducting pairing interaction in this family of compounds, and possibly beyond.

cond-mat.supr-con↗
arXiv2016

Self Duality and a possible Hall-insulator phase near the superconductor-to-insulator transition in two-dimensional indium-oxide films

We combine measurements of the longitudinal ($ρ_{xx}$) and Hall ($ρ_{xy}$) resistivities of disordered two dimensional amorphous indium-oxide films to study the magnetic-field tuned superconductor to insulator transition (H-SIT) in the $T \to 0$ limit. At the critical field, $H_c$, the full resistivity tensor is $T$ independent with $ρ_{xx}(H_c) = h/4e^2$ and $ρ_{xy}(H_c)=0$ within experimental uncertainty in all films (i.e. these appear to be "universal" values), this is strongly suggestive that there is a particle-vortex self-duality at $H=H_c$. The transition separates the (presumably) superconducting state at $H H_c$, at which the Hall resistance is $T$ independent and roughly equal to its classical value, $ρ_{xy}\approx H/nec$, marks an additional crossover to a highfield regime (probably to a Fermi-insulator) in which $ρ_{xy} > H/nec$ and possibly diverges as $T\to 0$. We also highlight a profound analogy between the H-SIT and quantum-Hall liquid to insulator transitions (QHIT).

cond-mat.supr-con↗
arXiv2015

Fluctuating orders and quenched randomness in the cuprates

We study a quasi-2D classical Landau-Ginzburg-Wilson effective field theory in the presence of quenched disorder in which incommensurate charge-density wave and superconducting orders are intertwined. The disorder precludes long-range charge-density wave order, but not superconducting or nematic order. We select three representative sets of input parameters and compute the corresponding charge-density wave structure factors using both large-$N$ techniques and classical Monte Carlo simulations. Where nematicity and superconductivity coexist at low temperature, the peak height of the charge-density wave structure factor decreases monotonically as a function of increasing temperature, unlike what is seen in X-ray experiments on YBa$_2$Cu$_3$O$_{6+x}$. Conversely, where the thermal evolution of the charge-density wave structure factor qualitatively agrees with experiments, the nematic correlation length, computed to one-loop order, is shorter than the charge-density wave correlation length.

cond-mat.supr-con↗
arXiv2015

Band-structure effects on superconductivity in Hubbard models

We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find: 1) As a function of increasing nematicity, starting from the square lattice (zero nematicity) limit where nodal d-wave state is strongly preferred, there is a smooth evolution to the quasi-1D limit, where a striking near-degeneracy is found between a p-wave- and a d-wave-type paired states with accidental nodes on the quasi-one-dimensional Fermi surfaces---a situation which may be relevant to the Bechgaard salts. 2) In a bilayer system, we find a phase transition as a function of increasing bilayer coupling from a d-wave to an $s_{\pm}$-wave state reminiscent of the iron-based superconductors. 3) When an antinodal gap is produced by charge-density-wave order, not only is the pairing scale reduced, but the symmetry of the pairs switches from $d_{x^2-y^2} to $d_{xy}$; in the context of the cuprates, this suggests that were the pseudo-gap entirely due to a competing order, this would likely cause a corresponding symmetry change of the superconducting order (which is not seen in experiment).

cond-mat.supr-con↗
arXiv2015

Nematicity and quantum paramagnetism in FeSe

In common with other iron-based high temperature superconductors, FeSe exhibits a transition to a ``nematic'' phase below 90Kelvin in which the crystal rotation symmetry is spontaneously broken. However, the absence of strong low-frequency magnetic fluctuations near or above the transition has been interpreted as implying the primacy of orbital ordering. In contrast, we establish that quantum fluctuations of spin-1 local moments with strongly frustrated exchange interactions can lead to a nematic quantum paramagnetic phase consistent with the observations in FeSe. We show that this phase is a fundamental expression of the existence of a Berry's phase associated with the topological defects of a Néel antiferromagnet, in a manner analogous to that which gives rise to valence bond crystal order for spin 1/2 systems. We present an exactly solvable model realizing the nematic quantum paramagnetic phase, discuss its relation with the spin-1 $J_1-J_2$ model, and construct a field theory of the Landau-forbidden transition between the Néel state and this nematic quantum paramagnet.

cond-mat.str-el↗
arXiv2015

The almost mobility edge in the almost Mathieu equation

Harper's equation (aka the "almost Mathieu" equation) famously describes the quantum dynamics of an electron on a one dimensional lattice in the presence of an incommensurate potential with magnitude $V$ and wave number $Q$. It has been proven that all states are delocalized if $V$ is less than a critical value $V_c=2t$ and localized if $V> V_c$. Here, we show that this result (while correct) is highly misleading, at least in the small $Q$ limit. In particular, for $V E_c$, form a set of narrow bands with exponentially small bandwidths $ \sim t\ \exp[-(2πα/Q)]$ (where $α$ is an energy dependent number of order 1) separated by band-gaps $ \sim t Q$. Thus, the states with $|E|> E_c$ are "almost localized" in that they have an exponentially large effective mass and are easily localized by small perturbations. We establish this both using exact numerical solution of the problem, and by exploiting the well known fact that the same eigenvalue problem arises in the Hofstadter problem of an electron moving on a 2D lattice in the presence of a magnetic field, $B=Q/2π$. From the 2D perspective, the almost localized states are simply the Landau levels associated with semiclassical precession around closed contours of constant quasiparticle energy; that they are not truly localized reflects an extremely subtle form of magnetic breakdown.

cond-mat.mes-hall↗
arXiv2015

Theory of Intertwined Orders in High Temperature Superconductors

The electronic phase diagrams of many highly correlated systems, and in particular the cuprate high temperature superconductors, are complex, with many different phases appearing with similar-sometimes identical-ordering temperatures even as material properties, such as a dopant concentration, are varied over wide ranges. This complexity is sometimes referred to as "competing orders." However, since the relation is intimate, and can even lead to the existence of new phases of matter such as the putative "pair-density-wave," the general relation is better thought of in terms of "intertwined orders." We selectively analyze some of the experiments in the cuprates which suggest that essential aspects of the physics are reflected in the intertwining of multiple orders-not just in the nature of each order by itself. We also summarize and critique several theoretical ideas concerning the origin and implications of this complexity.

cond-mat.supr-con↗
arXiv2015

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 non-critical interactions, but $T_c$ is enhanced by the nematic fluctuations in all channels; 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.

cond-mat.supr-con↗