Electronic Liquid Crystal Phases of a Doped Mott Insulator

The character of the ground state of an antiferromagnetic insulator is fundamentally altered upon addition of even a small amount of charge. The added charges agglomerate along domain walls at which the spin correlations, which may or may not remain long-ranged, suffer a $\pi$ phase shift. In two dimensions, these domain walls are ``stripes'' which are either insulating, or conducting, i.e. metallic rivers with their own low energy degrees of freedom. However, quasi one-dimensional metals typically undergo a transition to an insulating ordered charge density wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large in comparison to the CDW coupling between stripes. As a consequence, there exist novel, liquid-crystalline low-temperature phases -- an electron smectic, with crystalline order in one direction, but liquid-like correlations in the other, and an electron nematic with orientational order but no long-range positional order. These phases, which constitute new states of matter, can be either high temperature supeconductors or two-dimensional anisotropic ``metallic'' non-Fermi liquids. Evidence for the new phases may already have been obtained by neutron scattering experiments in the cuprate superconductor, La_{1.6-x}Nd_{0.4}Sr_xCuO_{4}.Comment: 5 pages in RevTex with two figures in ep

Thermally fluctuating superconductors in two dimensions

We describe the different regimes of finite temperature dynamics in the vicinity of a zero temperature superconductor to insulator quantum phase transition in two dimensions. New results are obtained for a low temperature phase-only hydrodynamics, and for the intermediate temperature quantum-critical region. In the latter case, we obtain a universal relationship between the frequency-dependence of the conductivity and the value of the d.c. resistance.Comment: Presentation completely revised; 4 pages, 2 figure

The connection between superconducting phase correlations and spin excitations in YBa2_2Cu3_3O6.6_{6.6}: A magnetic field study

One of the most striking universal properties of the high-transition-temperature (high-$T_c$) superconductors is that they are all derived from the hole-doping of their insulating antiferromagnetic (AF) parent compounds. From the outset, the intimate relationship between magnetism and superconductivity in these copper-oxides has intrigued researchers. Evidence for this link comes from neutron scattering experiments that show the unambiguous presence of short-range AF correlations (excitations) in cuprate superconductors. Even so, the role of such excitations in the pairing mechanism and superconductivity is still a subject of controversy. For YBa$_2$Cu$_3$O$_{6+x}$, where $x$ controls the hole-doping level, the most prominent feature in the magnetic excitations spectra is the ``resonance''. Here we show that for underdoped YBa$_2$Cu$_3$O$_{6.6}$, where $x$ and $T_c$ are below the optimal values, modest magnetic fields suppress the resonance significantly, much more so for fields approximately perpendicular rather than parallel to the CuO$_2$ planes. Our results indicate that the resonance measures pairing and phase coherence, suggesting that magnetism plays an important role in the superconductivity of cuprates. The persistence of a field effect above $T_c$ favors mechanisms with preformed pairs in the normal state of underdoped cuprates.Comment: 12 pages, 4 figures, Nature (in press

Vanishing of phase coherence in underdoped Bi_2Sr_2CaCu_2O_8+d

Coherent time-domain spectroscopy is used to measure the screening and dissipation of high-frequency electromagnetic fields in a set of underdoped Bi_2Sr_2CaCu_2O_8+d thin films. The measurements provide direct evidence for a phase-fluctuation driven transition from the superconductor to normal state, with dynamics described well by the Berezinskii-Kosterlitz-Thouless theory of vortex-pair unbinding.Comment: Nature, Vol. 398, 18 March 1999, pg. 221 4 pages with 4 included figure

A Common Origin for Neutrino Anarchy and Charged Hierarchies

The generation of exponential flavor hierarchies from extra-dimensional wavefunction overlaps is re-examined. We find, surprisingly, that coexistence of anarchic fermion mass matrices with such hierarchies is intrinsic and natural to this setting. The salient features of charged fermion and neutrino masses and mixings can thereby be captured within a single framework. Both Dirac and Majorana neutrinos can be realized. The minimal phenomenological consequences are discussed, including the need for a fundamental scale far above the weak scale to adequately suppress flavor-changing neutral currents. Two broad scenarios for stabilizing this electroweak hierarchy are studied, warped compactification and supersymmetry. In warped compactifications and "Flavorful Supersymmetry," where non-trivial flavor structure appears in the new TeV physics, Dirac neutrinos are strongly favored over Majorana by lepton flavor violation tests. We argue that this is part of a more general result for flavor-sensitive TeV-scale physics. Our scenario strongly suggests that the supersymmetric flavor problem is not solved locally in the extra dimension, but rather at or below the compactification scale. In the supersymmetric Dirac case, we discuss how the appearance of light right-handed sneutrinos considerably alters the physics of dark matter.Comment: Comparison with the Froggatt-Nielsen mechanism omitted. Some clarifications added. This is the version accepted by PRL with a longer abstract

Low temperature vortex liquid in La2−xSrxCuO4\rm La_{2-x}Sr_xCuO_4

In the cuprates, the lightly-doped region is of major interest because superconductivity, antiferromagnetism, and the pseudogap state \cite{Timusk,Lee,Anderson} come together near a critical doping value $x_c$. These states are deeply influenced by phase fluctuations \cite{Emery} which lead to a vortex-liquid state that surrounds the superconducting region \cite{WangPRB01,WangPRB06}. However, many questions \cite{Doniach,Fisher,FisherLee,Tesanovic,Sachdev} related to the nature of the transition and vortex-liquid state at very low tempera- tures $T$ remain open because the diamagnetic signal is difficult to resolve in this region. Here, we report torque magnetometry results on $\rm La_{2-x}Sr_xCuO_4$ (LSCO) which show that superconductivity is lost at $x_c$ by quantum phase fluctuations. We find that, in a magnetic field $H$, the vortex solid-to-liquid transition occurs at field $H_m$ much lower than the depairing field $H_{c2}$. The vortex liquid exists in the large field interval $H_m \ll H_{c2}$, even in the limit $T\to$0. The resulting phase diagram reveals the large fraction of the $x$-$H$ plane occupied by the quantum vortex liquid.Comment: 6 pages, 4 figures, submitted to Nature Physic

One-dimensional nature of the magnetic fluctuations in YBa2_2Cu3_3O6.6_{6.6}

There is increasing evidence that inhomogeneous distributions of charge and spin--so-called "striped phases"--play an important role in determining the properties of the high-temperature superconductors. For example, recent neutron-scattering measurements on the YBa$_2$Cu$_3$O$_{7-x}$ family of materials show both spin and charge fluctuations that are consistent with the striped-phase picture. But the fluctuations associated with a striped phase are expected to be one-dimensional, whereas the magnetic fluctuations observed to date appear to display two-dimensional symmetry. We show here that this apparent two-dimensionality results from measurements on twinned crystals, and that similar measurements on substantially detwinned crystals of YBa$_2$Cu$_3$O$_{6.6}$ reveal the one-dimensional character of the magnetic fluctuations, thus greatly strengthening the striped-phase interpretation. Moreover, our results also suggest that superconductivity originates in charge stripes that extend along the b crystal axis, where the superfluid density is found to be substantially larger than for the a direction.Comment: 3 pages, PDF onl

Spontaneous time reversal symmetry breaking in the pseudogap state of high-Tc superconductors

When matter undergoes a phase transition from one state to another, usually a change in symmetry is observed, as some of the symmetries exhibited are said to be spontaneously broken. The superconducting phase transition in the underdoped high-Tc superconductors is rather unusual, in that it is not a mean-field transition as other superconducting transitions are. Instead, it is observed that a pseudo-gap in the electronic excitation spectrum appears at temperatures T* higher than Tc, while phase coherence, and superconductivity, are established at Tc (Refs. 1, 2). One would then wish to understand if T* is just a crossover, controlled by fluctuations in order which will set in at the lower Tc (Refs. 3, 4), or whether some symmetry is spontaneously broken at T* (Refs. 5-10). Here, using angle-resolved photoemission with circularly polarized light, we find that, in the pseudogap state, left-circularly polarized photons give a different photocurrent than right-circularly polarized photons, and therefore the state below T* is rather unusual, in that it breaks time reversal symmetry11. This observation of a phase transition at T* provides the answer to a major mystery of the phase diagram of the cuprates. The appearance of the anomalies below T* must be related to the order parameter that sets in at this characteristic temperature .Comment: 11 pages, 4 figure

Criticality in correlated quantum matter

At quantum critical points (QCP) \cite{Pfeuty:1971,Young:1975,Hertz:1976,Chakravarty:1989,Millis:1993,Chubukov:1 994,Coleman:2005} there are quantum fluctuations on all length scales, from microscopic to macroscopic lengths, which, remarkably, can be observed at finite temperatures, the regime to which all experiments are necessarily confined. A fundamental question is how high in temperature can the effects of quantum criticality persist? That is, can physical observables be described in terms of universal scaling functions originating from the QCPs? Here we answer these questions by examining exact solutions of models of correlated systems and find that the temperature can be surprisingly high. As a powerful illustration of quantum criticality, we predict that the zero temperature superfluid density, $\rho_{s}(0)$, and the transition temperature, $T_{c}$, of the cuprates are related by $T_{c}\propto\rho_{s}(0)^y$, where the exponent $y$ is different at the two edges of the superconducting dome, signifying the respective QCPs. This relationship can be tested in high quality crystals.Comment: Final accepted version not including minor stylistic correction

An explanation for a universality of transition temperatures in families of copper oxide superconductors

A remarkable mystery of the copper oxide high-transition-temperature (Tc) superconductors is the dependence of Tc on the number of CuO2 layers, n, in the unit cell of a crystal. In a given family of these superconductors, Tc rises with the number of layers, reaching a peak at n=3, and then declines: the result is a bell-shaped curve. Despite the ubiquity of this phenomenon, it is still poorly understood and attention has instead been mainly focused on the properties of a single CuO2 plane. Here we show that the quantum tunnelling of Cooper pairs between the layers simply and naturally explains the experimental results, when combined with the recently quantified charge imbalance of the layers and the latest notion of a competing order nucleated by this charge imbalance that suppresses superconductivity. We calculate the bell-shaped curve and show that, if materials can be engineered so as to minimize the charge imbalance as n increases, Tc can be raised further.Comment: 15 pages, 3 figures. The version published in Natur