Session A53: Quantum Criticality and Fluctuations in Copper-oxide Superconductors

Quantum criticality in high temperature superconducting cuprates

Anomalous transport behavior in near-optimally-doped high temperature superconducting cuprates has been linked to fluctuations associated with a quantum critical point. Using resonant ultrasound spectroscopy we find evidence for a phase boundary inside the superconducting dome in the temperature-doping phase diagram of YBCO cuprates. This suggests a quantum critical point near optimal doping that is hidden by superconductivity.   

Weak phase stiffess and nature of the quantum critical point in underdoped cuprates

We demonstrate that the zero-temperature superconducting phase diagram of underdoped cuprates can be quantitatively understood in the strong binding limit, using only the experimental spectral function of the ``normal'' pseudo-gap phase without any free parameter. In the prototypical (La$_{1-x}$Sr$_x$)$_2$CuO$_4$, a kinetics-driven $d$-wave superconductivity is obtained above the critical doping $\delta_c\sim 5.2\%$, below which complete loss of superfluidity results from local quantum fluctuation involving local $p$-wave pairs. Near the critical doping, a enormous mass enhancement of the local pairs is found responsible for the observed rapid decrease of phase stiffness. Finally, a striking mass divergence is predicted at $\delta_c$ that dictates the occurrence of the observed quantum critical point and the sudden suppression of the Nernst effects in the nearby region.   

Conductivity near quantum criticality in two space dimensions

We study relativistic $U(1)$ field theories near the quantum critical point in two space dimensions [1]. We compute the dynamical optical conductivity by means of large scale Monte Carlo simulations and numerical analytic continuation. Our main focus is on the universal properties and their relation to the low energy excitation spectrum. In both phases, the spectral function exhibits a sharp rise above a threshold frequency corresponding to the Higgs mass [2] in the ordered phase and to twice the single particle gap in the disordered phase. We determine the high frequency critical conductivity to be $\sigma^*_{\rm c} = 0.3 (\pm 0.1) \times 4e^2/h$. In addition, we find an approximate charge-vortex duality that is reflected in the ratio of the imaginary conductivity on either side of the transition. Our results are relevant to recent experiments on the superfluid to Mott insulator transition in cold atomic optical lattices and to THz spectroscopy of the superconductor to insulator transition in superconducting thin films.[1] S. Gazit, D. Podolsky, A. Auerbach, and D. P. Arovas, arXiv:1309.1765 (2013) [2] S. Gazit, D. Podolsky, and A. Auerbach, Phys. Rev. Lett. 110, 140401 (2013)   

Quantum-critical point of charge-density-wave order under superconducting dome in hole-doped cuprates

We analyze, within the spin-fermion model, a charge-density-wave (CDW) order in hole-doped cuprates with incommensurate momenta $(\pm Q, 0)$ and $(0, \pm Q)$. We show that spin fluctuations mediate attractive interaction in the CDW channel at these momenta. Moreover, the enhancement of the CDW vertex is logarithmical. We solve for the onset of CDW order at the magnetic critical point (when fermionic self-energy cannot be neglected) and show that the corresponding critical temperature $T_{CDW}$ may in fact be larger than superconducting $T_c$. We further consider CDW instability at a finite magnetic correlation length $\xi$ and show that the logarithm is cut off by $\xi_{cr}$. As a result, $T_{CDW}$ monotonically decreases with decreasing $\xi$ and vanishes at some finite $\xi$. This gives rise to a quantum-critical point under the SC dome. As a consequence, the SC dome is divided into two regions, one in which only superconductivity is present, and the other in which CDW and superconducting orders co-exist. We show that a number of observed features of underdoped cuprates, including a non-monotonic dependence of $T_c$ on doping, can be explained by a competition between the two orders. We compute the fermionic spectral function and compare with recent ARPES results.   

Measurement of diamagnetic signal on UD YBCO

The ortho-II phase under-doped (UD) YBa$_2$Cu$_3$O$_{6+\delta}$ has shown a number of interesting phenomena such as quantum oscillations and field-driven charge ordering. An open question is the fate of the superconducting fluctuation in the magnetic field beyond the vortex melting field. To answer the question, we carried out the capacitance based cantilever torque magnetometry measurements on the $T_c = 60$ K phase YBa$_2$Cu$_3$O$_{6+\delta}$ up magnetic fields as high as 56T. At $T$ as low as 1.5 K, the magnetization hysteresis ends at 30 T, marking the melting of the vortex solid phase. Nonlinear diamagnetic signal exists beyond the melting field and persists at field 56T. Our observation suggests that the superconducting fluctuation persists into extensive field, as the Cooper pairing survives well above the vortex solid melting field.   

Spontaneously Generated Inhomogeneous Phases via Holography

We discuss a holographic model consisting of a $U(1)$ gauge field and a scalar field coupled to a charged AdS black hole under a spatially homogeneous chemical potential. By turning on a higher-derivative interaction term between the $U(1)$ gauge field and the scalar field, a spatially dependent profile of the scalar field is generated spontaneously. The critical temperature at which the transition to the inhomogeneous phase occurs is calculated for various values of the parameters of the system. By solving the equations of motion below the critical temperature we show that the dual gauge theory on the boundary spontaneously develops a spatially inhomogeneous charge density.   

Indications of a Quantum Critical Point in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ Using a Local Kondo Effect

A complete understanding of the complex phase diagrams that are present in high temperature superconductors remains elusive. While there is an overwhelming amount of experimental data on the existence and interplay of the phases present in high T$_{\mathrm{c}}$ superconductors from local probes, much of the existing data only looks at the charge degree of freedom of the material. By substituting Fe atoms for Cu atoms in the CuO plane of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212), we gain the ability to access the spin degree of freedom since the Fe atoms retain their magnetization below the superconducting transition temperature. This leads to a local Kondo effect which can be observed using Spectroscopic-Imaging Scanning Tunneling Microscopy (SI-STM) and the local Kondo temperature can be extracted from spectra via a theoretical model. We show that the examination of this local Kondo temperature across local and sample average doping leads to the observation of a change in the quasiparticle spin degree of freedom at a quantum critical point (QCP) with a nominal hole doping of roughly 0.22, in agreement with other probes. The observation of the QCP in Bi2212 with this new method to access the spin degree of freedom helps to unravel some of the mystery behind the complex phase diagram of Bi2212.   

Nodal Fermi surface pocket approaching an optimal quantum critical point in YBCO

I present new quantum oscillation measurements over the entire underdoped regime in YBa$_2$Cu$_3$O$_{6+x}$ and YBa$_2$Cu$_4$O$_8$ using ultra-high magnetic fields to destroy superconductivity and access the normal ground state. A robust small nodal Fermi surface created by charge order is found to extend over the entire underdoped range, exhibiting quantum critical signatures approaching optimal doping.   

Mott physics revealed in high temperature superconductors by resonant inelastic X-ray scattering experiments

In recent resonant inelastic X-ray scattering (RIXS) experiments, energy dispersions of measured spin-wave or paramagnon excitations of cuprates show no signs of softening up to 40\% hole doping or substantially hardening after only 15\% electron doping. In this talk the anomalous result is explained by a simple explanation based one the t-J model. It reveals the presence of the strong correlation of Mott physics in highly doped cuprates. Some predictions will be also presented.   

Impact of chain layer oxygen disorder on charge density wave order in YBa$_2$Cu$_3$O$_{6+\delta}$

Charge density wave (CDW) order in the CuO$_2$ planes of underdoped YBa$_2$Cu$_3$O$_{6+\delta}$ (YBCO) has been reported to coexist and compete with superconductivity. Here we investigate the sensitivity of the CDW order to oxygen disorder in the chain layer of YBCO using resonant soft x-ray scattering. We find that disordering the chains in o-V and o-VIII ordered YBCO$_{6.67}$ decreases the intensity of the CDW superlattice peak by a factor of $\sim2$, but unexpectedly has little effect on the incommensurability, correlation length or temperature dependence of the CDW peak. The same is true for o-III ordered YBCO$_{6.75}$, although the disordering has a smaller effect on the CDW peak intensity. The observed insensitivity of the incommensurability, correlation length and temperature dependence to chain layer oxygen disorder indicates that chain layer defects have a limited role in pinning the CDW order in the CuO$_2$ planes. We will discuss scenarios for the disorder effect, including a possible influence on CDW domain formation (CDW volume fraction) and the CDW order parameter.   

Monte Carlo simulations of an O(6) theory for the pseudogap regime of the cuprate superconductors

We present a theory that describes the pseudogap regime of the hole-doped cuprate superconductors by incorporating the competing effects of superconducting and charge density wave orders into 6-dimensional degrees of freedom on a 2-dimensional lattice [arXiv:1309.6639]. Using Monte Carlo simulations, we calculate the charge order correlations associated with this O(6) theory, and show that the results compare well with recent X-ray scattering experiments on hole-doped YBa$_2$Cu$_3$O$_{6.67}$. We compare our simulation data to large-N calculations for the theory, and also demonstrate that the charge order continues to increase with increasing temperature for a small temperature range above the superconducting transition. For temperatures above this transition, we study our theory's diamagnetic response to a magnetic field applied perpendicular to the plane.   

Quantum fluctuations in charge glass manifested by the hysteresis of Hall resistivity

The Hall effect studies on the underdoped La$_{\mathrm{2-x}}$Sr$_{\mathrm{x}}$CuO$_{\mathrm{4}}$ films grown by Molecular Beam epitaxy (MBE) show dramatic hysteretic behavior at temperatures below 1.5 K, in agreement with the hypothesis that the low temperature ground state is a Coulomb glass. The fluctuations in the Hall resistivity R$_{\mathrm{H}}$ reach several hundred percent and even change the sign of R$_{\mathrm{H}}$, thus making the Hall effect measurement a very sensitive probe of the glassy state. Using a continuous doping gradient (COMBE), we scanned the dependence of R$_{\mathrm{H}}$ on the doping level x in extremely fine steps (x \textless 0.0001), in order to precisely map out the phase boundary between the charge glass state and the superconducting state.   

Exploring Quasiparticles in High-T$_c$ Cuprates Through Photoemission, Tunneling, and X-ray Scattering Experiments

One of the key challenges in the field of high-temperature superconductivity is understanding the nature of fermionic quasiparticles. Experiments consistently demonstrate the existence of a second energy scale, distinct from the d-wave superconducting gap, that persists above the transition temperature into the ``pseudogap'' phase. One common class of models relates this energy scale to the quasiparticle gap due to a competing order, such as the incommensurate ``checkerboard'' order observed in scanning tunneling microscopy (STM) and resonant elastic X-ray scattering (REXS). In this paper we show that these experiments are better described by identifying the second energy scale with the inverse lifetime of quasiparticles. We develop a minimal phenomenological model that allows us to quantitatively describe STM and REXS experiments and compare them with angle-resolved photo-emission spectroscopy (ARPES). Our study refocuses questions about the nature of the pseudogap phase to the study of the origin of inelastic scattering.   

Current and Temperature Dependence of Resistance Fluctuations in the Striped Phase of La$_{2-x}$Ba$_x$CuO$_4$

The high-temperature superconductor La$_{2-x}$Ba$_x$CuO$_4$ is known for its unusual suppression of T$_c$ at x=1/8, accompanied by the emergence of a charge stripe phase. A dynamic stripe phase with local resistance anisotropy is expected to cause measurable resistance fluctuations in samples with small dimensions. We report measurements of the transport and noise in microscopic wires patterned from thin films of La$_{2-x}$Ba$_x$CuO$_4$ grown by pulsed laser deposition. We observe a sudden change in noise power spectral density at temperatures consistent with the charge ordering temperatures observed in scattering experiments. We present the evolution of resistance noise with temperature and bias current as a characterization of the strongly correlated state near x=1/8 doping.