Session A2: New Developments in HTSC I

Microscopic Theory of the Phenomena in Cuprates

This work is based on two principles, (1) that the microscopic model for the Cuprates must reflect their unique properties, and (2) that there exists a quantum critical point in the superconducting region of the phase diagram of the Cuprates which marks the end of an unusual ordered phase and whose quantum fluctuations determine the ``strange metal'' or marginal fermi-liquid properties. A mean-field theory of such a microscopic model predicts the time-reversal breaking order parameter in the underdoped region which has now been observed experimentally in four different families of Cuprates. The quantum critical fluctuations of this order parameter are governed by topological excitations and are derived to have the $\omega/T$ scaling and spatial locality suggested long ago for the marginal fermi-liquid phase. The coupling of the topological excitations to the fermions is shown to be $\propto {\bf \nabla}\times{\bf j}$, where ${\bf j}$ is the fermion current operator. Such a coupling produces an attractive pairing interaction in the $d$-wave channel. Experimental evidence for the applicability of the ideas and calculations to properties of cuprates and several predictions are provided. \newline \newline Work in the past three years on this problem was done in collaboration with Vivek Aji, Arcadi Shehter and Lijun Zhu.   

Dichroism in the pseudogap phase observed through high precision Sagnac interferometry

Polar Kerr effect in the high-$T_c$ superconductor $\mathrm{YBa_2Cu_3O}_{6+x}$\footnote{Jing Xia, Elizabeth Schemm, G. Deutscher, S. A. Kivelson, D. A. Bonn, W. N. Hardy, R. Liang, W. Siemons, G. Koster, M. M. Fejer, and A. Kapitulnik, arXiv:0711.2494 (2007).} was measured at zero magnetic field with high precision using a cryogenic Sagnac fiber interferometer. We observed non-zero Kerr rotations on the order of $\sim$ 1 $\mu$rad appearing near the pseudogap temperature $T^*$, and marking what appears to be a true phase transition. Anomalous magnetic behavior in magnetic-field training of the effect suggests that time reversal symmetry is already broken above room temperature. We will show results from single crystals and oriented films. Preliminary results on other high-temperature superconductors will also be discussed. \par Work done in collaboration with Jing Xia and Aharon Kapitulnik.   

Orbital-Current phases in one- and two-dimensional strongly correlated systems

Although we now know that strongly correlated systems can have several type of conventional order ranging from charge or spin order to superconductivity, the possibility that they present also more exotic phases remains an elusive but very challenging question. In particular whether such systems can have orbital current order for realistic interactions has been strongly debated. Recently this question has come to attention again due to theoretical proposals and subsequent neutron scattering experiments suggesting that this could be the case in the pseudogap phase of High Tc. Tackling this issue directly for the two dimensional case is difficult, since no uncontrolled method can be used beyond exact diagonalization for very small clusters. However this question can be looked at on the one dimensional (ladder) version of this problem, where such orbital current phases can be studied by well controlled methods such as bosonization. I will present the results we obtained on these systems and discuss in particular the comparison between the case of a simple Hubbard ladder [1] versus a three band model (Cu-O ladder) [2]. In order to tackle these issues for the two-dimensional case, we have performed a variational Monte Carlo analysis for a three band Cu-O model. This technique although depending on the quality of the variational wave function has the advantage of being essentially free of numerical problems. I will discuss the phases obtained by this approach as well as the possible experimental consequences. \\ These works are a collaboration with E. Orignac; P. Chudzinski and M. Gabay; C. Weber, A. La\"uchli and F. Mila.\\{} [1] E. Orignac and T. Giamarchi, PRB 56 7167 (1997); \\{} [2] P. Chudzinskii, M. Gabay and T. Giamarchi, PRB 76, 161101 (R) (2007);   

Inhomogeneous Superconductivity in YBa$_2$Cu$_3$O$_y$ and La$_{2-x}$Sr$_x$CuO$_4$ Above $T_c$

An exciting development in the immense research effort focused on resolving the origin of high-$T_c$ superconductivity, is the growing experimental evidence for signatures of superconductivity in cuprate materials at temperatures far above $T_c$. Recent STM experiments on Bi$_2 $Sr$_2$CaCu$_2$O$_{8+\delta}$ have provided new insight into the precise nature of these pairing correlations, by revealing the occurrence of nanometre-sized pairing regions above $T_c$. Whether nanoscale inhomogeneous superconductivity is universal to the cuprates, and whether $T_c$ is driven by Kosterlitz- Thouless physics or Josephson coupling between nanometre-sized superconducting regions are matters of current debate. Very recently we have used $\mu$SR to probe the local response in the bulk of YBa$_2$Cu$_3$O$_y$ and La$_{2-x}$Sr$_x$CuO$_4$ single crystals to a large applied magnetic field (H = 7 T). At temperatures above $T_c$, we detect a spatially inhomogeneous magnetic field that tracks the hole-doping dependences of both $T_c$ and the superfluid density at $T = 0$ K. Our experiments are inconsistent with the field inhomogeneity above $T_c$ being caused by electronic magnetic moments or a vortex liquid. Instead they are explained by the existence of nanometre-size superconducting regions with a local $T_c$ that exceeds the bulk $T_c$. In YBa$_2$Cu$_3$O$_y$, we detect a spatially inhomogeneous response to field that persists beyond $T = 200$ K, indicating that the basic ingredients for superconductivity near room temperature already exist in spatially localized regions of this material. A lingering question is the origin of the weak magnetism detected earlier in YBa$_2$Cu$_3$O$_y$ by zero-field $\mu$SR, at temperatures below the pseudogap temperature $T^*$.   

Observation of a Sharp Magnetic Transition at the Pseudogap Temperature in YBa$_{2}$Cu$_{3}$O$_{6.6}$

Polarized neutron diffraction has been used to demonstrate magnetic order in a crystal of YBa$_{2}$Cu$_{3}$O$_{6.6}$ that displays an exceptionally sharp superconducting transition. Earlier experiments showed a gradual increase of intensity of magnetically scattered neutrons from underdoped YBa$_{2}$Cu$_{3}$O$_{6+x}$ crystals for reflections that do not break translational symmetry. The present experiment confirms this but displays a much sharper transition demonstrating that the width of the magnetic transition depends on the quality of the superconducting transition. This relationship is strengthened by the fact that other magnetic properties sensitive to the superconductivity, such the resonance and excitation spectra are also exceptionally well defined when measured with the same sample. The magnetic order is observed at the temperature of the pseudogap transition and the close relationship between the quality of the magnetic properties and the superconductivity suggests that the pseudogap is directly connected to the magnetic order.