Session H40: Focus Session: Phonons and Electron Correlations in High Temperature Superconductors II

Percolative Theories of Strongly Disordered Ceramic High Temperature Superconductors

Optimally doped ceramic superconductors (cuprates, pnictides, ...) exhibit transition temperatures Tc much larger than strongly coupled metallic superconductors like Pb, and exhibit many universal features that appear to contradict the BCS theory of superconductivity based on attractive electron-phonon pairing interactions. These complex materials are strongly disordered and contain several competing nanophases which cannot be described effectively by parameterized Hamiltonian models, yet their phase diagrams also exhibit many universal features, not only in the normal state, but in the superconductive state as well. Here we review the rapidly growing body of experimental results which suggest that these universal features are the result of marginal stabilities of the ceramic electronic and lattice structures. These dual marginal stabilities favor both electronic percolation of a dopant network, and rigidity percolation of the deformed lattice network. This double percolation model has previously explained many features of the normal-state transport properties of these materials and is the only theory that has successfully predicted strict lowest upper bounds for Tc in the cuprate and pnictide families. Here it is extended to derive an angular energy gap equation, which rationalizes angularly averaged gapTc ratios, and shows that these are similar to those of conventional strongly coupled superconductors.   

Nonlinear Electron-lattice Coupling Solution to High Temperature Superconductivity in Cuprates

Resolving the High Temperature Superconductivity problem requires understanding both pseudogap and superconducting phenomenologies. Here we present a model, the Fluctuating Bond Model (FBM) based on strong, local, nonlinear electron-lattice coupling and now including long range Coulomb interactions (LRCI), which can claim to achieve this requirement. We summarize the results on the pseudogap temperature scale $T^*$ and pseudogap doping dependence, relating them to low temperature STM experiments (``C$4$ symmetry breaking'') and to ARPES data (``arcing'' of the Fermi surface). We also summarize results on the doping dependence of the superconducting $T_c$ and the isotope shift. We conclude with a list of challenges to be met by theory. \\[4pt] D.M.Newns and C.C. Tsuei, Nature Physics \textbf{3}, 184 (2007).   

Detecting the Majorana fermion surface state of $^3$He-B through spin relaxation

The concept of the Majorana fermion has been postulated more than eighty years ago; however, this elusive particle has never been observed in nature. The non-local character of the Majorana fermion can be useful for topological quantum computation. Recently, it has been shown that the 3He-B phase is a time-reversal invariant topological superfluid, with a single component of gapless Majorana fermion state localized on the surface. Such a Majorana surface state contains half the degrees of freedom of the single Dirac surface state recently observed in topological insulators. We show here that the Majorana surface state can be detected through an electron spin relaxation experiment. The Majorana nature of the surface state can be revealed though the striking angular dependence of the relaxation time on the magnetic field direction, $1/T_1 \propto sin^2 \theta$ where $\theta$ is the angle between the magnetic field and the surface normal. The temperature dependence of the spin relaxation rate can reveal the gapless linear dispersion of the Majorana surface state. We propose a spin relaxation experiment setup where we inject an electron inside a nano- sized bubble below the helium liquid surface.   

Topological Majorana and Dirac zero modes in superconducting vortex cores

We provide a simple argument based on flux insertion to show that certain superconductors with a non-trivial topological invariant such as a spinless $p_x + i p_{y}$ superconductor have protected zero modes in their vortex cores. This argument has the flavor of a two dimensional index theorem and applies to disordered systems as well. We study superconductors with and without time reversal and spin rotational symmetry and derive conditions under which superconductors in these classes have protected zero modes.   

Majorana Fermions Bound to Dislocations in 2d Weak Topological Superconductors

We propose a new method for generating Majorana fermion bound states in superconductors. For 2d weak topological superconductors edge dislocations can trap an odd number of Majorana fermion zero modes. These Majorana modes are similar to those found in the vortices of the chiral p+ip superconductor which lead to non-Abelian statistics. We discuss the criterion for the existence of such bound states in weak topological superconductors as well as their statistical properties. We also briefly mention the possiblity of finding such states in real materials with dislocations and the relation to the generic phase space Chern-Simons theory developed in the theory of topological insulators.   

Stable Topological Superconductivity in a Family of Fermion Lattice Models

Motivated by the exotic non-Abelian topological order emerging in $p_x+ip_y$ superconductor, we present a general theorem based on mean-field energetics and symmetry arguments that topological superconducting phase is stabilized in a large family of spinless fermion lattice models with very general band structures and attractive interactions. To illustrate the theorem, we examine the phase diagrams of two specific lattice models with nearest-neighbor hopping and attraction on a square lattice and a triangular lattice. The former one only supports a $p_x+ip_y$ pairing phase and the latter exhibits a topological phase transition driven by doping from $p+ip$-pairing state to topologically trivial $f$-wave state. This work is supported by DARPA-QuEST, JQI-NSF-PFC, and US-ARO   

Superconductivity on the surface of topological insulators and in two-dimensional noncentrosymmetric materials

We study the superconducting instabilities of a single species of two-dimensional Rashba-Dirac fermions, as it pertains to the surface of a three-dimensional time-reversal symmetric topological band insulator. We also discuss the similarities as well as the differences between this problem and that of superconductivity in two-dimensional time-reversal symmetric noncentrosymmetric materials with spin-orbit interactions. The superconducting order parameter has both $s$-wave and $p$-wave components. We identify one single superconducting regime in the case of superconductivity in the topological surface states (Rashba-Dirac limit), irrespective of the relative strength between singlet and triplet pair potentials. In contrast, in the Fermi limit relevant to the noncentrosymmetric materials we find two regimes depending on the value of the chemical potential and the relative strength between singlet and triplet potentials. We construct explicitly the Majorana bound states in these regimes. In the single regime for the case of the Rashba-Dirac limit, there exist one and only one Majorana fermion bound to the core of an isolated vortex. In the Fermi limit, there are always an even number (0 or 2) of Majorana fermions bound to the core of an isolated vortex.   

Normal State Transport of the Cuprates within Hidden Fermi Liquid Theory

The Hidden Fermi Liquid is an effective low-energy theory that seeks to directly account for the consequences of Gutzwiller projection in the cuprates. An overview of the framework will be presented along with a brief summary of previous successes and predictions for spectroscopic experiments, such as IR conductivity, photoemission, and tunneling. The anomalous transport properties, focusing on the Hall effect, will be discussed within this framework and self-consistently compared with experiments. The ``bottleneck'' connecting the hidden Fermi liquid excitations with those of the projected Hilbert space will be a common theme.   

Charge 2e Boson Underlies Two - Fluid Model of the Pseudogap in Cuprate Superconductors

Starting from the effective low energy theory of a doped Mott insulator, we show that the effective carrier density in the underdoped regime agrees with a two - fluid description. Namely, it has distinct temperature independent and thermally activated components. We identify the thermally activated component as the bound state of a hole and a charge 2e boson, which occurs naturally in the effective theory. The thermally activated unbinding of this state leads to the strange metal and subsequent T-linear resistivity. We find that the doping dependence of the binding energy is in excellent agreement with the experimentally determined pseudogap energy scale in cuprate superconductors.   

Crossover between $T$ and $T^2$ electrical resistivity near an antiferromagnetic quantum critical point

To understand the ubiquitous linear term in the resistivity observed for the cuprates and other unconventional superconductors, we generalize the Two-Particle-Self-Consistent approach for the Hubbard model to include vertex corrections in the calculation of conductivity. Spin and charge fluctuations are included at all wavelengths. The vertex corrections allow the f-sum rule to be satisfied very accurately and are crucial contributions to the resistivity. Fitting the temperature dependence to a quadratic form, we obtain a linear term that decreases with increasing doping close to the antiferromagnetic quantum critical point. The quadratic term has a much weaker doping dependence. The linear term is also correlated with the $T_c$ predicted by the same approach [1], in which both superconductivity and linear resistivity are caused by antiferromagnetic correlations. Our results agree qualitatively with recent experiments showing that the linear term vanishes concomitantly with the critical temperature $T_c$ in the overdoped regime [2]. [1] Kyung et al. PRB 68, 174502 (2003) [2] Doiron-Leyraud et al. arXiv:0905.0964