Superconducting gap for a two-leg t-J ladder

Analogies of phonon anomalies and electronic gap features in the infrared response of Sr14-xCaxCu24O41and underdoped YBa2Cu3O6+x

We present an experimental and theoretical study which compares the phonon anomalies and the electronic gap features in the infrared response of the weakly coupled two-leg-ladders in Sr14-xCa_xCu₂₄O₄₁(SCCO) with those of the underdoped high-T_csuperconductor YBa₂Cu₃O6+x(YBCO) and thereby reveals some surprising analogies. Specifically, we present a phenomenological model that describes the anomalous doping- and temperature-dependence of some of the phonon features in thea-axis response (field along the rungs of the ladders) of SCCO. It assumes that the phonons are coupled to charge oscillations within the ladders. Their changes with decreasing temperature reveal the formation of a crystal (density wave) of hole pairs that are oriented along the rungs. We also discuss the analogy to a similar model that was previously used to explain the phonon anomalies and an electronic plasma mode in thec-axis response (field perpendicular to the CuO₂planes) of YBCO. We further confirm that an insulator-like pseudogap develops in thea-axis conductivity of SCCO which closely resembles that in thec-axis conductivity of YBCO. Most surprisingly, we find that thec-axis conductivity (field along the legs of the ladders) of SCCO is strikingly similar to the in-plane one (field parallel to the CuO₂planes) of YBCO. Notably, in both cases a dip feature develops in the normal state spectra that is connected with a spectral weight shift toward low frequencies and can thus be associated with precursor superconducting pairing correlations that are lacking macroscopic phase coherence. This SCCO-YBCO analogy indicates that collective degrees of freedom contribute to the low-energy response of underdoped highT_ccuprates and it even suggests that the charges in the CuO₂planes tend to segregate forming quasi-one-dimensional structures similar to the two-leg ladders, as predicted for the stripe-scenario or certain intertwinned states.

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

Pseudogap in the c-axis (along the ladder) optical conductivity of t - J ladders and its quasiparticle interpretation

Motivated by similarities between cuprate superconductors and two-leg ladder copper-oxide compounds and in order to obtain a better understanding of optical properties of cuprate superconductors we have studied the c-axis (along the ladder) optical conductivity [Formula: see text] of a doped [Formula: see text] two-leg ladder. Using exact diagonalization, we have calculated the conductivity and related quantities for cyclic ladders of up to 13 rungs. In agreement with results of an early study by Hayward and coworkers (Hayward et al 1996 Phys. Rev. B 53 8863) we find that [Formula: see text] consists of a Drude peak at zero frequency and an absorption band in the infrared region that is separated from the former by a pseudogap. The width of the pseudogap [Formula: see text] increases with increasing J/t, in parallel with an increase of the magnitude [Formula: see text] of the gap in the quasiparticle excitation spectra. Our central finding is that [Formula: see text], where [Formula: see text] is the magnitude of the gap in the spin excitation spectra. We demonstrate that this approximate relation can be understood in terms of a phenomenological model involving a superconducting ladder and a coupling between charged quasiparticles and spin excitations. The relation is remarkably similar to the one between experimental values of the energy scale of a dip in the in-plane optical conductivity, the superconducting gap [Formula: see text] and the energy of the spin-resonance in cuprate superconductors (for a recent discussion of the optical data, see Šopík et al 2015 New J. Phys. 17 053022). Our findings support the point of view that low energy infrared active excited states of cuprate superconductors can be viewed as consisting of two charged quasiparticles connected with pair-breaking and a spin excitation.

Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Frequency-dependent correlations, such as the spectral function and the dynamical structure factor, help illustrate condensed matter experiments. Within the density matrix renormalization group (DMRG) framework, an accurate method for calculating spectral functions directly in frequency is the correction-vector method. The correction vector can be computed by solving a linear equation or by minimizing a functional. This paper proposes an alternative to calculate the correction vector: to use the Krylov-space approach. This paper then studies the accuracy and performance of the Krylov-space approach, when applied to the Heisenberg, the t-J, and the Hubbard models. The cases studied indicate that the Krylov-space approach can be more accurate and efficient than the conjugate gradient, and that the error of the former integrates best when a Krylov-space decomposition is also used for ground state DMRG.

Evolution of the dynamical pairing across the phase diagram of a strongly correlated high-temperature superconductor

We study the dynamics of the Cooper pairing across the T = 0 phase diagram of the two-dimensional Hubbard model, relevant for high-temperature superconductors, using a cluster extension of dynamical mean-field theory. We find that the superconducting pairing function evolves from an unconventional form in the overdoped region into a more conventional boson-mediated retarded form in the underdoped region of the phase diagram. The boson, however, promotes the rise of a pseudogap in the electron density of states rather than a superconducting gap as in the standard theory of superconductivity. We discuss our results in terms of Mott-related phenomena, and we show that they can be observed in tunneling experiments.