The temperature dependence of the scattering rate in cuprates : insights from strong-coupling diagrammatic methods

Abstract

Cuprates—beyond the unconventional superconductivity—feature an extraordinarily rich phase diagram, which has yet to be described in its full complexity. Among the various distinct phases, the DC resistivity most characteristically changes its temperature (T) dependence. Notwithstanding, in 2015 novel experimental findings by N. Barišić et al. have revealed a surprising universal temperature behaviour. In particular, the ratio of the DC resistivity over the Hall resistivity ρ/ρ H a very clear T 2 -dependence. This appears universally for the pseudogap phase, the strange metal phase, and the Fermi liquid phase across all hole-doping and temperature regimes, as well as in different compounds. In our work, we analyzed a possible connection between the experimentally observed quadratic T -dependence of ρ/ρ_H and the T -dependence of the electronic scattering rate. Our numerical calculations are based on the two dimensional single-band Hubbard model on a square lattice with next, 2nd next and 3rd next nearest neighbor hopping. Due to the combination of low dimensionality and strong electronic correlations in this system, non-local correlations are likely to provide important contributions to the solution. On the basis of this consideration we employed the ladder dynamical vertex approximation (DΓA) and the dual fermion (DF) theory, i.e. cutting edge many-body algorithms, capable of including antiferromagnetic fluctuations on all length scales. The DΓA and DF results yield strongly momentum dependent single particle quantities such as the electronic self-energy on the Matsubara axis. For the hole-dopings δ = 0.1, 0.15 and 0.2 we have observed that the momentum dependence appears stronger at small doping. To be more quantitative we approximated the scattering rate by two methods: First, we obtained the scattering rate by extracting the value of the imaginary part of the self-energy at the Fermi level. To this end we performed an analytic continuation of the Matsubara data by means of Padé approximation. Although the spectral function gave rise to plausible trends, the analytic continuation fails to reveal the T -dependence due to large uncertainties, which are intrinsic to the ill-defined problem of analytic continuation. Second, we approximated the spectral weight at the Fermi surface by means of the single-particle Green’s function at the imaginary time point equal to half the inverse temperature. In our case this could not be directly interpreted in terms of the scattering rate, though. Although we were not able to produce a stable prediction for the scattering rate the DΓA results revealed two physically interesting results: (i) The spin susceptibility shows commensurate and incommensurate fluctuations accompanied by a characteristic T -dependence of the correlation length w.r.t. the doping level in the intermediate temperature regime. (ii) The self-energy on the Matsubara axis strongly suggests the presence of a pseudogap as well as the absence of any universal behaviour w.r.t. different doping or different temperature regimes. We hence see the necessity to go beyond the single-particle scattering rate in order to describe the experimentally observed T -dependence of ρ/ρ_H . In particular, we became aware of expressions in the literature, which treat ρ/ρ_H within the linear response theory. In this work, we merely sketch them as a possible preparation for future studies in terms of the charge susceptibility.