Pressure-induced electronic topological transitions in low dimensional superconductors**EHPRG Award Lecture.

Abstract

The high-Tc cuprate superconductors are characterized by a quasi-two-dimensionallayered structure where most of the physics relevant forhigh-Tc superconductivity is believed to take place. In such compounds, the unusual dependence of the criticaltemperature Tc on external pressure results from the combination of the nonmonotonic dependence ofTc on hole doping or hole-doping distribution among inequivalent layers, and froman ‘intrinsic’ contribution. After reviewing our work on the interplay amongTc, hole content, and pressure in the bilayered and multilayered cuprate superconductors,we will discuss how the proximity to an electronic topological transition (ETT)may give a microscopic justification of the ‘intrinsic’ pressure dependence ofTc in the cuprates. An ETT takes place when some external agent, such as doping,hydrostatic pressure, or anisotropic strain, modifies the topology of theFermi surface of an electronic system. As a function of the critical parameterz, measuring the distance of the chemical potential from the ETT,we recover a nonmonotonic behaviour of the superconducting gap atT = 0,regardless of the pairing symmetry of the order parameter. This is in agreement with the trend observedfor Tc as a function of pressure and other material specific quantities in severalhigh-Tc cuprates and other low dimensional superconductors. In the case of epitaxiallystrained cuprate thin films, we argue that an ETT can be driven by a strain-inducedmodification of the in-plane band structure, at constant hole content, atvariance with a doping-induced ETT, as is usually assumed. We also find thatan increase of the in-plane anisotropy enhances the effect of fluctuations aboveTc on the normal-state transport properties, which is a fingerprint of quantum criticality atT = 0.