Pressure-induced electronic topological transitions in low dimensional superconductors (2003 EHPRG Award Lecture)

The high-T(c) cuprate superconductors are characterized by a quasi-two-dimensional layered structure where most of the physics relevant for high-T(c) superconductivity is believed to take place. In such compounds, the unusual dependence of the critical temperature T(c) on external pressure results from the combination of the nonmonotonic dependence of T(c) on hole doping or hole-doping distribution among inequivalent layers, and from an 'intrinsic' contribution. After reviewing our work on the interplay among T(c) 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 of T(c) in the cuprates. An ETT takes place when some external agent, such as doping, hydrostatic pressure, or anisotropic strain, modifies the topology of the Fermi surface of an electronic system. As a function of the critical parameter z, measuring the distance of the chemical potential from the ETT, we recover a nonmonotonic behaviour of the superconducting gap at T = 0, regardless of the pairing symmetry of the order parameter. This is in agreement with the trend observed for T(c) as a function of pressure and other material specific quantities in several high-T(c) cuprates and other low dimensional superconductors. In the case of epitaxially strained cuprate thin films, we argue that an ETT can be driven by a strain-induced modification of the in-plane band structure, at constant hole content, at variance with a doping-induced ETT, as is usually assumed. We also find that an increase of the in-plane anisotropy enhances the effect of fluctuations above T(c) on the normal-state transport properties, which is a fingerprint of quantum criticality at T = 0.