Pressure-induced electronic topological transitions in low dimensional superconductors

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.