Magnetotransport and Fermi surface segmentation in Pauli limited superconductors.

We report the first theoretical investigation of the spectroscopic, electrical and optical transport signatures of-wave Pauli limited superconductors, based on a non perturbative numerical approach. We demonstrate that the high magnetic field low temperature regime of these materials host a finite momentum paired superconducting phase. Multi-branched dispersion spectra with finite energy superconducting gaps, anisotropic segmentation of the Fermi surface and spatial modulations of the superconducting order characterizes this finite momentum paired phase and should be readily accessible through angle resolved photo emission spectroscopy, quasiparticle interference and differential conductance measurements. Based on the electrical and optical transport properties we capture the non Fermi liquid behavior of these systems at high temperatures, dominated by local superconducting correlations and characterized by resilient quasiparticles which survive the breakdown of the Fermi liquid description. We map out the generic thermal phase diagram of the-wave Pauli limited superconductors and provide for the first time the accurate estimates of the thermal scales corresponding to the: (a) loss of (quasi) long range superconducting phase coherence (), (b) loss of local pair correlations (), (c) breakdown of the Fermi liquid theory () and cross-over from the non Fermi liquid to the bad metallic phase (). Our thermal phase diagram mapped out on the basis of the spectroscopic and transport properties are found to be in qualitative agreement with the experimental observations on CeCoInand-BEDT, in terms of the thermodynamic phases and the phase transitions. The results presented in this paper are expected to initiate important transport and spectroscopic experiments on the Pauli limited-wave superconductors, providing sharp signatures of the finite momentum Cooper paired state in these materials.