Additional electron pairing in a d-wave superconductor driven by nematic order

Jing-Rong Wang,Guo-Zhu Liu

doi:10.1088/1367-2630/15/6/063007

Abstract

We perform a non-perturbative analysis of the strong interaction between gapless nodal fermions and the nematic order parameter in two-dimensional dx2−y2 superconductors. We predict that the critical nematic fluctuation can generate a dynamical nodal gap if the fermion flavor N is smaller than a threshold Nc. Such gap generation leads to an additional is-wave Cooper pairing instability, which induces a fully gapped dx2−y2 + is superconducting dome in the vicinity of the nematic quantum critical point. The opening of a dynamical gap has important consequences, including the saturation of fermion velocity renormalization, a weak confinement of fermions and the suppression of observable quantities.

Highlights

One of the most prominent properties of high-Tc copper-oxide superconductors is that they exhibit a number of long-range orders upon changing the chemical doping, such as antiferromagnetism, superconductivity, stripe, nematic state, and so on
We demonstrate that the dynamical gap m induced by nematic order corresponds to a secondary is-wave Cooper pairing formation, so the critical nematic fluctuation drives a transition from a pure dx2−y2 superconducting state to a dx2−y2 + is superconducting state in the vicinity of nematic critical point
We can infer that a small dx2−y2 + is superconducting dome emerges around the nematic quantum critical point (QCP), which is schematically shown in figure 3

Summary

Introduction

One of the most prominent properties of high-Tc copper-oxide superconductors is that they exhibit a number of long-range orders upon changing the chemical doping, such as antiferromagnetism, superconductivity, stripe, nematic state, and so on. In principle there could be the fourth term, mτ y, which is defined by the third Pauli matrix τ y and corresponds to a nonzero mass gap term of the nodal qps This mass term can never be obtained to any finite order of the perturbative expansion of fermion self-energy, but may be dynamically generated if one performs non-perturbative calculations. With the help of Dyson-Schwinger (DS) equation that connects the free and complete propagators of nodal qps, we obtain a nonlinear gap equation of fermion mass m in the vicinity of nematic QCP After solving this equation, we find that a nonzero mass gap, mτ y, is dynamically generated when the fermion flavor N is below certain critical value Nc, i.e. N < Nc. We demonstrate that the dynamical gap m induced by nematic order corresponds to a secondary is-wave Cooper pairing formation, so the critical nematic fluctuation drives a transition from a pure dx2−y2 superconducting state to a dx2−y2 + is superconducting state in the vicinity of nematic critical point.

Non-perturbative calculations and gap generation

Physical implications of dynamical gap

Summary and discussions