A phenomenological theory of heavy fermion superconductivity in CeCoIn<sub>5</sub>

Abstract

Unconventional superconductivity was first discovered in heavy fermion materials which exhibit a rich variety of superconducting quantum phenomena. Understanding the microscopic origin of heavy fermion superconductivity will help us understand the nature of high-temperature superconductivity and explore new class of unconventional superconductors. In this article, we give a brief introduction to the recent theoretical and experimental studies on heavy fermion superconductors. In particular, it has been shown that previous understandings of the pairing mechanism based on oversimplified single-band model calculations may not explain the recent experimental observations of the superconducting gap symmetry and therefore need to be revisited. For example, the heavy fermion superconductors CeCu2Si2 and UBe13, which have long been believed to have nodal superconducting gap structures for over three decades, are now found to exhibit nodeless behaviors in many new experiments. While these may be partially explained by using realistic band structures in combination with random phase approximation (RPA) for the dynamic susceptibility, we point out that for strongly correlated systems such as heavy fermions, RPA fails to capture the true behavior of quantum critical fluctuations which act as the pairing force for the unconventional superconductivity. We argue that there are three major issues that need to be taken into account in order to develop a good understanding of the heavy fermion superconductivity: (1) the strong electronic correlations and the two-fluid behavior of the f electrons; (2) the quantum critical nature of the superconducting pairing force that cannot be obtained based on RPA; (3) the multi-band or multi-orbital properties that rely on real materials and may be crucial for the gap structures. Following these considerations, we propose a new framework based on the strong-coupling Eliashberg theory that combines previous phenomenological theory of the spin-fluctuation-induced pairing mechanism and realistic band structures from either experimental measurements or first-principles calculations. As an example, we apply our model to the prototype heavy fermion superconductors CeCoIn5 and CeRhIn5. By using a single-band model derived from the scanning tunneling spectroscopy, we solve the linearized Eliashberg equation and produce the correct d-wave superconducting gap structure, in agreement with experimental observations. We further predict a simple formula for the superconducting transition temperature T c as a function of the pairing strength and the spin fluctuation energy. We then extend the formula to general cases and use the two-fluid prediction on the heavy electron density of states to calculate the pressure-variation of T c. Our results agree well with experiment and explain the dome structure of T c. For multi-band systems, we have studied the superconductivity in CeCu2Si2. In contrast to previous calculations that predict either d-wave or nodal s-wave gap, we found that the inter-band scattering plays an essential role and may cause a nodeless gap structure. This work is still under progress. We believe that the success of the new framework suggests that it may provide a promising basis for treating the above issues and will help our understanding of the properties of heavy fermion superconductivity. In the future, we hope to extend our study to other heavy fermion superconductors and take into consideration the detailed orbital characters and the dual nature of f electrons. The latter would possibly require a reformulation of the Eliashberg equations.