Tuning macroscopic phase frustration in multiorbital superconductors

Abstract

Time-reversal symmetry-breaking (TRSB) superconductivity has been reported in a growing number of materials. In some cases, TRSB arises naturally from chiral superconductivity, but in many low-symmetry systems this explanation is not viable. In these latter cases, TRSB is often attributed to phase frustration among multiple superconducting gaps on different Fermi surfaces. Yet, the microscopic conditions enabling such frustration remain poorly understood. Here, inspired by the TRSB reported in the superconducting state of iron-based materials, we demonstrate that a minimal two-orbital model can support a TRSB superconducting state via phase frustration. We identify the key microscopic parameters that stabilize TRSB in d-electron systems with orthorhombic symmetry and provide a framework to systematically enlarge the region of parameter space within which TRSB is expected in materials with other electronic content and crystalline symmetries. Our results offer a simple and experimentally relevant route to understand and control TRSB in multiorbital superconductors.

Figures (2)

• Figure 1: Schematic representation of the three pairing functions in a $\{d_{xz}, d_{yz}\}$-orbital system. $J_{12}, J_{13},$ and $J_{23}$ indicate the three Josephson couplings relating the three superconducting order parameter components $\Delta_i(\textbf{k})$. Two components are related to intra-orbital spin-singlet pairing, and one is related to inter-orbital spin-triplet pairing. Indicated are also the correspondence between the two order-parameter notations used in this work, based on $d_{ab}(\textbf{k})$ or $\Delta_i(\textbf{k})$ parametrizations.
• Figure 2: Upper panel: Density of states (arbitrary units) of the two bands as a function of the external chemical potential $\mu$ (in units of $|t_1| = 0.33$ eV) for the orthorhombic parameter $\alpha_o=0.1$. The parameters of the two-orbital model are given in the main text. The shaded yellow region marks the range of chemical pontential ($\Delta \mu$) within which a TRSB superconducting state emerges. Inset: $\Delta \mu$ as a function of $\alpha_o$. The dotted gray line is a linear fit, $\Delta \mu = 0.17 \alpha_o$. Lower panels: Color map of the sign of $\tilde{h}_{23}(\mathbf{k}) \tilde{h}_{30}(\mathbf{k})$ in the $k_xk_y$ plane for three values of $\mu$, with the Fermi pockets of the two bands overlaid. Here, gray indicates negative and light blue positive values.