Topological phase transition from nodal to nodeless d-wave superconductivity in electron-doped cuprate superconductors

Abstract

-Unlike the hole-doped cuprates, both nodal and nodeless superconductivity (SC) are observed in the electron-doped cuprates. To understand these two types of SC states, we propose a unified theory by considering the two-dimensional t-J model in proximity to an antiferromagnetic (AF) long-range ordering state. Within the slave-boson mean-field approximation, the d-wave pairing symmetry is still the most energetically favorable even in the presence of the external AF field. In the nodal phase, it is found that the nodes carry vorticity and are protected by the adjoint symmetry of time-reversal and one unit lattice translation. Robust edge modes are obtained, suggesting the nodal d-wave SC being a topological weak-pairing phase. As decreasing the doping concentration or increasing the AF field, the nodes with opposite vorticity annihilate and the nodeless strong-pairing phase emerges. The topological phase transition is characterized by a critical point with anisotropic Bogoliubov quasiparticles, and a universal understanding is thus established for all electron-doped cuprates.Introduction. -Over thirty-year-effort, the consensus has been reached that the rich phase diagram in cuprate superconductors mainly arises from the strong electronic correlations [1,2]. The low-energy theory of the doped Mott insulator is believed to be captured by the single band t-J model [3]. There have been tremendous studies on the t-J model [4,5], most of which show d-wave pairing superconductivity (SC), which has been confirmed by hole-doped cuprates [6][7][8]. However, a remarkable asymmetry exists between hole doping (p-type) and electron doping (n-type) cuprates [9]. One of the most studied ntype family Re 2−x Ce x CuO 4 (Re is a trivalent rare-earth cation) displays antiferromagnetic (AF) long-range order up to a relatively high dopant concentration 0.14 (Ref. [10,11]) before the nodal d-wave SC appears. In contrast, the other n-type family A 1−x La x CuO 2 (A=Sr,Ca) compound has a nodeless SC gap, and the d-wave pairing symmetry is suspected [12][13][14][15].

Superconductivity, Pair Density Wave, and Néel Order in Cuprates*

“…In another context, the d-wave pairing was shown by MFT to be stable, and the quasiparticle excitation becomes nodeless, on a strong Neel background. 42,43 It is natural that the energetic ordering of the states in different symmetries depends on the starting model, and on the method by which the strong correlation effects are addressed.…”

Plaquette-centered rotation symmetry and octet-nodal superconductivity in $\text{KFe}_{2}\text{As}_{2}$

“…Note that the interband pairing between hole band and high energy electron band only contributes second order perturbation corrections to the gap structure, but is unable to alter its symmetry. The d-wave gap nodes carrying one unit of vorticity in the Nambu space are topologically protected [42,43]. Within the AB layer, there are only two ways to destroy these nodes.…”