Minimal two band model and experimental proposals to distinguish pairing mechanisms of the high-T$_c$ superconductor La$_3$Ni$_2$O$_7$

TL;DR

This work addresses how to experimentally distinguish competing pairing mechanisms in the high-$T_c$ nickelate La$_3$Ni$_2$O$_7$. It introduces a minimal two-band model that reproduces the observed Fermi surface and analyzes superconductivity under two limits: weak-$U$ with spin/charge fluctuations and large-$U$ with interlayer superexchange. A key result is that a perpendicular electric field $D$ drives qualitatively different transitions in the two pictures—$s_{\pm}$ to $d$-wave in the weak-$U$ case, and a transition to a pair-density-wave (PDW) state with a Pauli-like compensation effect in the large-$U$ case—offering concrete experimental signatures. Three experimental proposals (not detailed here) are offered to identify the dominant pairing mechanism, with realistic field scales of tens of meV, enabling targeted thin-film device tests to clarify the physics and potentially guide routes to higher $T_c$.

Abstract

The discovery of high-T$_c$ superconductivity in La$_3$Ni$_2$O$_7$ has opened the door to a new route to high temperature superconductivity, distinct from that in cuprates and iron-based materials. Yet, despite intense recent activity, we lack experimentally testable protocols for distinguishing between different pairing scenarios. In this Letter, we construct a minimal two-band model that reproduces the Fermi-surface topology observed in recent ARPES measurements and DFT calculations, and we analyze superconductivity arising from two distinct pairing mechanisms. We show that these mechanisms yield sharply different responses to an applied perpendicular electric field. Thus, La$_3$Ni$_2$O$_7$ offers the unique opportunity to cleanly distinguish between different pairing scenarios. Finally, we propose three concrete experimental proposals designed to distinguish these scenarios and thereby identify the pairing mechanism most relevant to the real material.

Figures (5)

• Figure 1: (a) Fermi surface of our minimal two band model, with parameters (in eV) $t=0.6, \, t'=-0.12, \, t_z=0.4, \, \mu=-1.1$. (b) The band structure of the minimal two band model.
• Figure 2: Schematic of the proposed setup with perpendicular electric field E applied to 1 unit cell and 2 unit cell films.
• Figure 3: Electronic configuration of top layer and bottom layer atoms, vertically stacked above a single planar site.
• Figure 4: RPA calculation at U=1.6 eV. (a) Dimensionless pairing strength $\lambda$, which shows a phase transition from $s_\pm$ to $d$ wave on increasing $D$. (b) and (c) The gap functions of $s_\pm$ and $d$ waves at D=0 eV. (d) and (e) the gap function of $s_\pm$ and $d$ waves at D=0.02 eV.
• Figure 5: (a) Mean field phase diagram of the BCS and FF states. The gap value is encoded by color: $|\Delta_{\text{BCS}}|$ (blue) and $-|\Delta_{\text{FF}}|$ (red). t=V=1, $\mu=-1.4$ (so that filling is 1/4). The inset is an illustration of FF Ansatz. (b) Schematic bands shift after applying perpendicular electric field and parallel magnetic field. (c) Superconducting $\text{T}_c$ as a function of parallel magnetic field for $D = 2\frac{\Delta_0}{\sqrt{2}}$, illustrating the compensation effect of the two fields.