Enhanced Superconducting Diode Effect in the Asymmetric Hatsugai-Kohmoto Model

TL;DR

The study addresses how strong electron-electron interactions influence the superconducting diode effect (SDE) in an asymmetric band metal by employing the momentum-local Hatsugai-Kohmoto (HK) model, which is exactly solvable. It combines a low-energy theoretical framework with self-consistent Bogoliubov–de Gennes (BdG) numerics to reveal that HK-induced band splitting into Hubbard-like subbands creates two inequivalent Cooper-pair momenta where the superconducting spectrum closes, leading to nonreciprocal critical currents. The key finding is that the SDE quality factor $\eta$ grows with the HK interaction strength $U$ (e.g., from $\eta \approx 0.046$ at $U=0$ to $\eta \approx 0.19$ at $U=4$ at $T=0.03$), demonstrating a correlation-driven mechanism to enhance nonreciprocity. This work provides a concrete design principle for engineering nonreciprocal superconductivity in strongly correlated materials by tuning many-body interactions.

Abstract

The superconducting diode effect (SDE), characterized by a nonreciprocal supercurrent, has attracted significant attention in recent years due to its potential applications. However, most studies have focused on weakly correlated models, leaving the impact of strong electron-electron interactions on the SDE largely unexplored. In this work, we bridge this gap by investigating the SDE in asymmetric band metals with Hatsugai-Kohmoto (HK) interaction, which are exactly solvable due to their locality in Bloch momentum space. Through a combination of low-energy analysis and a numerical self-consistent approach, we demonstrate that HK interaction can enhance the SDE's quality factor. Our findings shed light on the role of strong electron-electron correlations in shaping the SDE.

Figures (4)

• Figure 1: Properties of the asymmetric HK model. (a) Spectral function $A(\omega,k)$ and particle number distribution $n(k)$ at $U=0$. The Fermi momenta $k_{F\pm}$ are indicated by green points. (b) Spectral function and particle number distribution at $U=4$. The Fermi momenta $k_{F\pm}^{(1)}$ and $k_{F\pm}^{(2)}$ are marked by pink stars and red points, respectively.
• Figure 2: Superconducting energy spectra $E(k)$ for different Cooper pair momenta $q$. (a--c) $U=0$ and (d--f) $U=2$. The spectra $E_1$, $E_2$ and $E'_1$, $E'_2$ are obtained from the Bogoliubov-de Gennes (BdG) Hamiltonian with normal-state dispersions $\xi_k$ and $\xi_k+U$, respectively. Gapless points are highlighted by yellow hexagons. The pairing strength is $\Delta=0.5$.
• Figure 3: Condensation energy $F_q$ and supercurrent $J_q$ as functions of the Cooper pair momentum $q$. (a, b) Results for the HK interaction strength $U = 0$. (c, d) Results for $U = 4$. The temperature $T=0.03$.
• Figure 4: The Cooper pair momentum asymmetry quantifier $\delta$ and the superconducting diode efficiency $\eta$ as functions of the HK interaction strength $U$, calculated at a temperature $T=0.03$.