Spin Gap and Superconductivity in Weakly Coupled Ladders: Interladder One-particle vs. Two-particle Crossover

TL;DR

This paper investigates how interladder hopping influences the transition from a spin gap metal to a superconducting phase in weakly coupled Hubbard ladders, revealing a crossover between one-particle and two-particle regimes.

Contribution

It introduces a detailed analysis of the crossover behavior driven by interladder hopping in Hubbard ladders using renormalization-group methods.

Findings

Existence of a critical interladder hopping $t_{ot c}$ separating different phases.

Transition from spin gap metal to d-wave superconductivity via a two-particle crossover.

Crossover to a 2D phase with coherent band motion at higher interladder hopping.

Abstract

Effects of the interladder one-particle hopping, $t_{\perp}$, on the low-energy asymptotics of a weakly coupled Hubbard ladder system have been studied, based on the perturbative renormalization-group approach. We found that for finite intraladder Hubbard repulsion, $U$, there exists a crossover value of the interladder one-particle hopping, $t_{\perp c}$. For $0<t_{\perp}<t_{\perp c}$, the spin gap metal (SGM) phase of the isolated ladder transits at a finite transition temperature, $T_{c}$, to the d-wave superconducting (SCd) phase via a two-particle crossover. In the temperature region, $T<T_{c}$, interladder coherent Josephson tunneling of the Cooper pairs occurs, while the interladder coherent one-particle process is strongly suppressed. For $t_{\perp c}<t_{\perp}$, around a crossover temperature, $T_{cross}$, the system crosses over to the two-dimensional (2D) phase via a one-particle crossover. In the temperature region, $T<T_{cross}$, the interladdercoherent band motion occurs.