Low Energy Effective Action of Lightly Doped Two-Leg t-J Ladders

TL;DR

This paper develops a low energy effective theory for lightly doped two-leg t-J ladders, revealing dominant superconducting instability and classifying the system within the Luther-Emery universality class.

Contribution

It introduces a novel effective Hamiltonian combining gauge interactions and short-range antiferromagnetic forces for doped ladders.

Findings

Superconducting instability dominates over charge density wave.

Effective Hamiltonian is a bosonic Gaussian model describing density fluctuations.

Identifies two types of gapped spin excitations.

Abstract

We propose a low energy effective theory of lightly doped two-leg t-J ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions which are coupled to the O(3) non-linear sigma model in terms of the gauge coupling with opposite sign of "charges". In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg t-J ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave (CDW) and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.