Lightly Doped t-J Three-Leg Ladders - an Analog for the Underdoped Cuprates

TL;DR

This paper models lightly doped three-leg t-J ladders, revealing a phase with coexisting conducting and insulating behaviors that resembles the underdoped cuprates, and predicts a quantum phase transition at higher doping levels.

Contribution

It introduces a detailed numerical and mean field analysis of three-leg t-J ladders, highlighting their similarity to underdoped cuprates and proposing a quantum phase transition at increased doping.

Findings

Coexistence of Luttinger liquid and spin liquid phases at low doping

Violation of Luttinger theorem due to partial Fermi surface truncation

Prediction of a quantum phase transition leading to d-wave hole pairing

Abstract

The three-leg ladder has one odd-parity and two even-parity channels. At low doping these behave quite differently. Numerical calculations for a t-J model show that the initial phase upon hole doping has two components - a conducting Luttinger liquid in the odd-parity channel, coexisting with an insulating (i.e. undoped) spin liquid phase in the even-parity channels. This phase has a partially truncated Fermi surface and violates the Luttinger theorem. This coexistence of conducting fermionic and insulating paired bosonic degrees of freedom is similar to the recent proposal of Geshkenbein, Ioffe, and Larkin for the underdoped spin-gap normal phase of the cuprates. A mean field approximation is derived which has many similarities to the numerical results. One difference however is an induced hole pairing in the odd-parity channel at arbitrary small dopings, similar to that proposed by Geshkenbein, Ioffe, and Larkin for the two-dimensional case. At higher dopings, we propose that a quantum phase transition will occur as holes enter the even-parity channels, resulting in a Luther-Emery liquid with hole pairing with essentially d-wave character. In the mean field approximation a crossover occurs which we interpret as a reflection of this quantum phase transition deduced from the numerical results.