LIGHTLY DOPED T-J 3-LEG LADDERS - AN ANALOG FOR THE UNDERDOPED CUPRATES

The three-leg ladder has one odd-parity and two even-parity channels. At low doping these behave guile differently. Numerical calculations f or a t-J model show that the initial phase upon hole doping has two co mponents-a conducting Luttinger liquid in the odd-parity channel, coex isting with an insulating (i.e., undoped) spin-liquid phase in the eve n-parity channels. This phase has a partially truncated Fermi surface and violates the Luttinger theorem. This coexistence of conducting fer mionic and insulating paired bosonic degrees of freedom is similar to the recent proposal of Geshkenbein, Ioffe, and Larkin [Phys. Rev. B 55 , 3173 (1997)] for the underdoped spin-gap normal phase of the cuprate s. A mean-field approximation is derived which has many similarities t o the numerical results. One difference however is an induced hole par ing in the odd-parity channel at arbitrary small dopings, similar to t hat proposed by Geshkenbein, Ioffe, and Larkin for the two-dimensional case. At higher dopings, we propose that a quantum phase transition w ill occur as holes enter the even-parity channels, resulting in a Luth er-Emery liquid with hole pairing with essentially d-wave character. I n the mean-field approximation a crossover occurs which we interpret a s a reflection of this quantum phase transition deduced from the numer ical results.