Kohn-Luttinger instability of the t-t' Hubbard model in two dimensions: variational approach

TL;DR

This paper investigates the Kohn-Luttinger instability in the two-dimensional t-t' Hubbard model using a variational approach, revealing insights into superconducting phases and gap structures relevant to cuprates.

Contribution

It introduces a variational method to analyze the Kohn-Luttinger superconductor in the t-t' Hubbard model, highlighting weak-coupling analogs of spin liquids and detailed gap behaviors.

Findings

Superconducting phase diagram at half filling resembles spin liquid states.

Nontrivial energy dependence of the d-wave gap in cuprate-relevant parameters.

Weak hot spot effect on the angular gap dependence.

Abstract

An effective Hamiltonian for the Kohn-Luttinger superconductor is constructed and solved in the BCS approximation. The method is applied to the t-t' Hubbard model in two dimensions with the following results: (i) The superconducting phase diagram at half filling is shown to provide a weak-coupling analog of the recently proposed spin liquid state in the J_1-J_2 Heisenberg model. (ii) In the parameter region relevant for the cuprates we have found a nontrivial energy dependence of the gap function in the dominant d-wave pairing sector. The hot spot effect in the angular dependence of the superconducting gap is shown to be quite weak.