Repulsive electron bound pairs in a two-leg ladder

Cooper pair is the basic ingredient for superconductivity and it is of great interest to understand the pairing mechanisms in different conditions. The experimental formation of bound two-atom pairs with a repulsive potential [1] was explained by analyzing the Hubbard Hamiltonian of two-boson states [2,3] in a 1D chain. In this work, we solve the two-electron repulsive bound states in a two-leg ladder within the Hubbard Hamiltonian. We found three bound electron pair bands, two bands have energies E≈U and properties very similar to the bound pairs found in [3] but a third band has surprisingly energies E≤0 for any value of U>0. The band structure and wavefunctions of the bound pairs are presented. We show the conditions of t, t' and U needed to find bound pairs with energies E<0 that are not the sum of two non-interacting electrons.

[1] K. Winkler, G. Thalhammer, F. Lang, R. Grimm, J. Hecker Denschlag, A. Daley, A. Kantian, H.P. Buchler, and P. Zoller, Repulsively bound atom pairs in an optical lattice, Nature, 441 (2006) 853.

[2] ] M. Valiente, and D. Petrosyan, Two-particles states in the Hubbard model, J. Phys. B, 41 (2008) 161002.

[3] M. Di Liberto, A. Recati, I. Carusotto, and C. Menotti, Two-body physics in the Su-Schrieffer-Heeger model, Phys. Rev. A, 94 (2016) 062704.