Ubiquitous light real-space pairing from long-range hopping and interactions

Abstract

We systematically examine how long-range hopping and its synergy with extended interactions leads to light bound pairs. Pair properties are determined for a dilute extended Hubbard model with large on-site repulsion ($U$) and both near- and next-nearest neighbour hopping ($t$ and $t^{\prime }$) and attraction ($V$ and $V^{\prime }$), for cubic and tetragonal lattices. The presence of $t^{\prime }$ and $V^{\prime }$ promotes light pairs. For tetragonal lattices, $t^{\prime }<0$ pairs can be lighter than non-interacting particles, and $d$-symmetric pairs form. Close packing transition temperatures, $T^{\ast }$ are estimated for the Bose-Einstein condensation (BEC) of pairs to be $k_B{T}^{\ast }\sim \overline{t}0.1$, where $\overline{t}$ is the geometric mean of the hoppings on the Cartesian axes. When pairs have $d$-symmetry, the condensate has $d$-wave character. Thus, the presence of both $t^{\prime }$ and $V^{\prime }$ leads ubiquitously to small strongly bound pairs with an inverse mass that is linear in hopping, which could lead to high temperature BECs.

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