Dx2−y2pairing of composite excitations in the two-dimensional Hubbard model

Abstract

We report on a strong coupling approach (on-site Coulomb repulsion, U larger than the nearest-neighbor hopping energy $|t|)$ to the Hubbard model. Starting from the Hubbard operators that diagonalize the interaction term, we generate a hierarchy of composite operators from the equations of motion. Using the Hubbard operators as a basis, we are able to compute the associated Green functions including the anomalous Green functions that describe pair formation. We show explicitly that these anomalous Green functions are nonzero in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ channel; however, the entities that pair up are not single-electron-like particles but rather composite excitations (that we call cexons) made out of an electron and a hole on nearest-neighbor sites. Cexons are fermionic in nature as they have spin 1/2 and also have unit charge. Our calculations of the chemical potential reveal that negative compressibility in the 2D Hubbard model and composite excitation pairing are intimately connected, namely, the larger the negative compressibility, the larger the pairing amplitude. Our observation of negative compressibility in the underdoped regime is consistent with phase segregation or stripe formation in the normal state. While pairing ameliorates the negative compresssibility, it does not eliminate it entirely. In addition, we find that the anomalous correlation functions are particle-hole symmetric and exhibit a maximum at a doping level of roughly $10%$ as measured from half-filling. For $U=8|t|,$ the onset temperature for pair formation is $0.02|t|.$ The effect of nearest-neighbor Coulomb repulsions is discussed.