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Journal of Physics and Chemistry of Solids

Theory of the quasiparticle spectra around a vortex in the two-dimensional t–t′–J model

Masao Ogata, Akihiro Himeda, Yukio Tanaka, Satoshi Kashiwaya

Published Oct 1, 1998• 3 citations
Publisher
DOI
10.1016/s0022-3697(98)00116-4

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An exact-diagonalization technique on finite-size clusters is used to study the ground state and excitation spectra of the two-dimensional effective-fermion model, a fictious model of hole quasiparticles derived from numerical studies of the two-dimensional $t\ensuremath{-}J$ model at low doping. We show that there is actually a reasonable range of parameter values where the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave pairing of holes occurs and the low-lying excitation can be described by the picture of Bogoliubov quasiparticles in the BCS pairing theory. The gap parameter of a size ${\ensuremath{\Delta}}_{d}\ensuremath{\simeq}0.13|V|$ (where VVV is the attractive interaction between holes) is estimated at low doping levels. The paired state gives way to the state of clustering of holes for some stronger attractions.
We investigate the properties of a neutral impurity atom coupled with the Tkachenko modes of a two-dimensional vortex lattice in a Bose-Einstein condensate. In contrast with polarons in homogeneous condensates, the marginal impurity-boson interaction in the vortex lattice leads to infrared singularities in perturbation theory and to the breakdown of the quasiparticle picture in the low-energy limit. These infrared singularities are interpreted in terms of a renormalization of the coupling constant, quasiparticle weight, and effective impurity mass. The divergence of the effective mass in the low-energy limit gives rise to a power-law singularity in the impurity spectral function and provides an example of an emergent orthogonality catastrophe in a bosonic system.
Using a proposed numerical technique for calculating anomalous Green's functions characteristic of superconductivity, we show that the low-lying excitations in a wide parameter and doping region of the two-dimensional t-J model are well described by the picture of dressed Bogoliubov quasiparticles in the BCS pairing theory. The pairing occurs predominantly in the dx2{\mathit{d}}_{\mathit{x}}^{2}dx2​-y2{\mathit{y}}^{2}y2-wave channel and the energy gap has a size ${\mathrm{\ensuremath{\Delta}}}_{\mathit{d}}$\ensuremath{\simeq}0.15J--0.27J between quarter and half fillings. Opening of the superconducting gap in the photoemission and inverse-photoemission spectra is demonstrated.