Abstract
A microscopic theory of electronic spectrum and superconductivity within the $t$-$J$ model on the honeycomb lattice is formulated. The Dyson equation for the normal and anomalous Green functions for the two-band model in terms of the Hubbard operators is derived by applying the Mori-type projection technique. The self-energy is evaluated in the self-consistent Born approximation for electron scattering on spin and charge fluctuations induced by the kinematical interaction for the Hubbard operators. Superconducting pairing mediated by the antiferromagnetic exchange and spin fluctuations is discussed.
Highlights
One of the crucial issues in the current theory of condensed matter is the study of superconductivity in strongly correlated electronic systems, as in the cuprate high-temperature superconductors
We derive Dyson equation for the normal and anomalous matrix Green functions (GFs) with the self-energy evaluated in the self-consistent Born approximation (SCBA) as for the one-band t-J model in [13] and the Hubbard model in [14, 15] on the square lattice
Similar calculations of the anomalous self-energy (3.27), (3.28) give an equation for the frequency dependent gap (3.15). Implementation of this program demands complicated self-consistent numerical computations for the two-band t-J model which are much more complicated than similar calculations performed for the one-band t-J model on the square lattice in [13]
Summary
One of the crucial issues in the current theory of condensed matter is the study of superconductivity in strongly correlated electronic systems, as in the cuprate high-temperature superconductors (see, e.g., [1]). Studies of the graphene beyond the simple model of noninteracting electrons by taking into account the Coulomb interaction reveal a rich phase diagram with phase transitions to the antiferromagnetic (AF) state, spin-density wave (SDW), charge-density wave (CDW), and nonconventional superconductivity (SC). Superconducting phase transitions in the Hubbard model on the honeycomb lattice have been considered in several. In the above cited papers, mostly the phase diagram of the models with the Coulomb interaction on the honeycomb lattice was studied at zero temperature by numerical methods. We derive Dyson equation for the normal and anomalous matrix GFs with the self-energy evaluated in the self-consistent Born approximation (SCBA) as for the one-band t-J model in [13] and the Hubbard model in [14, 15] on the square lattice.
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