Spectral behavior of the electronic states of bilayer cuprate systems using a slave fermion approach

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The spectral function for electrons in the normal state of a bilayer cuprate is calculated by employing a slave fermion approach. The electron correlations in the ${\mathrm{CuO}}_{2}$ layers in these cuprates are described by a t-J model, and the electronic coupling between the two ${\mathrm{CuO}}_{2}$ layers within the same unit cell is introduced via a hopping matrix element ${(t}_{\ensuremath{\perp}})$ and an exchange interaction ${(J}_{\ensuremath{\perp}}).$ The spectral function is calculated for different values of the hole concentration, temperature, and anisotropy at various values of the momentum ${(k}_{x}{,k}_{y}).$ It is found that the bilayer coupling ${(t}_{\ensuremath{\perp}})$ significantly affects the behavior of the spectral function. The spectral function around the momentum value (\ensuremath{\pi}, 0) for a coupled bilayer cuprate shows a peak much sharper than that for a system of uncoupled layers. Our calculation also suggests a splitting of electronic states of the bilayer cuprates along the (\ensuremath{\pi}, 0) direction for the heavily overdoped regime. Calculations of the imaginary part of the self-energy ${\ensuremath{\Sigma}}_{1}^{\ensuremath{''}}(k,\ensuremath{\omega})$ for a bilayer system have also been presented. It is found that ${\ensuremath{\Sigma}}_{1}^{\ensuremath{''}}(k,\ensuremath{\omega})$ depends strongly on the momentum and shows a ${\ensuremath{\omega}}^{\ensuremath{\alpha}}$ dependence on energy with $1.2<\ensuremath{\alpha}<1.5$ for values of the parameters t and J considered in the present calculations.