The dispersion relation for plasmons in a layered crystal with a single conducting layer in the unit cell in terms of the longitudinal momentum for continuous variation in the transverse momentum from 0 to . The lower curve is the upper bound of the quantum Landau damping region (a). Same with two conducting layers in the unit cell. In the region between the lower boundary of the plasmon band and the upper boundary of the damping region there is an additional quasiacoustic plasma branch associated with counterphase collective oscillations28 of the electron density in different sublattices generated by 2D layers shifted relative to one another by a distance (b).
The plasmon spectral function in a layered crystal with a single layer in the unit cell and the band spectrum of Ref. 25, normalized to frequency and averaged over , for . The two sharp peaks correspond to singularities in the density of states on the optical (high frequency peak) and quasiacoustic (low frequency) boundaries of the plasmon dispersion region with respect to . In addition, the function has a smeared out low-frequency peak associated with the strong anisotropy of the Fermi velocity in the plane of the 2D layers (a). The plasmon spectral function in a layered crystal with two sublattices of 2D layers in the unit cell and the band spectrum of Ref. 25, normalized to frequency and averaged over , for . Besides the features owing to the presence of extended saddle singularities, one can also see a structure of additional peaks associated with counterphase oscillations of the electron density in different sublattices (b). The insets show the shape of the low frequency region of the plasmon spectrum in more detail.
Momentum dependence of the real part of the electron eigenenergy (11) at a frequency of along the principal directions of the Brillouin zone for two different doping levels in YBaCuO crystals corresponding to different values of the unrenormalized chemical potential for the falling spectrum of Ref. 25, (1) and (2).
Renormalized quasiparticle spectrum (below the Fermi level) for the same values of the chemical potential as in Fig. 3, with a characteristic kink feature at energies . The region of the kink is shown with an expanded momentum scale in the inset.
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