Quantum magnetic oscillations and angle-resolved photoemission from impurity bands in cuprate superconductors

Present-day angle-resolved photoemission spectroscopy (ARPES) has offered a tremendous advance in the understanding of electron energy spectra in cuprate superconductors and some related compounds. However, in high magnetic field, magnetic quantum oscillations at low temperatures indicate the existence of small electron (hole) Fermi pockets seemingly missing in ARPES of hole (electron) doped cuprates. Here ARPES and quantum oscillations are reconciled in the framework of an impurity band in the charge-transfer Mott-Hubbard insulator.

Figure 1

The ortho-II phase of YBa${}_2$Cu${}_3$O${}_{6.5}$ is characterized by a periodic alternation of empty Cu and filled Cu-O $b$-axis chains doubling the unit cell in the $a$ direction. Extra oxygen in the full chains gives rise to an attractive potential for the holes (upper panel) creating a coherent band inside the charge-transfer gap of the Mott-Hubbard insulator (lower panel).

Figure 2

The impurity-band energy dispersion in YBa${}_2$Cu${}_3$O${}_{6.5}$ with four small electron pockets at the reduced Brillouin zone boundary (dark oval spots) as described by Eq. (4) with $t^{\prime }=0.7t$ and the Fermi level $\mu =-2.5t$ (Energy is measured in $2t$ and $a=1$, left panel). Right panel: The momentum-distribution map of the impurity-band spectral function at the Fermi surface with the same parameters and $\gamma =0.04t$.

Figure 3

ARPES momentum-distribution map of the impurity-band (left panel), Eq. (5), with ${(a_{im}/a)}^2=0.4$, $t^{\prime }=0.7t$, and $\gamma =0.94t$. Right panel: the experimental map of the Fermi surface in YBCO6.5 (Ref. 9) (here $a=1$).