Fermi-surface reconstruction in a smectic phase of a high-temperature superconductor

It is shown that, in the presence of a moderately strong $C_4$ symmetry breaking (which could be produced either by lattice orthorhombicity or the presence of an electron nematic phase), a weak, period 4, unidirectional charge density wave (“charge stripe”) order can reconstruct the Fermi surface of a typical hole-doped cuprate to produce a small electron pocket. This form of charge density wave order is consistent with that adduced from recent high field NMR experiments in YBCO. The Fermi pocket has an area and effective mass which is a rough caricature of those seen in recent high field quantum oscillation experiments.

Figure 1

The schematic representation of the Fermi surface with (solid line) and without (dashed line) nematic ordering. (a) $t^{\prime }/t=-0.3$ and ${\phi }_N=0.074$; (b) $t^{\prime }/t=-0.4$ and ${\phi }_N=0.143$. In both cases, the doping is $x=1/8$.

Figure 2

Schematic representation (thick black lines) of the folded Fermi surface with nematic ordering and period-4 charge stripe order and $x=1/8$. In (a), $t^{\prime }/t=-0.3$, ${\phi }_N=0.074$, $V_0=0.15t$, and $V_2=0.10t$, while in (b), $t^{\prime }/t=-0.4$, ${\phi }_N=0.143$, $V_0=0.11t$, and $V_2=0.09t$, and the electron pocket encloses roughly 1% of the unreconstructed BZ. The parameters have been chosen for graphical clarity. When comparing with experiment, we have taken $V_0=0.02t$, and $V_2=0.01t$, so that the electron pockets are roughly 2% of the BZ, but then the gaps between Fermi surface segments are quite small. The thin (red) lines are the zone-folded Fermi surfaces in the limit of vanishing stripe order, $V_0=V_2=0$, and the (blue) shaded line is the unfolded Fermi surface.