  We investigate the holographic entanglement entropy (HEE) and the holographic
subregion complexity (HSC) for holographic superconductors, both in the
Einstein and in the Einstein-Gauss-Bonnet gravitational theories. For both
ground and excited states, we show that, in the Einstein gravity, the HSC
decreases as the temperature increases and the normal phase has a smaller HSC
than the superconducting phase, which is opposite to the behavior of the HEE.
Moreover, we find out that, for a given temperature $T$ in the superconducting
phase, the higher excited state leads to a lager value of the HEE but a smaller
value of the HSC. However, the Einstein-Gauss-Bonnet gravity has significantly
different effect on the HSC, while the HEE always increases monotonously as the
temperature increases and its value in the normal phase always larger than that
in the superconducting phase. Our results indicate that the HEE and HSC provide
richer physics in phase transitions and condensation of scalar hair for
holographic superconductors with excited states.

High Energy Physics - Theory;General Relativity and Quantum Cosmology