  High harmonic generation (HHG) from condensed matter phase holds promise to
promote future cutting-edge research in the emerging field of attosecond
nanoscopy. The key for the progress of the field relies on the capability of
the existing schemes to enhance the harmonic yield and to push the photon
energy cutoff to the extreme ultraviolet (XUV, 10-100 eV) regime and beyond
towards the spectral "water window" region (282-533 eV). Here, we demonstrate a
coherent control scheme of HHG, which we show to give rise to quantum
modulations in the XUV region. The control scheme is based on exploring surface
states in transition-metal surfaces, and specifically by tuning the electronic
structure of the metal surface itself together with the use of optimal chirped
pulses. Moreover, we show that the use of such pulses having moderate
intensities permits to push the harmonic cutoff further to the spectral water
window region, and that the extension is found to be robust against the change
of the intrinsic properties of the material. The scenario is numerically
implemented using a minimal model by solving the time-dependent Schrodinger
equation for the metal surface Cu(111) initially prepared in the surface state.
Our findings elucidate the importance of metal surfaces for generating coherent
isolated attosecond XUV and soft-x-ray pulses and for designing compact
solid-state HHG devices.
