  Photoemission driven by a strong electric field of near-infrared or visible
light, referred to as strong-field photoemission, produces attosecond electron
pulses that are synchronized to the waveform of the incident light, and this
principle lies at the heart of current attosecond technologies. However, full
access to strong-field photoemission regimes at near-infrared wavelengths based
on solid-state materials is restricted by space-charge screening and material
damage at high optical-field strengths, which significantly hampers the
realization of predicted attosecond technologies, such as ultra-sensitive
optical phase modulation. Here, we demonstrate a new type of strong-field
photoemission behaviour with extreme nonlinearity -- photoemission current
scales follow a 40th power law of the optical-field strength, making use of
sub-nanometric carbon nanotubes and 800 nm pulses. As a result, the total
photoemission current depends on the carrier-envelope phase with a greatly
improved photoemission current modulation depth of up to 100%, which has not
previously been achieved. Time-dependent density functional calculations reveal
the completely new behaviour of the optical-field induced tunnelling emission
process directly from the valence band of the carbon nanotubes, which is an
indication of full access to a strong-field photoemission regime. Furthermore,
the nonlinear dynamics are observed to be tunable by changing the binding
energy of the valence-band-maximum, as confirmed by Simpleman model
calculations. We believe that such extreme nonlinear photoemission from
nanotips offers a new means of producing extreme temporal-spatial resolved
electron pulses. These results additionally provide a new design philosophy for
attosecond electronics and optics by making use of tunable band structures in
nanomaterials.
