Carrier-Envelope-Phase Modulated Currents in Scanning Tunneling Microscopy

Carrier-envelope-phase (CEP) stable optical pulses combined with state-of-the-art scanning tunneling microscopy (STM) can track and control ultrafast electronic tunneling currents. On the basis of nonequilibrium Green's function formalism, we present a time and frequency domain theoretical study of CEP-stable pulse-induced tunneling currents between an STM tip and a metal substrate. It is revealed that the experimentally observed phase shift between the maximum tunneling current and maximum electric field is caused by the third-order response to the electric field. The shift is also found to be sensitive to the duration of pulses. The tunneling process can thus be precisely manipulated by varying the phase and duration of these pulses.