Robust strong-field theory model for ultrafast electron transport through metal-insulator-metal tunneling nanojunctions

Ultrafast science studies the dynamics of electrons in matter with extreme temporal precision, typically in the attosecond and femtosecond time domain. Recent experimental and theoretical progress has put metal-insulator-metal (MIM) tunneling nanojunctions in the spotlight of ultrafast science. Waveform-controlled laser fields can induce ultrafast currents in these junctions, opening the door to petahertz electronic operation and attosecond-scale scanning tunneling microscopy. Inspired by our strong-field model for attosecond tunneling microscopy [B. Ma and M. Krüger, ], here we generalize our model to MIM nanojunctions. We introduce several refinements and corrections, accounting for the image potential inside the gap and boundary effects. Moreover, we also find that the Keldysh parameter, which is a hallmark parameter for ultrafast light-matter interactions, alone is insufficient for describing the physics in thin MIM nanojunctions. We introduce a new parameter <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>ζ</a:mi></a:math> that accounts for the effects of the limited size of the junction and provide several interpretations of the parameter that shed new light on the complex physics in the light-driven junction. Most strikingly, we find that for <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>ζ</b:mi><b:mo>></b:mo><b:mn>1</b:mn></b:mrow></b:math> photon-assisted tunneling is dominating the ultrafast electron transport across the junction, regardless of the value of the Keldysh parameter. Here one or more photons are absorbed and the electron undergoes static tunneling through the barrier. <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>ζ</c:mi><c:mo><</c:mo><c:mn>1</c:mn></c:mrow></c:math> is required for a regime in which the laser field and the Keldysh parameter dominate the transport. We also discuss the three-step model of electron transport across the nanojunction in the adiabatic regime, the energy cutoff of the transported electrons, and the carrier-envelope phase control of the net current. Our theory model provides a rich toolbox for understanding and predicting the physics of ultrafast MIM nanojunctions.