Analytical Model of Optical-Field-Driven Subcycle Electron Tunneling Pulses from Two-Dimensional Materials

Abstract

We develop analytical models of optical-field-driven electron tunneling from the edge and surface of free-standing twodimensional (2D) materials. We discover a universal scaling between the tunneling current density (J) and the electric field near the barrier (F): In(J/|F| β ) ∝ 1/|F| with β values of 3 / 2 and 1 for edge emission and vertical surface emission, respectively. At ultrahigh values of F, the current density exhibits an unexpected high-field saturation effect due to the reduced dimensionality of the 2D material, which is absent in the traditional bulk material. Our calculation reveals the dc bias as an efficient method for modulating the optical-field tunneling subcycle emission characteristics. Importantly, our model is in excellent agreement with a recent experiment on graphene. Our results offer a useful framework for understanding optical-field tunneling emission from 2D materials, which are helpful for the development of optoelectronics and emerging petahertz vacuum nanoelectronics.

Designing edge states from fractional polarization insulators

“…Due to the existence of delocalized states around the k x = 0 momenta, the finite size effect, which can destroy the quantum spin and anomalous hall effect [45,46], can be exploited to produce disconnected edge states analogous to helical-like and chiral-like edge states, not possible through the chiral symmetry-breaking terms. The tunability of these disconnected edge states can provide new avenues in designing topological domain walls in electronic devices [30,50,51] and heterojunctions [52,53], and also yield unusual behaviors in physical mechanisms such as in electron emission [54][55][56][57] and transport [26,30].…”