Scaling of Time-Dependent Tunneling Current in Terahertz Scanning Tunneling Microscopes

Abstract

Terahertz scanning tunneling microscopy (THz-STM) has enabled spatiotemporal imaging with femtosecond temporal resolution and angstrom spatial resolution. In THz-STMs, the junction bias is modulated by coupling THz pulses, which results in transient voltage bias and extremely high transient tunneling currents. In order to have efficient imaging of the sample surface, it is important to understand the nonlinear tunneling current response and its parametric dependence. In this work, we theoretically investigate the basic scaling of rectified electrons in a THz-STM junction. We use a self-consistent quantum model that includes both space-charge potential and exchange-correlation potential, which were ignored in previous studies. Since THz-STMs are operated at high transient voltage in field emission regime, the effects of exchange-correlation potential become crucial. We validate our calculation with recently reported experimental data and investigate the rectification property of the tip-sample junction for different parameters. We find that the time-dependent tunneling current and the electron transport can be manipulated by varying the dc bias voltage (polarity, amplitude), incident THz field (polarity, shape, peak amplitude), work functions of STM tip and sample---especially their difference $\mathrm{\ensuremath{\Delta}}W$, and the tip-sample separation. Our study provides an important framework that can be used in the future to characterize, control, and improve THz-induced currents and probing techniques at the nanometer scale over subpicosecond time periods.