Anomalous quantum scattering and transport of electrons with Mexican-hat band structure induced by electrical potential

We theoretically study the quantum scattering and transport of electrons with Mexican-hat dispersion through both step and rectangular potential barriers by using the transfer matrix method. Owing to the torus-like iso-energy lines of the Mexican-hat dispersion, abnormal retro-reflection (RR) and specular transmission (ST) are generated besides the normal reflection (NR) and transmission (NT). For the step potential with electrons incident from the large wavevector, the transmission is primarily governed by NT with nearly negligible ST, while the reflection is dominant by RR (NR) within (outside) the critical angle. Additionally, for electrons incident from the small wavevector, the NT can be reduced to zero by adjusting the barrier, resulting in a significant enhancement of ST and RR. For the rectangular barrier, the transmission and reflection spectra resemble those of the step barrier, but there are two kinds of resonant tunneling which can lead to perfect NT or ST. Due to the anomalous scattering process, the conductance of the system can be effectively controlled by adjusting the height and width of the barrier as well as the incident energy. Our results provide a deeper understanding of the electron states governed by the Mexican-hat dispersion.