Effects of strain on Goos-Hänchen shifts of monolayer phosphorene

We investigate the Goos-Hänchen(GH) shift for ballistic electrons (i) reflected from a step-like inhomogeneity of strain, and (ii) transmitted through a monolayer phosphoresce junction consisting of a positive strained region and two normal regions (or a normal region and two negative strained regions). Refraction occurs at the interface between the unstrained/positive-strain(negative-strain/unstrained), in analogy with optical refraction. The critical angle is different for different strengths and directions of the strains. The critical angles for electrons tunneling through unstrained/positive-strain junction can even decrease to zero when the positive strain exceeds a critical value. For the monolayer phosphorene junction consisting of a positive strain region and two normal regions (or a normal region and two negative strain regions), we find that the GH shifts resonantly depends on the middle region width. The resonant values and the plus-minus sign of the displacement can be controlled by the incident angle, incident energy and the strain. These properties will be useful for the applications in phosphorene-based electronic devices.