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The calculated relative change of the LDOS in (left) graphene and (right) two-dimensional electron gas (2DEG) due to a 10 x 20 nm rectangular arrangement of 36, identical scatterers (radius of 1 nm).
Scattering in Graphene
Scattering in Graphene
We developed a theory to calculate the local density of states (LDOS) in single layer graphene in the presence of localized scatterers based upon multiple scattering theory. The scatterer size was much larger than the size of the graphene unit cell in order to avoid intervalley scattering. Knowledge of the wave function and its derivatives, which can be determined self-consistently using Foldy-Lax multiple scattering theory, the Green's function and hence LDOS can be calculated. The spinor nature and linear dispersion relation for the quasiparticles in graphene lead to structures in the LDOS that should be observable using STM. Possible extensions of the theory include applications to multilayer graphene and/or intervalley scattering.
Suppressing Klein Tunneling
Suppressing Klein Tunneling
The unit cell of single-layer graphene consists of two inequivalent carbon atoms. As a result of this and the honeycomb lattice structure of graphene, the electronic band structure of graphene is linear in wave vector k and has a "pseudospin" character, where wave vectors moving in opposite directions are associated with opposite "pseudospin" states. One consequence of this is that if an electron is normal to an electrostatic barrier, the electron is transmitted 100% of the time even if the barrier potential goes to infinity since the potential cannot "flip" the pseudospin in order to reflect the electron (in a regular 2DEG, transmission would go to zero). However, we demonstrated that if you actually place openings in the barrier (making it presumably "leaky"), the transmission is reduced and can go close to zero. This is a consequence of opening up Bragg scattering due to periodic array of scatterers. Possible extensions of our theory can look at "trapping" graphene inside quantum dot using localized scatterers.
Plot of dimensionless probability density in graphene for an incident wave from the left to a one-dimensional scattering array (unit cell a single scatterer with lattice constant 30 nm). The Talbot effect is seen in the transmitted wave (right side), although the reflect wave also exhibits a periodic interference pattern.
When a monochromatic wave is transmitted through a periodic diffraction grating of spacing, the transmitted wave exhibits revivals or "self-imaging" periodically away from the grating. This coherent transport phenomenon, named the Talbot effect, as been observed in photonic crystals, plasmonic devices, and even electron beams. Our group investigated the nature of the Talbot effect in graphene. We found that a Talbot effect should exist in graphene, and that due to the "pseudospin" nature of electrons in graphene, there are additional small oscillations in intensity that could be observed. Possible extensions of this work are to incorporate intervalley scattering, "magnetic" scatterers, and a possible view of whether the angular Talbot effect could be observed in graphene.
A 2DEG with spin-orbit coupling has, similar to graphene, electronic states where the momentum is coupled to the spin of the electron. Unlike graphene, however, there are two bands with nonzero energies that for momentum in a certain direction, have both opposite spins with with wavevectors with slightly different magnitudes. As such, when a monochromatic beam of electrons is incident to a periodic scattering array (magenta in Fig. to the right), the scattered waves can be in both the + (blue) and - (red) spin bands. When these waves interfere, an additional modulation occurs due to interference between waves in different spin subbands. While the Talbot length usually depends only upon the incident wavelength, an additional Talbot length due to intersubband interference arises (essentially one "color" has become two after scattering). This can be seen in the plots of the transmitted probability densities where both the full (bottom, inter and intra subband interference) and only intrasubband interference (top) are shown. Slices through these probability densities show additional peaks that are present due to intersubband interference. Possible extensions would be to consider magnetic scatterers, the combined effects of Rashba and Dresselhaus coupling, and the effects of spin-orbit coupling on the angular Talbot effect.
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