Understanding magnetic focusing in graphene p−n junctions through quantum modeling

Abstract

We present a quantum model which provides enhanced understanding of recent transverse magnetic focusing experiments on graphene p-n junctions. Spatially resolved flow maps of local particle current density show quantum interference and p-n junction filtering effects, which are crucial to explaining the device operation. The Landauer-Büttiker formula is used alongside dephasing edge contacts to give exceptional agreement between simulated nonlocal resistance and the recent experiment by Chen et al. [Science 353, 1522[Science 353, (2016]. The origin of positive and negative focusing resonances and off-resonance characteristics are explained in terms of quantum transmission functions. Our model also captures subtle features from experiment, such as the p-p − to p-p + transition and the second p-n focusing resonance.

A two-dimensional Dirac fermion microscope

“…In the ballistic limit, reflecting walls may add a non-trivial background to the conductance signal of interest, which may become more complex in coherent conditions (see, for example, ref. 53 , Fig. 4 ), analogous to reverberation and standing acoustic waves in a poorly dampened room.…”

Electron collimation at van der Waals domain walls in bilayer graphene

“…This behavior is the analog of a Veselago lens 18 that was realized earlier in photonic crystals 19,20 and metamaterials [21][22][23] . These findings led to profound theoretical investigations of electron focusing in SLG [24][25][26] as well as in AA- 27 and AB-BLG 28 where a valley selective electronic Veselago lens was proposed.…”

Precision measurement of electron-electron scattering in GaAs/AlGaAs using transverse magnetic focusing

“…The vortices cannot be understood by examining individual single-particle trajectories, but rather appear as collective phenomena of all the particles as a whole, in currents resulting from a vector sum over all the trajectories. While TMF has seen extensive numerical study 41 – 46 , current vortices have not been reported till this work. A probable reason lies in the observation that current computation may be dominated by shot noise in TMF simulations performed using particle schemes 44 , 45 , a limitation not suffered by the present high-resolution kinetic scheme.…”

“…A probable reason lies in the observation that current computation may be dominated by shot noise in TMF simulations performed using particle schemes 44 , 45 , a limitation not suffered by the present high-resolution kinetic scheme. It would be interesting to check if vortices persist in the coherent transport regime 43 , 46 .…”