Wave-packet dynamics and valley filter in strained graphene

Abstract

The time evolution of a wavepacket in strained graphene is studied within the tight-binding model and continuum model. The effect of an external magnetic field, as well as a strain-induced pseudomagnetic field, on the wave packet trajectories and zitterbewegung are analyzed. Combining the effects of strain with those of an external magnetic field produces an effective magnetic field which is large in one of the Dirac cones, but can be practically zero in the other. We construct an efficient valley filter, where for a propagating incoming wave packet consisting of momenta around the K and K ′ Dirac points, the outgoing wave packet exhibits momenta in only one of these Dirac points, while the components of the packet that belong to the other Dirac point are reflected due to the Lorentz force. We also found that the zitterbewegung is permanent in time in the presence of either external or strain-induced magnetic fields, but when both the external and strain-induced magnetic fields are present, the zitterbewegung is transient in one of the Dirac cones, whereas in the other cone the wave packet exhibits permanent spatial oscillations.

Localization and circulating currents in curved graphene devices

“…26 Alternately, weak intervalley scattering has been shown to lift the valley degeneracy. 16,27 Experimentally one can measure the angular distribution of the probability density using a scanning tunneling microscope (STM). To get an estimate for the order of magnitude of the magnetic fields produced we approximate the current density depicted in Fig.…”

Graphene Nanobubbles as Valley Filters and Beam Splitters

“…Different routes have been suggested to create valley polarization in graphene [13][14][15][16][17], relying on nanoribbons or constrictions [17][18][19][20][21], interplays between external fields [22][23][24][25], spin-orbit coupling [26,27], or spatial or temporal combinations of gating and magnetic fields [28][29][30]. However, an experimental verification has proven to be challenging as practical and effective methods to manipulate the valleys in realistic setups still need to be established.…”

Geometric valley Hall effect and valley filtering through a singular Berry flux

“…In graphene, due to its synthetic nature, the valley isospin can be manipulated for various valley filtering designs via strategies such as perfect zigzag edge confinements 1 , staggered sublattice potentials 2 , trigonal warping effect of the band structures 15 , line defects 17 , and strain engineering 10,11,[18][19][20] . A viable mechanism to realize valley filtering is through the valley Hall effect (VHE) 2,5,7,[21][22][23][24][25][26][27][28] , where electrons with different valley quantum numbers are separated and move in spatially distinct regions.…”

“…Alternative mechanisms for VHE require external magnetic fields, strain-induced pseudo magnetic fields, or magnetic materials that have an opposite effect on the two valleys 10,11,[18][19][20] . We ask the following question: when Berry curvatures vanish does nontrivial valleycontrasting physics exist without any valley-resolved perturbation?…”