Mesoscopic valley filter in graphene Corbino disk containing a p–n junction

Abstract

The Corbino geometry allows one to investigate the propagation of electric current along ap-n interface in ballistic graphene in the absence of edge states appearing for the familiar Hall-bar geometry. Using the transfer matrix in the angular-momentum space we find that for sufficiently strong magnetic fields the current propagates only in one direction, determined by the magnetic field direction and the interface orientation, and the two valleys, K and K′, are equally occupied. Spatiallyanisotropic effective mass may suppress one of the valley currents, selected by the external electric field, transforming the system into amesoscopic version of the valley filter. The filtering mechanism can be fully understood within the effective Dirac theory, without referring to atomic-scale effects which are significant in proposals operating on localized edge states.

Wiedemann–Franz Law for Massless Dirac Fermions with Implications for Graphene

“…The exact transmission-energy dependence can be given for two special device geometries in graphene: a rectangular sample attached to heavily-doped graphene leads [ 19 , 20 , 21 ] and for the Corbino disk [ 22 , 23 ]. Although these systems posses peculiar symmetries, allowing one to solve the scattering problem employing analytical mode-matching method (in particular, the mode mixing does not occur), both solutions were proven to be robust against various symmetry-breaking perturbations [ 48 , 49 , 50 , 51 ]. More importantly, several features of the results have been confirmed in the experiments [ 33 , 34 , 52 , 53 ] showing that even such idealized systems provide valuable insights into the quantum transport phenomena involving Dirac fermions in graphene.…”

Wiedemann-Franz law for massless Dirac fermions with implications for graphene

“…The exact transmission-energy dependence T (ε) can be given for two special device geometries in graphene: a rectangular sample attached to heavily-doped graphene leads [16][17][18] and for the Corbino disk [19,20]. Although these systems posses peculiar symmetries, allowing one to solve the scattering problem employing analytical mode-matching method (in particular, the mode mixing does not occur), both the solutions were proven to be robust against various symmetrybreaking perturbations [46][47][48]. More importantly, several features of the results have been confirmed in the experiments [30,31,50,51] showing that even such idealized systems provide valuable insights into the quantum transport phenomena involving Dirac fermions in graphene.…”

Development of gateless quantum Hall checkerboard p–n junction devices

“…The advantage of these complex configurations is that a whole set of quantized resistances becomes accessible and can provide overwhelming evidence of device functionality in addition to being a future application for quantum-based electrical standards. Specific applications of general checkerboard devices, much like those that will be demonstrated and proposed, also include the construction of a multi-interfaced, twodimensional Dirac fermion microscope [31], custom programmable quantized resistors [32], and mesoscopic valley filters [33]. It is therefore also important to verify these checkerboard devices as functional so that their fabrication methods can be justified for use in other applications.…”