Time-dependent transport in graphene Mach-Zender interferometers

Abstract

Graphene nanoribbons provide an ideal platform for electronic interferometry in the integer quantum Hall regime. Here, we solve the time-dependent four-component Schrödinger equation for single carriers in graphene and expose several dynamical effects of the carrier localization on their transport characteristics in pn junctions. We simulate two kinds of Mach-Zender interferometers (MZI). The first is based on quantum point contacts and is similar to traditional GaAs/AlGaAs interferometers. As expected, we observe Aharonov-Bohm oscillations and phase averaging. The second is based on valley beam splitters, where we observe unexpected phenomena due to the intersection of the edge channels that constitute the MZI. Our results provide further insights into the behavior of graphene interferometers. Additionally, they highlight the operative regime of such nanodevices for feasible single-particle implementations.

Electronic analogue of Fourier optics with massless Dirac fermions scattered by quantum dot lattice

“…In order to observe a clear diffraction pattern in the optical case, the aperture length must be comparable to the wavelength of light [36,37]. This is ensured in our analogue solid-state system by considering that the lattice spacing (∼ 40 nm) and characteristic length (∼ 10 nm) of each barrier [52] in this QD lattice are smaller than the de Broglie wavelength calculated from the incident energy of the graphene electrons (∼30-40 meV) [20]. Also, for the typical energy range we have considered, the wavevector of the MDF is much smaller than the Fermi wave vector, i.e.…”

“…The unique transmission properties of massless Dirac fermions (MDF) in graphene through potential landscapes created by a variety of electromagnetic (EM) fields, particularly in the ballistic regime [1][2][3][4][5][6], and its similarity with the light transmission through an optical medium with unconventional dielectric properties such as metamaterials [7,8] make graphene an excellent material to realize electron optics-based devices in a solid state system. The realization of negative refraction [9], chiral Veselago lensing of MDF in two [10] and three dimensions [11], tunable Veselago interference in a bipolar graphene microcavity [12], creation of a Dirac fermion microscope [13], collimation [14][15][16], and different type of interferometers [17][18][19][20], gate tunable beam-splitter of such MDF [21], Fabry-Pérot resonator in graphene/hBN moiré super-lattice [22], gradient index electron optics in graphene p-n junction [23], Mie scattering in graphene, [24] are few milestones in this direction. Most of these experimental and theoretical studies are based on theoretical modelling of Dirac fermions scattered by the potential, which are constant in one direction [1-6, 14, 25-30], and hence limit the range of applications in this fast-growing field.…”