Graphene n−p junctions in the quantum Hall regime: Numerical study of incoherent scattering effects

Abstract

We investigate electronic transport through a graphene n-p junction in the quantum Hall effect regime at high perpendicular magnetic field, when the filling factors in the n-doped and p-doped regions are fixed to 2 and -2 respectively. We compute numerically the conductance G, the noise Q and the Fano factor F of the junction when inelastic effects are included along the interface in a phenomenological way, by means of fictitious voltage probes. Using a scaling approach, we extract the system coherence length L φ and describe the full crossover between the coherent limit (W L φ ) and the incoherent limit (W L φ ), W being the interface length. While G saturates at the value e 2 /h in the incoherent regime, Q and F are found to vanish exponentially for large length W . Corrections due to disorder are also investigated. Our results are finally compared to available experimental data.

Interplay of filling fraction and coherence in symmetry broken graphene p-n junction

“…This can be qualitatively understood from the increased mesoscopic conductance fluctuations of the junction, observed at higher filling factors plateaus. As the coherence increases, conductance fluctuation increases 23,31 , as can be seen in Fig. 1b, d.…”

“…A graphene p-n junction (PNJ) naturally harboring co-propagating electron and hole-like edge states offers an ideal platform [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] to study the edge or equilibration dynamics. The equilibration of such edge states is predicted to be facilitated by inter-channel tunneling via either incoherent or coherent scattering mechanism [23][24][25][26][27][28][29][30][31] depending on the microscopic details of the interface. As suggested by Abanin and Levitov 24 , for a graphene PNJ interface with random disorders, the edge mixing is expected to be dominated by the incoherent process.…”

Valley isospin of interface states in a graphene pn junction in the quantum Hall regime

“…13, for which the disagreement between simulation and theory is in the range of a few percent only. Without a smoothly vanishing magnetic field at the armchair boundaries, no quantitative agreement between the theoretical predictions (21) and (23) and the numerical simulations could be obtained (data not shown). We note that a significant difference between the theoretical prediction and numerically observed conductance value was previously seen in Ref.…”

“…A system that has received considerable theoretical [12][13][14][15][16][17][18][19][20][21][22][23] and experimental attention is a graphene pn junction in a quantizing magnetic field. [24][25][26][27][28][29][30][31][32][33][34][35][36] The chiral edge states in such a pn junction move in opposite directions in the p-and n-type regions.…”

Electrostatic superlattices on scaled graphene lattices

“…To perform quantum transport simulations for graphene working in real-space, the scalable tight-binding model [33] has been proved to be a very convenient numerical trick (see, for example, [34][35][36][37][38]): the physics of a graphene system can be captured by a graphene lattice scaled by a factor of s f such that the lattice spacing is given by a = s f a 0 with a 0 ≈ 0.142 nm the carbon-carbon distance and the nearest neighbor hopping is t = t 0 /s f with t 0 ≈ 3 eV the hopping parameter for a genuine graphene lattice, as long as the scaled lattice spacing a remains much shorter than all important physical length scales in the graphene system of interest.…”