Graphene n-p junction in a strong magnetic field: a semiclassical study

We provide a semiclassical description of the electronic transport through graphene n-p junctions in the quantum Hall regime. A semiclassical approximation for the conductance is derived in terms of the various snake-like trajectories at the interface of the junction. For a symmetric (ambipolar) configuration, the general result can be recovered by means of a simple scattering approach, providing a very transparent qualitative description of the problem under study. Consequences of our findings for the understanding of recent experiments are discussed.Comment: 10 pages, 2 figure

Semiclassical magnetotransport in graphene n-p junctions

We provide a semiclassical description of the electronic transport through graphene n-p junctions in the quantum Hall regime. This framework is known to experimentally exhibit conductance plateaus whose origin is still not fully understood. In the magnetic regime (E < vF B), we show the conductance of excited states is essentially zero, while that of the ground state depends on the boundary conditions considered at the edge of the sample. In the electric regime (E > vF B), for a step-like electrostatic potential (abrupt on the scale of the magnetic length), we derive a semiclassical approximation for the conductance in terms of the various snake-like trajectories at the interface of the junction. For a symmetric configuration, the general result can be recovered using a simple scattering approach, providing a transparent analysis of the problem under study. We thoroughly discuss the semiclassical predicted behavior for the conductance and conclude that any approach using fully phase-coherent electrons will hardly account for the experimentally observed plateaus.Comment: 22 pages, 19 figure

Generalized second law of thermodynamics in the Glosten-Milgrom model

We derive an upper bound for the expected gain of informed traders in the Glosten-Milgrom model with finite horizon, fully analogous to a generalized second law of thermodynamics. This result extends that obtained by Touzo et al. a couple of years ago. The proof relies on Bayesian inference (exploiting the invariance of the problem under consecutive game sequences) and an interesting entropic inequality. We also provide numerical results both supporting the existence of a characteristic timescale in the model and illustrating the magnitude of gain fluctuations. Other possible extensions are discussed.Comment: 13 pages, 6 figure

Tunable thermopower in a graphene-based topological insulator

Following the recent proposal by Weeks et al., which suggested that indium (or thallium) adatoms deposited on the surface of graphene should turn the latter into a quantum spin Hall (QSH) insulator characterized by a sizeable gap, we perform a systematic study of the transport properties of this system as a function of the density of randomly distributed adatoms. While the samples are, by construction, very disordered, we find that they exhibit an extremely stable QSH phase with no signature of the spatial inhomogeneities of the adatom configuration. We find that a simple rescaling of the spin-orbit coupling parameter allows us to account for the behaviour of the inhomogeneous system using a homogeneous model. This robustness opens the route to a much easier experimental realization of this topological insulator. We additionally find this material to be a very promising candidate for thermopower generation with a target temperature tunable from 1 to 80K and an efficiency ZT close to 1.Comment: 7 pages, 5 figure

Graphene-based heterojunction between two topological insulators

Quantum Hall (QH) and quantum spin Hall (QSH) phases have very different edge states and, when going from one phase to the other, the direction of one edge state must be reversed. We study this phenomena in graphene in presence of a strong perpendicular magnetic field on top of a spin-orbit (SO) induced QSH phase. We show that, below the SO gap, the QSH phase is virtually unaffected by the presence of the magnetic field. Above the SO gap, the QH phase is restored. An electrostatic gate placed on top of the system allows to create a QSH-QH junction which is characterized by the existence of a spin-polarized chiral state, propagating along the topological interface. We find that such a setup naturally provides an extremely sensitive spin-polarized current switch.Comment: 10 pages, 5 figure

Berry phase in graphene: a semiclassical perspective

We derive a semiclassical expression for the Green's function in graphene, in which the presence of a semiclassical phase is made apparent. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. These phases coincide for the perfectly linear Dirac dispersion relation. They differ however when a gap is opened at the Dirac point. We furthermore present several applications of our semiclassical formalism. In particular we provide, for various configurations, a semiclassical derivation of the electron's Landau levels, illustrating the role of the semiclassical ``Berry-like'' phas