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Register a new userLocalization and circulating currents in curved graphene devices
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We calculate the energy spectrum and eigenstates of a graphene sheet which contains a circular deformation. Using time-independent perturbation theory with the ratio of the height and width of the deformation as the small parameter, we find that due to the curvature the wavefunctions for the various states acquire unique angular asymmetry. We demonstrate that the pseudo-magnetic fields induced by the curvature result in circulating probability currents. These circulating currents in turn produce local textit{real} magnetic fields $sim$ 100 $mu$T which can be measured using current technology.
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We study the time evolving currents flowing in an interacting, ring-shaped nanostructure after a bias voltage has been switched on. The source-to-drain current exhibits the expected relaxation towards its quasi-static equilibrium value at a rate $Gamma_0$ reflecting the lead-induced broadening of the ring states. In contrast, the current circulating within the ring decays with a different rate $Gamma$, which is a rapidly decaying function of the interaction strength and thus can take values orders of magnitude below $Gamma_0$. This implies the existence of a regime in which the nanostructure is far from equilibrium even though the transmitted current is already stationary. We discuss experimental setups to observe the long-lived ring transients.
A variational approach is used in order to study the stationary states of Hall devices. Charge accumulation, electric potentials and electric currents are investigated on the basis of the Kirchhoff-Helmholtz principle of least heat dissipation. A simple expression for the state of minimum power dissipated -- that corresponds to zero transverse current and harmonic chemical potential -- is derived. It is shown that a longitudinal surface current proportional to the charge accumulation is flowing near the edges of the device. Charge accumulation and surface currents define a boundary layer over a distance of the order of the Debye-Fermi length.
We study the effects of strain on the electronic properties and persistent current characteristics of a graphene ring using the Dirac representation. For a slightly deformed graphene ring flake, one obtains sizable pseudomagnetic (gauge) fields that may effectively reduce or enhance locally the applied magnetic flux through the ring. Flux-induced persistent currents in a flat ring have full rotational symmetry throughout the structure; in contrast, we show that currents in the presence of a circularly symmetric deformation are strongly inhomogeneous, due to the underlying symmetries of graphene. This result illustrates the inherent competition between the `real magnetic field and the `pseudo field arising from strains, and suggest an alternative way to probe the strength and symmetries of pseudomagnetic fields on graphene systems.
We study the Landau levels in curved graphene sheets by measuring the discrete energy spectrum in the presence of a magnetic field. We observe that in rippled graphene sheets, the Landau energy levels satisfy the same square root dependence on the energy quantum number as in flat sheets, $E_n sim sqrt{n}$. Though, we find that the Landau levels in curved sheets are shifted towards lower energies by an amount proportional to the average spatial deformation of the sheet. Our findings are relevant for the quantum Hall effect in curved graphene sheets, which is directly related to Landau quantization. For the purpose of this study, we develop a new numerical method, based on the quantum lattice Boltzmann method, to solve the Dirac equation on curved manifolds, describing the low-energetic states in strained graphene sheets.
We study theoretically the interaction of ultrashort optical pulses with gapped graphene. Such strong pulse results in finite conduction band population and corresponding electric current both during and after the pulse. Since gapped graphene has broken inversion symmetry, it has an axial symmetry about the $y$-axis but not about the $x$-axis. We show that, in this case, if the linear pulse is polarized along the $x$-axis, the rectified electric current is generated in the $y$ direction. At the same time, the conduction band population distribution in the reciprocal space is symmetric about the $x$-axis. Thus, the rectified current in gapped graphene has inter-band origin, while the intra-band contribution to the rectified current is zero.
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