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Register a new userRippled Graphene in an In-Plane Magnetic Field: Effects of a Random Vector Potential
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We report measurements of the effects of a random vector potential generated by applying an in-plane magnetic field to a graphene flake. Magnetic flux through the ripples cause orbital effects: phase-coherent weak localization is suppressed, while quasi-random Lorentz forces lead to anisotropic magnetoresistance. Distinct signatures of these two effects enable an independent estimation of the ripple amplitude and correlation length.
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An analysis of electron transport in graphene is presented in the presence of various arrangement of delta-function like magnetic barriers. The motion through one such barrier gives an unusual non specular refraction leading to asymmetric transmission. The symmetry is restored by putting two such barriers in opposite direction side by side. Periodic arrangements of such barriers can be used as Bragg reflectors whose reflectivity has been calculated using a transfer matrix formalism. Such Bragg reflectors can be used to make resonant cavities. We also analyze the associated band structure for the case of infinite periodic structures.
A weak perpendicular magnetic field, $B$, breaks the chiral symmetry of each valley in the electron spectrum of graphene, preserving the overall chiral symmetry in the Brillouin zone. We explore the consequences of this symmetry breaking for the interaction effects in graphene. In particular, we demonstrate that the electron-electron interaction lifetime acquires an anomalous $B$-dependence. Also, the ballistic zero-bias anomaly, $delta u(omega)$, where $omega$ is the energy measured from the Fermi level, emerges at a weak $B$ and has the form $delta u(B)sim B^2/omega^2$. Temperature dependence of the magnetic-field corrections to the thermodynamic characteristics of graphene is also anomalous. We discuss experimental manifestations of the effects predicted. The microscopic origin of the $B$-field sensitivity is an extra phase acquired by the electron wave-function resulting from the chirality-induced pseudospin precession.
We study the effects that ripples induce on the electrical and magnetic properties of graphene. The variation of the interatomic distance created by the ripples translates in a modulation of the hopping parameter between carbon atoms. A tight binding Hamiltonian including a Hubbard interaction term is solved self consistently for ripples with different amplitudes and periods. We find that, for values of the Hubbard interaction $U$ above a critical value $U_C$, the system displays a superposition of local ferromagnetic and antiferromagnetic ordered states. Nonetheless the global ferromagnetic order parameter is zero. The $U_C$ depends only on the product of the period and hopping amplitude modulation. When the Hubbard interaction is close to the critical value of the antiferromagnetic transition in pristine graphene, the antiferromagnetic order parameter becomes much larger than the ferromagnetic one, being the ground state similar to that of flat graphene.
The exceptionally high mobility of carriers in graphene is one of its defining characteristics, especially in view of potential applications. Therefore it is of both practical and fundamental importance to understand the mechanisms responsible for limiting the values of mobility. The aim of the paper is to study theoretically one such mechanism, i.e. scattering on ripples. The transport properties of rippled graphene are studied using using single-band tight-binding model. Both the bond-length variation, corresponding to the vector potential in the effective mass picture, and fluctuating scalar potential are included in the formalism. The samples are modeled as self-similar surfaces characterized by the roughness exponent with values ranging from typical for graphene on SiO$_{2}$ to seen in suspended samples. The range of calculated resistivities and mobilities overlaps with experiment. The results presented here support the notion of rippling as one of the factors limiting the mobility.
We investigate the electronic transport properties of unbiased and biased bilayer graphene nanoribbon in n-p and n-n junctions subject to a perpendicular magnetic field. Using the non-equilibrium Greens function method and the Landauer-B{u}ttiker formalism, the conductance is studied for the cases of clean, on-site, and edge disordered bilayer graphene. We show that the lowest Hall plateau remains unchanged in the presence of disorder, whereas asymmetry destroys both the plateaus and conductance quantization. In addition, we show that disorder induces an enhancement of the conductance in the n-p region in the presence of magnetic fields. Finally, we show that the equilibration of quantum Hall edge states between distinctively doped regions causes Hall plateaus to appear in the regime of complete mode mixing.
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