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We carry out an explicit calculation of the vacuum polarization tensor for an effective low-energy model of monolayer graphene in the presence of a weak magnetic field of intensity $B$ perpendicularly aligned to the membrane. By expanding the quasiparticle propagator in the Schwinger proper time representation up to order $(eB)^2$, where $e$ is the unit charge, we find an explicitly transverse tensor, consistent with gauge invariance. Furthermore, assuming that graphene is radiated with monochromatic light of frequency $omega$ along the external field direction, from the modified Maxwells equations we derive the intensity of transmitted light and the angle of polarization rotation in terms of the longitudinal ($sigma_{xx}$) and transverse ($sigma_{xy}$) conductivities. Corrections to these quantities, both calculated and measured, are of order $(eB)^2/omega^4$. Our findings generalize and complement previously known results reported in literature regarding the light absorption problem in graphene from the experimental and theoretical points of view, with and without external magnetic fields.
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We demonstrate that the electronic spectrum of graphene in a one-dimensional periodic potential will develop a Landau level spectrum when the potential magnitude varies slowly in space. The effect is related to extra Dirac points generated by the potential whose positions are sensitive to its magnitude. We develop an effective theory that exploits a chiral symmetry in the Dirac Hamiltonian description with a superlattice potential, to show that the low energy theory contains an effective magnetic field. Numerical diagonalization of the Dirac equation confirms the presence of Landau levels. Possible consequences for transport are discussed.
We theoretically study electronic properties of a graphene sheet on xy plane in a spatially nonuniform magnetic field, $B = B_0 hat{z}$ in one domain and $B = B_1 hat{z}$ in the other domain, in the quantum Hall regime and in the low-energy limit. We find that the magnetic edge states of the Dirac fermions, formed along the boundary between the two domains, have features strongly dependent on whether $B_0$ is parallel or antiparallel to $B_1$. In the parallel case, when the Zeeman spin splitting can be ignored, the magnetic edge states originating from the $n=0$ Landau levels of the two domains have dispersionless energy levels, contrary to those from the $n e 0$ levels. Here, $n$ is the graphene Landau-level index. They become dispersive as the Zeeman splitting becomes finite or as an electrostatic step potential is additionally applied. In the antiparallel case, the $n=0$ magnetic edge states split into electron-like and hole-like current-carrying states. The energy gap between the electron-like and hole-like states can be created by the Zeeman splitting or by the step potential. These features are attributed to the fact that the pseudo-spin of the magnetic edge states couples to the direction of the magnetic field. We propose an Aharonov-Bohm interferometry setup in a graphene ribbon for experimental study of the magnetic edge states.
We report transport experiments on graphene quantum dots. We focus on excited state spectra in the near vicinity of the charge neutrality point and signatures of the electron-hole crossover as a function of a perpendicular magnetic field. Coulomb blockade resonances of a 50 nm wide and 80 nm long dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 40 states as a function of the back gate voltage can be interpreted in terms of the unique evolution of the diamagnetic spectrum of a graphene dot including the formation of the E = 0 Landau level, situated in the center of the transport gap, and marking the electron-hole crossover.
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.
The quantum Hall (QH) effect in two-dimensional (2D) electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors $ u=0,pm 1,pm 4$ are discovered at magnetic fields $B>$20 T, indicating the lifting of the four-fold degeneracy of the previously observed QH states at $ u=pm(|n|+1/2)$, where $n$ is the Landau level index. In particular, the presence of the $ u=0, pm 1$ QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at $ u=pm 4$ is investigated in tilted magnetic field and can be attributed to lifting of the spin-degeneracy of the $n=1$ Landau level.
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