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Register a new userStacking order, interaction and weak surface magnetism in layered graphene sheets
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Recent transport experiments have demonstrated that the rhombohedral stacking trilayer graphene is an insulator with an intrinsic gap of 6meV and the Bernal stacking trilayer one is a metal. We propose a Hubbard model with a moderate $U$ for layered graphene sheets, and show that the model well explains the experiments of the stacking dependent energy gap. The on-site Coulomb repulsion drives the metallic phase of the non-interacting system to a weak surface antiferromagnetic insulator for the rhombohedral stacking layers, but does not alter the metallic phase for the Bernal stacking layers.
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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.
Single-layer graphene sheets are typically characterized by long-wavelength corrugations (ripples) which can be shown to be at the origin of rather strong potentials with both scalar and vector components. We present an extensive microscopic study, based on a self-consistent Kohn-Sham-Dirac density-functional method, of the carrier density distribution in the presence of these ripple-induced external fields. We find that spatial density fluctuations are essentially controlled by the scalar component, especially in nearly-neutral graphene sheets, and that in-plane atomic displacements are as important as out-of-plane ones. The latter fact is at the origin of a complicated spatial distribution of electron-hole puddles which has no evident correlation with the out-of-plane topographic corrugations. In the range of parameters we have explored, exchange and correlation contributions to the Kohn-Sham potential seem to play a minor role.
We investigate the size scaling of the conductance of surface disordered graphene sheets of width W and length L. Metallic leads are attached to the sample ends across its width. At E ~ 0, the conductance scales with the system size as follows: i) For constant W/L, it remains constant as size is increased, at a value which depends almost lineally on that ratio; this scaling allows the definition of a conductivity value that results similar to the experimental one. ii) For fixed width, the conductance decreases exponentially with length L, both for ordered and disordered samples. Disorder reduces the exponential decay, leading to a higher conductance. iii) For constant length, conductance increases linearly with width W, a result that is exclusively due to the tails of the states of the metallic wide contact. iv) The average conductance does not show an appreciable dependence on magnetic field. Away from E = 0, the conductance shows the behavior expected in two-dimensional systems with surface disorder, i.e., ballistic transport.
We study the magnetic properties of nanometer-sized graphene structures with triangular and hexagonal shapes terminated by zig-zag edges. We discuss how the shape of the island, the imbalance in the number of atoms belonging to the two graphene sublattices, the existence of zero-energy states, and the total and local magnetic moment are intimately related. We consider electronic interactions both in a mean-field approximation of the one-orbital Hubbard model and with density functional calculations. Both descriptions yield values for the ground state total spin, $S$, consistent with Liebs theorem for bipartite lattices. Triangles have a finite $S$ for all sizes whereas hexagons have S=0 and develop local moments above a critical size of $approx 1.5$ nm.
It is argued that the subtle crossover from decoherence-dominated classical magnetism to fluctuation-dominated quantum magnetism is experimentally accessible in graphene nanoribbons. We show that the width of a nanoribbon determines whether the edge magnetism is on the classical side, on the quantum side, or in between. In the classical regime, decoherence is dominant and leads to static spin polarizations at the ribbon edges, which are well described by mean-field theories. The quantum Zeno effect is identified as the basic mechanism which is responsible for the spin polarization and thereby enables the application of graphene in spintronics. On the quantum side, however, the spin polarization is destroyed by dynamical processes. The great tunability of graphene magnetism thus offers a viable route for the study of the quantum-classical crossover.
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