Orbital Magnetism of Graphene Nanostructures: Bulk and Confinement Effects

Abstract

We consider the orbital magnetic properties of non-interacting charge carriers in graphene-based nanostructures in the low-energy regime. The magnetic response of such systems results both, frombulk contributions and from confinement effects that can be particularly strong in ballistic quantum dots. First we provide a comprehensive study of the magnetic susceptibility $\chi$ of bulk graphene in a magnetic field for the different regimes arising from the relative magnitudes of the energy scales involved, i.e. temperature, Landau level spacing and chemical potential. We show that for finite temperature or chemical potential, $\chi$ is not divergent although the diamagnetic contribution ${\chi }_0$ from the filled valance band exhibits the well-known $-B^{-1/2}$ dependence. We further derive oscillatory modulations of $\chi$, corresponding to de Haas-van Alphen oscillations of conventional two-dimensional electron gases. These oscillations can be large in graphene, thereby compensating the diamagnetic contribution ${\chi }_0$ and yielding a net paramagnetic susceptibility for certain energy and magnetic field regimes. Second, we predict and analyze corresponding strong, confinement-induced susceptibility oscillations in graphene-based quantum dots with amplitudes distincly exceeding the corresponding bulk susceptibility. Within a semiclassical approach we derive generic expressions for orbital magnetism of graphene quantum dots with regular classical dynamics. Graphene-specific features can be traced back to pseudospin interference along the underlying periodic orbits. We demonstrate the quality of the semiclassical approximation by comparison with quantum mechanical results for two exemplary mesoscopic systems, a graphene disk with infinite mass-type edges and a rectangular graphene structure with armchair and zigzag edges, using numerical tight-binding calculations in the latter case.

arXiv comment21 pages, 16 figures

References in corpus (28)

• The electronic properties of graphene
• Observation of Landau levels of Dirac fermions in graphite
• Cyclotron Resonance study of the electron and hole velocity in graphene monolayers
• Aharonov-Bohm effect and broken valley-degeneracy in graphene rings
• Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations
• Energy levels of triangular and hexagonal graphene quantum dots: a comparative study between the tight-binding and the Dirac approach
• Orbital Magnetism in the Ballistic Regime: Geometrical Effects
• Linear response of doped graphene sheets to vector potentials
• Diamagnetism in disordered graphene
• Many-body orbital paramagnetism in doped graphene sheets
• Optimal block-tridiagonalization of matrices for coherent charge transport
• Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
• Orbital magnetism of graphene flakes
• Transition to Landau Levels in Graphene Quantum Dots
• Magnetic field screening and mirroring in graphene
• Orbital Magnetism and Transport Phenomena in Two Dimensional Dirac Fermions in Weak Magnetic Field
• Diamagnetism of nodal fermions
• Many-Body Physics and Quantum Chaos
• Dynamical current-current susceptibility of gapped graphene
• Chaos and Interacting Electrons in Ballistic Quantum Dots
• The Modulation of de Haas-van Alphen Effect in Graphene by Electric Field
• Edge effects in graphene nanostructures: II. Semiclassical theory of spectral fluctuations and quantum transport
• Uniform trace formulae for SU(2) and SO(3) symmetry breaking
• Nonlinear magnetization of graphene
• Semiclassical Approach to Orbital Magnetism of Interacting Diffusive Quantum Systems
• The magnetic susceptibility of disordered non-diffusive mesoscopic systems
• From clean to diffusive mesoscopic systems: A semiclassical approach to the magnetic susceptibility
• Diamagnetism of Confined Dirac Fermions in Disordered Graphene

Cited by in corpus (5)

• Optical and magnetic measurements of gyroscopically stabilized graphene nanoplatelets levitated in an ion trap
• Time-Reversal Symmetry Breaking and Decoherence in Chaotic Dirac Billiards
• A general formulation for the magnetic oscillations in two dimensional systems
• Temperature effect on the magnetic oscillations in 2D materials
• Orbital magnetization of interacting Dirac fermions in graphene