Orbital magnetism of graphene nanostructures: Bulk and confinement effects

Abstract

We consider the orbital magnetic properties of noninteracting charge carriers in graphene-based nanostructures in the low-energy regime. The magnetic response of such systems results both from bulk contributions and from confinement effects that can be particularly strong in ballistic quantum dots. First we provide a comprehensive study of the magnetic susceptibility χ 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, χ is not divergent although the diamagnetic contribution χ 0 from the filled valance band exhibits the well-known −B −1/2 dependence. We further derive oscillatory modulations of χ , 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 χ 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 distinctly 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.

Optical and magnetic measurements of gyroscopically stabilized graphene nanoplatelets levitated in an ion trap

“…Our measurements imply a magnetic moment sensitivity of order 10 −20 J T −1 and a torque sensitivity of order 10 −22 J. While our measurements are on rather poorly characterized samples (they are multilayer with an uncertain number of layers), the technique holds great promise for future measurements of the magnetic properties of single layer graphene and other two dimensional materials, a subject of significant theoretical research [16] [17] [18], or indeed of any µm-scale material with an anisotropic magnetic response.…”

A general formulation for the magnetic oscillations in two dimensional systems

“…Despite the recent advances in the study of the MO in 2D materials [41][42][43][44][45][46][47][48], the analysis usually considers special cases, such as assuming only a perpendicular magnetic or electric field [49][50][51][52][53][54]. There is no general formulation of the MO, in case the LL depend on other variables or indices.…”

A general formulation for the magnetic oscillations in two dimensional systems

“…Despite the recent advances in the study of the MO in 2D materials [41][42][43][44][45][46][47][48], the analysis usually considers special cases, such as assuming only a perpendicular magnetic or electric field [49][50][51][52][53][54]. There is no general formulation of the MO, in case the LL depend on other variables or indices.…”