"A tale of many electrons: orbital paramagnetism in graphene"

Giovanni Vignale
Univ. of Missouri-Columbia
Wednesday, May 2, 2012
4:00 pm
NS2 1201

Orbital magnetism in thermodynamic equilibrium is an exquisitely quantum mechanical phenomenon, which does not occur  in classical physics.

The orbital response of electrons to an externally imposed magnetic field is usually {\it diamagnetic}, i.e., the magnetization tends to oppose the external field.  This effect is particularly strong in ``closed-shell" systems, leading to the extreme phenomenon of the Meissner effect (perfect diamagnetism) in  superconductors.  But it also occurs in the normal uniform electron gas (Landau diamagnetism), and it can be larger than spin paramagnetism if the effective mass of the electrons is sufficiently small. 

Orbital {\it paramagnetism}, whereby the magnetization enhances an externally imposed magnetic field,  can also occur in a variety of systems ranging from open-shell atoms to nanoparticles to solids with non-parabolic band structures. 

Electron-electron interaction effects have so far been found to play a minor role, not remotely comparable to the  big role they play in spin paramagnetism.   For example, in the electron gas at metallic densities one calculates only a few percent  correction to the Landau diamagnetism.
The orbital magnetic susceptibility of two-dimensional graphene sheets presents a remarkable exception to the standard scenario.  At the ``neutrality point" the orbital magnetic susceptibility is large and diamagnetic, leading to perfect diamagnetism in the limit of zero temperature.  But,  as electrons or holes are created in the conduction or in the valence band, the orbital susceptibility rapidly decreases: in the absence of electron-electron interactions it tends exponentially to zero as the Fermi energy becomes larger that $k_BT$. 
This is due to the peculiar linear-in-k dispersion of the massless Dirac fermions in graphene.   Inclusion of electron-electron interactions changes the picture.  At the neutrality point,  one still finds perfect diamagnetism.  But, for finite carrier concentration  the susceptibility is found to be finite and positive, i.e., paramagnetic.  The value of the susceptibility, in this case, is 100\% determined by the electron-electron interaction, and would vanish if the latter were neglected.  Graphene sheets are thus unique systems, in which the orbital susceptibility is completely controlled by many-body effects.  We discuss the prospects to observe experimentally this unusual behavior.

Kieron Burke