Interaction induced enhancement of spin-splitting in graphene
Electron spins in graphene interact via quantum mechanical exchange, an effect which enhances their g-factor compared to the free electron value g=2. We have measured this g-factor enhancement by means of tilted-field experiments in high magnetic field up to 30 T.
The Zeeman splitting in graphene is generally smaller than the Landau level width and is therefore not straightforwardly to access. By investigating Shubnikov-de Haas oscillations in tilted magnetic fields, we were nevertheless able to measure this subtle effect. The technique allows adjusting the ratio between the spin splitting and the Landau level splitting, by controlling the ratio between a total magnetic field and a component perpendicular to a two-dimensional graphene flake. Increasing of spin splitting with increasing total field first leads to a decrease of the SdH oscillation amplitudes and eventually to an appearance of two spin-resolved peaks.
The effective g-factor extracted from these experiments yields a value g* = 2.7±0.2 which is enhanced compared to the free electron value g = 2. This enhancement is caused by electron-electron exchange interaction with a common strength for other graphitic materials.
Schematic representation of the density of states (DOS) for a spin-split Landau level ENwith an increasing total magnetic field Btot at a constant perpendicular component Bn.
In a perpendicular magnetic field (top) the level width largely exceeds the splitting between the two spin levels EN↓ and EN↑(horizontally dashed orange and vertically dashed red, respectively) resulting into the a total DOS of a spin unresolved Landau level (green solid).
When increasing the total field (middle) the spin levels move apart yielding a more broadened Landau level, the two spin levels are not yet resolved individually.
Finally when the spin splitting exceeds the level width (bottom), a minimum starts to develop in the total DOS between the two spin levels.
Experimental realization of this scenario for the N = 9 and the N = 10 Shubnuikov-de Haas maxima in single-layer graphene at a constant perpendicular magnetic field Bn = 5 T. When increasing the spin splitting, the reduced DOS results into a reduced resistance at the maxima and finally, at 28 T, the maxima start splitting into two thereby resolving the two individual spin states of a Landau level.
This work is published in:
E. V. Kurganova, H. J. van Elferen, A. McCollam, L. A. Ponomarenko, K. S. Novoselov, A. Veligura, B. J. van Wees, J. C. Maan, and U. Zeitler
Spin splitting in graphene studied by means of tilted magnetic-field experiments
Phys. Rev. B 84, 121407(R) (2011) (DOI: 10.1103/PhysRevB.84.121407)