The splitting of the Landau levels of graphene investigated in a tilted magnetic field
Researchers of the HFML have investigated the splitting of the Landau levels of single layer graphene with experiments in tilted magnetic fields. Thanks to the high quality of the devices, fabricated by researchers of the University of Manchester, the scientists could detect the complete lifting of the Landau level degeneracy. This allowed them to address the role of electron-electron interactions and single particle effects in determining the electronic properties of the observed states. The results have been published as a Rapid Communication in Physical Review B on November 24, 2015.
When a two-dimensional material is subjected to an external magnetic field, the energy spectrum for the charge carriers evolves into discrete energy levels called Landau levels. In case of graphene, each of these levels is four times degenerate because of the spin and the sub-lattice degeneracy. However, under the extreme conditions of high magnetic fields and low temperatures, the level degeneracy can be removed and several additional electronic states can be observed. The nature of the resulting ground states has been object of intense theoretical and experimental investigations.
In order to study the electronic states resulting from the splitting of the Landau levels, the HFML researchers have employed two different experimental techniques: magneto-transport and capacitance spectroscopy. The latter is a very powerful technique which allows direct measurements of the density of state of the sample under investigation.
In a tilted magnetic field, one can decouple the effects related to the orbital motion of the electrons (e.g. Landau quantization and electron-electron interactions) dependent only on the perpendicular component of the field, from those related to the spin and thus sensitive to the total magnetic field applied. Upon tilting the sample and observing the changes in resistance and capacitance of the devices (Figure 1), it is possible to discriminate between the different mechanisms that can cause the splitting of the levels.
Figure 1. Splitting of the higher Landau levels in a tilted magnetic field observed in the resistance (left) and the capacitance (right) of two devices made of graphene encapsulated in h-BN.
The researchers showed that the valley and spin degeneracy are removed in the higher Landau levels, at odd and even filling factors, respectively. The energy gap for the even filling factors is set by the single-particle Zeeman energy. By contrast, electron-electron interactions determinate the splitting of the lowest energy level, where filling factors ±1 is associated to the lifting of the spin degeneracy with a strongly enhanced energy gap.
These observations provide new insights in the full splitting of Landau levels in graphene and highlight the interplay of both electron-electron interactions and single-particle effects in the removal of the Landau level degeneracy.
Lifting of the Landau level degeneracy in graphene devices in a tilted magnetic field
F. Chiappini, S. Wiedmann, K. Novoselov, A. Mishchenko, A. K. Geim, J. C. Maan, and U. Zeitler
Phys. Rev. B 92, 201412(R) (2015).