Lifting of the Landau level degeneracy in graphene devices in a tilted magnetic field

TL;DR

This study investigates how magnetic fields affect the degeneracy of Landau levels in graphene, revealing spin and valley splitting phenomena and the dominant role of Zeeman energy in energy gaps.

Contribution

It provides new insights into the mechanisms of Landau level splitting in graphene under tilted magnetic fields, highlighting the roles of spin, valley, and Zeeman effects.

Findings

Spin degeneracy is lifted at filling factors ±1 with increased energy gap.

Valley degeneracy is removed at odd filling factors in higher Landau levels.

Zeeman energy mainly accounts for gaps at certain filling factors (-4, -8, -12).

Abstract

We report on transport and capacitance measurements of graphene devices in magnetic fields up to 30 T. In both techniques, we observe the full splitting of Landau levels and we employ tilted field experiments to address the origin of the observed broken symmetry states. In the lowest energy level, the spin degeneracy is removed at filling factors $\nu=\pm1$ and we observe an enhanced energy gap. In the higher levels, the valley degeneracy is removed at odd filling factors while spin polarized states are formed at even $\nu$. Although the observation of odd filling factors in the higher levels points towards the spontaneous origin of the splitting, we find that the main contribution to the gap at $\nu= -4,-8$, and $-12$ is due to the Zeeman energy.