Wydarzenia

Seminarium "Coherence-Correlations-Complexity" (KFT, PWr)

Edge states in graphene: Intrinsic gap, Spin Hall effect and  mean-field correlations

dr Marta Prada

I. Institut für Theoretische Physik, Universität Hamburg

The fundamental assumption of graphene is the celebrated linear energy dispersion relation for charge carriers, as it occurs in the Dirac equation. However, zooming in the low energy scales, a finite gap, and hence, a finite mass is expected. The magnitude of this gap in graphene is of great interest, determining the possibility to observe the most recently discovered state of matter: the topological (spin Hall) insulator [1].  However, controversy exists around the value of this gap, with theoretical predictions varying within two orders of magnitude [2], while an experimental value has not been determined to this date. Controversy exists as well on the magnetism on the edges, a theoretical prediction that has not been to this date corroborated [3]. 

We develop a tight-binding based theory in a rectangular sample of graphene. We characterise the relevant states according to their chirality, spin, and pseudo-spin. We include electron-electron correlations on a mean field level. Assuming the experimentally relevant broken electron-hole symmetry, we find that  the edges are not magnetic, implying the survival of the Spin Hall insulator state. We discuss on the ferromagnetic edge state found by assuming broken time-reversal symmetry. 

We present as well experimental evidence that intrinsic spin-orbit interaction in monolayer graphene leads to a measurable bulk gap and to the emergence of topological phases in graphene, yielding finite-mass states in the bulk, and massless edge states. Spin and pseudo-spin states can be experimentally resolved using microwave excitation in a resistively detected electron spin resonance experiment (ESR). This allows us to extract the size of the intrinsic spin orbit energy gap at the Dirac point to be 42 μeV [4],  following the selection rules that the spin and pseudo-spin degrees of freedom dictate. 

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2. S. Konschuh, M. Gmitra, and J. Fabian, Phys. Rev. B 82, 245412 (2010); H. Min, J. E. Hill, N. A. Sinitsyn, B. R. Sahu, L. Kleinman, and A. H. MacDonald, Phys. Rev. B 74, 165310 (2006); Y. Yao, F. Ye, X.-L. Qi, S.-C. Zhang, and Z. Fang, Phys. Rev. B 75, 041401(R) (2007); J. C. Boettger, and S. B. Trickey, Phys. Rev. B 75, 121402(R) (2007).
3. J. Kunstmann, C. Özdoğan, A. Quandt, and H. Fehske, Phys. Rev. B 83, 045414 (2011); W. Yao, S. A. Yang, and Q. Niu, Phys. Rev. Lett. 102, 096801 (2009); J. Lado, N. Garcia, J. Fernandez Rossier, Synthetic Metals, 210, 56 (2015).
4. J. Sichau, M. Prada, T. Lyon, L. Tiemann, and R. H. Blick, https://arxiv.org/abs/1709.05705.