Degeneracy enhancement of Landau Levels in graphene 1D superlattices

Alina Mrenca-Kolasinska^1*, Ming-Hao Liu²

¹Faculty of Physics and Applied Computer Science, AGH University of Krakow, Krakow, Poland
²Department of Physics and Center for Quantum Frontiers of Research and Technology (QFort), National Cheng Kung University, Tainan, Taiwan

* Presenter:Alina Mrenca-Kolasinska, email:alina.mrenca@fis.agh.edu.pl

The presence of a one-dimensional (1D) superlattice (SL) in graphene can lead to the modification of the band structure, anisotropic renormalization of velocity transverse to the SL modulation [1], and formation of 2N+1 multiple zero-energy Dirac cones, where their number (with N = 0, 1, 2, ...) is tunable by the SL modulation strength [2]. This leads to increase of the zero-energy Landau level degeneracy, resulting in the Hall conductivity step of 4(2N + 1)e^2/h [3], namely, skipping the lowest plateaus. 1D SLs can for example be introduced into graphene via periodically patterned electrostatic gates, which induce a modulated potential profile.
The main focus of this work is a theoretical study of the magnetotransport in 1D induced superlattices within the Landauer-Büttiker formalism, and investigation of the conditions necessary for the observation of degeneracy enhancement. We find that the higher order conductance plateaus (with N ≥ 1) are strongly affected by the modulation asymmetry, inherent of realistic gate-induced superlattices. In such scenarios we observe a modified sequence of conductance plateaus. We confront our findings with experimental transport measurements. Our results provide a tool for characterization of the electronic structure induced by the SL modulation.

References
[1] ] C.-H. Park, L. Yang, Y.-W. Son, M. L. Cohen, and S. G. Louie, Nat. Phys. 4, 213 (2008).
[2] L. Brey and H. A. Fertig, Phys. Rev. Lett. 103, 046809 (2009).
[3] C.-H. Park, Y.-W. Son, L. Yang, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 103, 046808 (2009).

Keywords: electrostatic superlattices, quantum transport, Hall effect