[Paper Review] Landau level evolution driven by band hybridization in mirror symmetry broken ABA-stacked trilayer graphene

Yuya Shimazaki, Tôru Yoshizawa+8 more|arXiv (Cornell University)|Nov 8, 2016

Graphene research and applications6 citations

TL;DR

This study investigates Landau level (LL) evolution in ABA-stacked trilayer graphene under a perpendicular electric field, which breaks mirror symmetry and induces hybridization between monolayer-like (MLG-like) and bilayer-like (BLG-like) bands. The key finding is that electric-field-tuned LL crossings and valley/orbital-dependent splittings arise from hybridization between adjacent LLs and every third LLs due to trigonal warping, with experimental observations matching tight-binding numerical calculations.

ABSTRACT

Layer stacking and crystal lattice symmetry play important roles in the band structure and the Landau levels of multilayer graphene. ABA-stacked trilayer graphene possesses mirror-symmetry-protected monolayer-like and bilayer-like band structures. Broken mirror symmetry by a perpendicular electric field therefore induces hybridization between these bands and various quantum Hall phases emerge. We experimentally explore the evolution of Landau levels in ABA-stacked trilayer graphene under electric field. We observe a variety of valley and orbital dependent Landau level evolutions. These evolutions are qualitatively well explained by considering the hybridization between multiple Landau levels possessing close Landau level indices and the hybridization between every third Landau level orbitals due to the trigonal warping effect. These observations are consistent with numerical calculations. The combination of experimental and numerical analysis thus reveals the entire picture of Landau level evolutions decomposed into the monolayer- and bilayer-like band contributions in ABA-stacked trilayer graphene.

Motivation & Objective

• To understand the evolution of Landau levels in ABA-stacked trilayer graphene under broken mirror symmetry.
• To investigate how band hybridization between MLG-like and BLG-like bands influences Landau level structure.
• To identify the role of trigonal warping and electric field in inducing LL anti-crossings and valley splitting.
• To establish a comprehensive picture of Landau level evolution by combining experiment and tight-binding modeling.
• To explore the emergence of novel quantum Hall phases through tunable band hybridization.

Proposed method

• Employed dual-gated h-BN-encapsulated ABA-stacked trilayer graphene devices with precise electric field control via top and back gates.
• Measured longitudinal resistance $ R_{xx} $ as a function of carrier density $ n $ and electric displacement field $ D $ at low temperature (10 K).
• Used a tight-binding Hamiltonian model with parameters from Koshino and McCann (2009, 2011) to simulate band structure and Landau level spectra.
• Analyzed Landau level crossings and anti-crossings by tracking energy-level evolution across $ D $ and magnetic field $ B $.
• Identified hybridization processes: (H1) between $ \rm{LL}^\mathrm{m}_-^0 $ and $ \rm{LL}^\mathrm{b}_-^0 $, (H3) and (H4) between $ \rm{LL}^\mathrm{b}_-^2 $ and $ \rm{LL}^\mathrm{m}_-^2 $, and $ \rm{LL}^\mathrm{b}_+^2 $ and $ \rm{LL}^\mathrm{m}_+^1 $, respectively.
• Correlated experimental LL features with numerical calculations to validate the role of $ \gamma_3 $ (trigonal warping) and mirror symmetry breaking.

Experimental results

Research questions

• RQ1 How does mirror symmetry breaking via an electric field modify the Landau level spectrum in ABA-stacked trilayer graphene?
• RQ2 What is the origin of observed Landau level anti-crossings and their dependence on valley and orbital quantum numbers?
• RQ3 To what extent do trigonal warping effects and interband hybridization between MLG-like and BLG-like bands govern the LL evolution?
• RQ4 How do the experimental Landau level features compare quantitatively with tight-binding model predictions?
• RQ5 Can electric field tuning induce distinct quantum Hall phases through controlled band hybridization?

Key findings

• Electric field-induced mirror symmetry breaking leads to hybridization between MLG-like and BLG-like bands, resulting in complex Landau level anti-crossings.
• Anti-crossing between $ \rm{LL}^\mathrm{b}_-^0 $ and $ -\rm{LL}^\mathrm{b}_-^3 $ is observed at $ B = 2.8\ \rm{T} $, driven by trigonal warping ($ \gamma_3 $) and electric field.
• A second anti-crossing between $ \rm{LL}^\mathrm{m}_-^0 $ and $ +\rm{LL}^\mathrm{b}_-^3 $ appears at $ D < 0 $, indicating hybridization between different band components.
• Spin splitting of $ \rm{LL}^\mathrm{m}_-^0 $ disappears and recovers across the anti-crossing, confirming level mixing and preserved LL index.
• Valley splitting of $ -\rm{LL}^\mathrm{b}_\pm^2 $ is observed for $ |D| > 0.3\ \rm{V/nm} $, with stronger hybridization for $ -\rm{LL}^\mathrm{b}_+^2 $ due to smaller energy gap to $ -\rm{LL}^\mathrm{m}_+^1 $.
• Experimental Landau level evolution shows excellent agreement with numerical tight-binding calculations, validating the role of $ \gamma_3 $ and electric field in inducing hybridization.