Chiral limits and effect of light on the Hofstadter butterfly in twisted bilayer graphene
arXiv:2112.13614 · doi:10.1103/PhysRevB.105.125423
Abstract
We study the magnetic field induced Hofstadter butterfly in twisted bilayer graphene (TBG) in various kinds of situations. First, we study the equilibrium case and identify the interlayer hopping processes that are most crucial for the appearance of a Hofstadter butterfly. Surprisingly, the hopping processes that are important for the appearance of the Hofstadter butterfly can be categorized as AA stacking type - that is interlayer hoppings between equivalent sublattices. This is in contrast to AB/BA-type hoppings that are important for the appearance of flat bands in magic angle TBG and were discussed in [Phys. Rev. Lett. 122, 106405 (2019)]. We also find that if AB-type interlayer-hopping processes are turned off the resulting model is chiral but differs from the model discussed in \cite{Tarnopolsky}. Therefore, TBG has two separate chiral limits - one of them is important to understand the formation of flat bands and the other for the Hofstadter butterfly. Taking this as motivation we discuss how the role of AA-type hoppings in combination with lattice relaxation effects can make individual Landau levels slightly harder to resolve in an experimental setting than one would expect from a non-relaxed lattice setting. Finally, we consider the impact of different forms of light on the fractal structure of the butterfly. Particularly, we study the impact of circularly polarized light and longitudinal light originating from a waveguide. As the system is exposed to circularly polarized light we find butterflies with increasingly pronounced asymmetry with respect to energy . This is due to the introduction of a gap term that breaks the chiral symmetries for both of the two chiral limits mentioned above. Lastly, we study the effect of longitudinal light that can be produced at the exit of a waveguide, in a slightly simplified model. Here, we find ...
13 Figures
References in corpus (25)
- Electric Field Effect in Atomically Thin Carbon Films
- The electronic properties of graphene
- Photovoltaic Hall effect in graphene
- Single Layer Behavior and Its Breakdown in Twisted Graphene Layers
- Lattice relaxation and energy band modulation in twisted bilayer graphenes
- Metal to insulator transition in epitaxial graphene induced by molecular doping
- Out of equilibrium electrons and the Hall conductance of a Floquet topological insulator
- Zero Energy Modes and Gate-Tunable Gap in Graphene on hexagonal Boron Nitride
- Ballistic transmission through a graphene bilayer
- Spontaneous Strains and Gap in Graphene on Boron Nitride
- Universal moiré nematic phase in twisted graphitic systems
- Moiré metrology of energy landscapes in van der Waals heterostructures
- Landau levels in twisted bilayer graphene and semiclassical orbits
- Correlated insulators, semimetals, and superconductivity in twisted trilayer graphene
- Floquet edge states in a harmonically driven integer quantum Hall system
- Brillouin-Wigner Theory for Floquet Topological Phase Transitions in Spin-orbit Coupled Materials
- Floquet engineering of twisted double bilayer graphene
- Reduction of the Twisted Bilayer Graphene Chiral Hamiltonian into a matrix operator and physical origin of flat-bands at magic angles
- Why the first magic-angle is different from others in twisted graphene bilayers: interlayer currents, kinetic and confinement energy and wavefunction localization
- Quantum Hall effect in ac driven graphene: from half-integer to integer case
- Ab-initio analysis of superstructures revealed by STM on bilayer graphene
- Transport Properties in Gapped Bilayer Graphene
- Spectral Relationships Between Kicked Harper and On-Resonance Double Kicked Rotor Operators
- Tuning of Bilayer Graphene Heterostructure by Horizontally Incident Circular Polarized Light
- Observation of re-entrant correlated insulators and interaction driven Fermi surface reconstructions at one magnetic flux quantum per moiré unit cell in magic-angle twisted bilayer graphene
Cited by in corpus (6)
- Recent Developments in Fractional Chern Insulators
- Atomistic theory of moiré Hofstadter's butterfly in magic-angle graphene
- Magnetic field effect on tunneling through triple barrier in AB bilayer graphene
- Floquet Fractional Chern Insulators and Competing Phases in Twisted Bilayer Graphene
- Twist Angle, Strain, Corrugation and Moire Unit cell in Twisted Bilayer Graphene
- Floquet Hofstadter butterfly in trilayer graphene with a twisted top layer