Topological Floquet states on a Möbius band irradiated by circularly polarised light

Abstract

Topological states of matter in equilibrium, as well as out of equilibrium, have been thoroughly investigated during the last years in condensed-matter and cold-atom systems. However, the geometric topology of the studied samples is usually trivial, such as a ribbon or a cylinder. In this paper, we consider a graphene Möbius band irradiated with circularly polarised light. Interestingly, due to the non-orientability of the Möbius band, a homogeneous quantum Hall effect cannot exist in this system, but the quantum spin Hall effect can. To avoid this restriction, the irradiation is applied in a longitudinal-domain-wall configuration. In this way, the periodic time-dependent driving term tends to generate the quantum anomalous Hall effect. On the other hand, due to the bent geometry of the Möbius band, we expect a strong spin-orbit coupling, which may lead to quantum spin Hall-like topological states. Here, we investigate the competition between these two phenomena upon varying the amplitude and the frequency of the light, for a fixed value of the spin-orbit coupling strength. The topological properties are analysed by identifying the edge states in the Floquet spectrum at intermediate frequencies, when there are resonances between the light frequency and the energy difference between the conduction and valence bands of the graphene system.

arXiv comment9 pages, 5 figures

References in corpus (42)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Large-gap quantum spin Hall insulators in tin films
• Observation of Floquet-Bloch states on the surface of a topological insulator
• Topological characterization of periodically-driven quantum systems
• The quantum spin Hall effect and topological insulators
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• The Quantum Spin Hall Effect: Theory and Experiment
• The space group classification of topological band insulators
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Photo-Induced Topological Phase Transition and a Single Dirac-Cone State in Silicene
• Superfluid-insulator transition in a periodically driven optical lattice
• Floquet Spectrum and Transport Through an Irradiated Graphene Ribbon
• Irradiated graphene as a tunable Floquet topological insulator
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Time-reversal-symmetry-broken quantum spin Hall effect
• Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
• Modulated Floquet Topological Insulators
• Topological index for periodically driven time-reversal invariant 2D systems
• Large spin-orbit coupling in carbon nanotubes
• Engineering Quantum Anomalous Hall Plateaus and Anti-Chiral States with AC Fields
• Topological phases in a two-dimensional lattice: Magnetic field versus spin-orbit coupling
• Magnetic Structure of Nano-Graphite Moebius Ribbon
• Möbius and twisted graphene nanoribbons: stability, geometry and electronic properties
• Topological phase transitions between chiral and helical spin textures in a lattice with spin-orbit coupling and a magnetic field
• Effective time-independent description of optical lattices with periodic driving
• Observable Topological Effects of Mobius Molecular Devices
• Spin states of zigzag-edged Mobius graphene nanoribbons from first principles
• Defects in Graphene-Based Twisted Nanoribbons: Structural, Electronic and Optical Properties
• Nontrivial topological states on a Möbius band
• Novel Electronic States in Graphene Ribbons -Competing Spin and Charge Orders-
• Topological insulators on a Mobius Strip
• Topological effect on thermal conductivity in graphene
• Dynamical competition between Quantum Hall and Quantum Spin Hall effects
• Electronic Structure Trends of Möbius Graphene Nanoribbons from Minimal-Cell Simulations

Cited by in corpus (7)

• Floquet interface states in illuminated three-dimensional topological insulators
• Scattering matrix invariants of Floquet topological insulators
• Floquet analysis of a quantum system with modulated periodic driving
• Quantum simulation of non-trivial topology
• Bandwidth-resonant Floquet states in honeycomb optical lattices
• Non-Abelian geometric phases in periodically driven systems
• Non-Abelian geometric potentials and spin-orbit coupling for periodically driven systems