Polaritonic Hofstadter Butterfly and Cavity-Control of the Quantized Hall Conductance

Abstract

In a previous work [Phys. Rev. Lett. 123, 047202 (2019)] a translationally invariant framework called quantum-electrodynamical Bloch (QED-Bloch) theory was introduced for the description of periodic materials in homogeneous magnetic fields and strongly coupled to the quantized photon field in the optical limit. For such systems, we show that QED-Bloch theory predicts the existence of fractal polaritonic spectra as a function of the cavity coupling strength. In addition, for the energy spectrum as a function of the relative magnetic flux we find that a terahertz cavity can modify the standard Hofstadter butterfly. In the limit of no quantized photon field, QED-Bloch theory captures the well-known fractal spectrum of the Hofstadter butterfly and can be used for the description of 2D materials in strong magnetic fields, which are of great experimental interest. As a further application, we consider Landau levels under cavity confinement and show that the cavity alters the quantized Hall conductance and that the Hall plateaus are modified as ${\sigma }_{xy}=e^2\nu /h(1+{\eta }^2)$ by the light-matter coupling $\eta$. Most of the aforementioned phenomena should be experimentally accessible and corresponding implications are discussed.

References in corpus (49)

• Quantum Spin Hall Effect in Graphene
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Hofstadter's butterfly in moire superlattices: A fractal quantum Hall effect
• Chiral Quantum Optics
• Ultrastrong coupling between light and matter
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Light-induced anomalous Hall effect in graphene
• Chiral nanophotonic waveguide interface based on spin-orbit coupling of light
• Conductivity in organic semiconductors hybridized with the vacuum field
• Atoms and Molecules in Cavities: From Weak to Strong Coupling in QED Chemistry
• Moiré heterostructures as a condensed matter quantum simulator
• Ultrastrong coupling of the cyclotron transition of a two-dimensional electron gas to a THz metamaterial
• Suppressing photochemical reactions with quantized light fields
• Quantum Electrodynamical Density-Functional Theory: Bridging Quantum Optics and Electronic-Structure Theory
• Light-matter interaction in the long-wavelength limit: no ground-state without dipole self-energy
• Cavity-mediated electron-photon superconductivity
• Band Structure Engineering of 2D Materials using Patterned Dielectric Superlattices
• Fractional fractal quantum Hall effect in graphene superlattices
• Breakdown of the topological protection by cavity vacuum fields in the integer quantum Hall effect
• Time-dependent density functional theory for many-electron systems interacting with cavity photons
• Magneto-transport controlled by Landau polariton states
• Ab-initio non-relativistic quantum electrodynamics: Bridging quantum chemistry and quantum optics from weak to strong coupling
• Quantum Electrodynamic Control of Matter: Cavity-Enhanced Ferroelectric Phase Transition
• Cavity Quantum Eliashberg Enhancement of Superconductivity
• Ultrastrong coupling between a cavity resonator and the cyclotron transition of a 2D electron gas in the case of integer filling factor
• Lectures on the Quantum Hall Effect
• Superconductivity and other phase transitions in a hybrid Bose-Fermi mixture formed by a polariton condensate and an electron system in two dimensions
• Cavity control of Excitons in two dimensional Materials
• Cavity Quantum-Electrodynamical Chern Insulator: Route Towards Light-Induced Quantized Anomalous Hall Effect in Graphene
• The Ferroelectric Photo-Groundstate of SrTiO${}_3$: Cavity Materials Engineering
• Time Dependent Floquet Theory and Absence of an Adiabatic Limit
• Cavity-control of bright and dark interlayer excitons in van der Waals heterostructures
• The Free Electron Gas in Cavity Quantum Electrodynamics
• Exploring Superconductivity under Strong Coupling with the Vacuum Electromagnetic Field
• Quantum to classical crossover of Floquet engineering in correlated quantum systems
• Polaron-Polaritons in the Integer and Fractional Quantum Hall Regimes
• Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields
• Quantum Floquet engineering with an exactly solvable tight-binding chain in a cavity
• Landau polaritons in highly non-parabolic 2D gases in the ultra-strong coupling regime
• Enhanced optical nonlinearities under strong light-matter coupling
• The Ten Martini Problem
• Floquet Hofstadter Butterfly on the Kagome and Triangular Lattices
• Genesis of the Floquet Hofstadter butterfly
• Ground-State Quantum-Electrodynamical Density-Functional Theory
• Hofstadter's Butterfly and Langlands Duality
• Floquet engineering the Hofstadter butterfly in the square lattice and its effective Hamiltonian
• Cavity-mediated electron hopping in disordered quantum Hall systems
• Condensed Matter Systems in Cavity Quantum Electrodynamics

Cited by in corpus (31)

• Cavity Quantum Materials
• Breakdown of the topological protection by cavity vacuum fields in the integer quantum Hall effect
• Quantum electron transport controlled by cavity vacuum fields
• Cavity Quantum Electrodynamics with Hyperbolic van der Waals Materials
• Weakened Topological Protection of the Quantum Hall Effect in a Cavity
• Berry Phase and Topology in Ultrastrongly Coupled Quantum Light-Matter Systems
• Cavity engineering of solid-state materials without external driving
• Critical light-matter entanglement at cavity mediated phase transition
• Vacuum-Induced Symmetry Breaking of Chiral Enantiomer Formation in Chemical Reactions
• Cavity Moiré Materials: Controlling Magnetic Frustration with Quantum Light-Matter Interaction
• Cavity Induced Collective Behavior in the Polaritonic Ground State
• Unified Light-Matter Floquet Theory and its Application to Quantum Communication
• Cavity-enhanced superconductivity via band engineering
• Non-Fermi-Liquid Behavior from Cavity Electromagnetic Vacuum Fluctuations at the Superradiant Transition
• Cavity-induced charge transfer in periodic systems: length-gauge formalism
• Theory of fractional quantum Hall liquids coupled to quantum light and emergent graviton-polaritons
• Understanding polaritonic chemistry from ab initio quantum electrodynamics
• Linear response theory for cavity QED materials at arbitrary light-matter coupling strengths
• Cavity-enhanced Kondo effect
• Controlling the excitation spectrum of a quantum dot array with a photon cavity
• Cavity-induced coherent magnetization and polaritons in altermagnets
• Quantum Electrodynamics of graphene Landau levels in a deep-subwavelength hyperbolic phonon polariton cavity
• A New Era of Quantum Materials Mastery and Quantum Simulators In and Out of Equilibrium
• Cavity-assisted magnetization switching in a quantum spin-phonon chain
• Spin-phase transition in an array of quantum rings controlled by cavity photons
• Optical conductivity and orbital magnetization of Floquet vortex states
• Robust translational invariance in topological bands against lattice potentials and disorders
• Cavity-Modified Zeeman Effect via Spin-Polariton Formation
• A protected spin-orbit induced absorption divergence in distorted Landau levels
• Signatures of broken symmetries in the excitations of a periodic 2DEG coupled to a cylindrical photon cavity
• Fractional quantum Hall edge polaritons