Nonlinear Dirac Cones

Abstract

Physics arising from two-dimensional~(2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such $2$D Dirac cones are often characterized by a $\pi$ Berry phase and are destroyed by a perturbative mass term. By considering mean-field nonlinearity in a minimal two-band Chern insulator model, we obtain a novel type of Dirac cones that are robust to local perturbations without symmetry restrictions. Due to a different pseudo-spin texture, the Berry phase of the Dirac cone is no longer quantized in $\pi$, and can be continuously tuned as an order parameter. Furthermore, in an Aharonov-Bohm~(AB) interference setup to detect such Dirac cones, the adiabatic AB phase is found to be $\pi$ both theoretically and computationally, offering an observable topological invariant and a fascinating example where the Berry phase and AB phase are fundamentally different. We hence discover a nonlinearity-induced quantum phase transition from a known topological insulating phase to an unusual gapless topological phase.

26 pages, 4 figures

References in corpus (51)

• Two-Dimensional Gas of Massless Dirac Fermions in Graphene
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Theory of Bose-Einstein condensation in trapped gases
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Topological Photonics
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Discovery of a Weyl Fermion Semimetal and Topological Fermi Arcs
• Experimental realisation of the topological Haldane model
• Dirac semimetal and topological phase transitions in A3Bi (A=Na, K, Rb)
• Dirac semimetal in three dimensions
• Formation and Propagation of Matter Wave Soliton Trains
• Topological nodal semimetals
• Dark Solitons in Bose-Einstein Condensates
• Weyl semimetal phase in non-centrosymmetric transition metal monophosphides
• Topological nodal line semimetals with and without spin-orbital coupling
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Topological phases of fermions in one dimension
• Topological nodal line semimetals
• Dirac Semimetals in Two Dimensions
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• The effects of interactions on the topological classification of free fermion systems
• Observation of novel edge states in photonic graphene
• Hysteresis in a quantized, superfluid atomtronic circuit
• Edge Solitons in Nonlinear Photonic Topological Insulators
• Drumhead Surface States and Topological Nodal-Line Fermions in TlTaSe2
• Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Classification of interacting electronic topological insulators in three dimensions
• Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models
• Band structure, elementary excitations, and stability of a Bose-Einstein condensate in a periodic potential
• Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface
• Superfluidity and Swallowtails; Hysteretic Behavior in Bose Condensates
• Chiral Bogoliubons in Nonlinear Bosonic Systems
• Theory of interacting topological crystalline insulators
• Exploring nonlinear topological states of matter with exciton-polaritons: Edge solitons in kagome lattice
• Topological Phase Transitions for Interacting Finite Systems
• Interacting quantum fluid in a polariton topological insulator
• Landau-Zener Tunnelling in a Nonlinear Three-level System
• Two-mode Bose-Einstein condensate in a high-frequency driving field that directly couples the two modes
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Photonic Versus Electronic Quantum Anomalous Hall Effect
• Nonlinear looped band structure of Bose-Einstein condensates in an optical lattice
• Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States
• Superluminal Tachyonlike Excitations of Dirac Fermions in a Topological Insulator Junction
• Topologically nontrivial states in one-dimensional nonlinear bichromatic superlattices
• Dynamical fluctuations in classical adiabatic processes: General description and their implications
• Interacting topological phases in thin films of topological mirror Kondo insulators

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• Nonlinearity induced topological physics in momentum space and real space
• Stability of topological edge states under strong nonlinear effects
• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
• Nonlinear dynamics of a spin-orbit-coupled Bose-Einstein condensate
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• Light-induced half-quantized Hall effect and axion insulator
• Probing band topology using modulational instability
• Nonlinear Topological Mechanics in Elliptically Geared Isostatic Metamaterials
• Gradient catastrophe of nonlinear photonic valley-Hall edge pulses
• $Z_4$ parafermion $\pm \pi /2$ modes in interacting periodically driven superconducting chain
• Breakdown of quantization in nonlinear Thouless pumping
• Strongly Nonlinear Topological Phases of Cascaded Topoelectrical Circuits
• Floquet eigenspectra of a nonlinear two-mode system under periodic driving: the emergence of "ring" structures
• Moiré exciton condensate: nonlinear Dirac point, broken-symmetry Bloch waves and unusual optical selection rules
• Nonlinear Bloch-Zener oscillations for Bose-Einstein condensates in a Lieb optical lattice
• Topological characteristics of gap closing points in nonlinear Weyl semimetals
• On the quantization of AB phase in nonlinear systems
• Floquet solitons in square lattices: Existence, Stability and Dynamics
• Nonlinear Dirac Points and topological invariant in coupled hexagonal lattices