Nonlinear magnetotransport in a two-dimensional system with merging Dirac points

Abstract

We study the linear, second-order nonlinear (NL) current and voltage responses of a two-dimensional gapped semi-Dirac system with merging Dirac nodes along the $x$ direction under the influence of a weak magnetic field ($B$), using the semiclassical Boltzmann formalism. We investigate the effect of band geometric quantities like Berry curvature and orbital magnetic moment in the responses up to linear order in $B$. We derive exact analytical expressions of the linear magnetoconductivities, second-harmonic NL anomalous Hall (NAH), and anomalous velocity and Lorentz force induced (NAL) conductivities, unveiling their dependence on Fermi energy and a gap parameter ${\delta }_0$. For ${\delta }_0>0$, the Fermi surface topology changes at a particular Fermi energy, which is reflected in the nature of conductivities through a kink. The ratio of NAL and NAH conductivities is found to be independent of ${\delta }_0$ and inversely related to Fermi energy. The NL dc current exhibits distinct orientations depending on the Fermi energy, magnetic field, polarization of the electromagnetic wave. In the presence of magnetic field, the NL dc current vector can be rotated through large angles on variation of Fermi energy. For high Fermi energies, the NL dc current is directed nearly along the $y$-axis for $x$-polarized and low-frequency circularly polarized light, whereas it aligns close to $x$-axis for high-frequency circularly polarized light. These orientations of the NL dc current are predominantly governed by the mirror symmetry of the system along the $x$ direction. Additionally, we also study the NL voltage responses of the system by applying current along the $x$ and $y$ directions. The system exhibits asymmetry in the $B$-dependencies of the NL resistivities, which may serve as an experimentally relevant signature for band geometric quantities and merging Dirac nodes in such systems.

References in corpus (66)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Berry Phase Effects on Electronic Properties
• Weyl Semimetal in a Topological Insulator Multilayer
• Valley contrasting physics in graphene: magnetic moment and topological transport
• Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
• Observation of the nonlinear Hall effect under time reversal symmetric conditions
• Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property
• Semimetallic Two-Dimensional Boron Allotrope with Massless Dirac Fermions
• Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
• Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons
• Artificial graphene as a tunable Dirac material
• Tilted anisotropic Dirac cones in quinoid-type graphene and alpha-(BEDT-TTF)_2I_3
• Axionic field theory of (3+1)-dimensional Weyl semi-metals
• Merging of Dirac points in a two-dimensional crystal
• Chiral anomaly as origin of planar Hall effect in Weyl semimetals
• Semiclassical theories of the anomalous Hall effect
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Half-metallic semiDirac point generated by quantum confinement in TiO${}_2$/VO${}_2$ nanostructures
• Disorder-induced nonlinear Hall effect with time-reversal symmetry
• A new magnetic field dependence of Landau levels on a graphene like structure
• Giant Planar Hall Effect in Topological Metals
• Confinement-induced Berry phase and helicity-dependent photocurrents
• Zero modes of tight binding electrons on the honeycomb lattice
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• Energy Magnetization and Thermal Hall Effect
• A universal Hamiltonian for the motion and the merging of Dirac cones in a two-dimensional crystal
• High-frequency rectification via chiral Bloch electrons
• Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals
• Dirac-point engineering and topological phase transitions in honeycomb optical lattices
• Topological transition of Dirac points in a microwave experiment
• Strain-engineering of Berry curvature dipole and valley magnetization in monolayer MoS${}_2$
• Bilinear magneto-electric resistance as a probe of three-dimensional spin texture in topological surface states
• Strongly enhanced Berry dipole at topological phase transitions in BiTeI
• Strain-induced pseudomagnetic field in Dirac semimetal borophene
• Quantum theory of the nonlinear Hall effect
• Boltzmann-equation approach to anomalous transport in a Weyl metal
• Nonlinear planar Hall effect
• Observation of a Dirac point in microwave experiments with a photonic crystal modeling graphene
• Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics
• Berry Curvature Dipole in Strained Graphene: a Fermi Surface Warping Effect
• Semi-Dirac dispersion relation in photonic crystals
• Photoinduced Chern insulating states in semi-Dirac materials
• A semi-Dirac point in the Hofstadter spectrum
• Anomalous Spin Correlations and Mass-Generating Excitonic Instability of Interacting Weyl Fermions
• Highly tunable nonlinear Hall effects induced by spin-orbit couplings in strained polar transition-metal dichalcogenides
• Massless Dirac Fermions in a Square Optical Lattice
• Diffusion of Dirac fermions across a topological merging transition in two dimensions
• Necessary and sufficient condition for longitudinal magnetoresistance
• Dynamical polarization and plasmons in a two-dimensional system with merging Dirac points
• Direction dependent giant optical conductivity in 2D \textit{semi}-Dirac materials
• Optical conductivity of black phosphorus with a tunable electronic structure
• Optical conductivity of semi-Dirac and pseudospin-1 models: Zitterbewegung approach
• Non-linear transport without spin-orbit coupling or warping in two-dimensional Dirac semimetals
• Berry curvature induced nonlinear magnetoresistivity in two dimensional systems
• Signatures of merging Dirac points in optics and transport
• Anisotropic magneto-optical absorption and linear dichroism in two-dimensional semi-Dirac electron systems
• Berry Curvature of the Dirac Particle in $\alpha$-(BEDT-TTF)${}_2$I${}_3$
• Quantum Hall studies of a Semi-Dirac Nanoribbon
• Photoemission study of TiO2/VO2 interfaces
• Valley-Contrasting Orbital Magnetic Moment Induced Negative Magnetoresistance
• Novel topological phases of a semi-Dirac Chern insulator in presence of extended range hopping

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• Photoinduced metallic Volkov-Pankratov states in semi-Dirac material