Magnetic catalysis in weakly interacting hyperbolic Dirac materials

Abstract

Due to the linearly vanishing density of states, emergent massless Dirac quasiparticles resulting from the free fermion motion in a family of two-dimensional half-filled bipartite hyperbolic lattices feature dynamic mass generation through quantum phase transitions only for sufficiently strong finite-range Coulomb repulsion. As such, strong nearest-neighbor Coulomb repulsion ($V$) favors the nucleation of a charge-density-wave (CDW) order with a staggered pattern of average fermionic density between two sublattices of bipartite hyperbolic lattices. Considering a collection of spinless fermions (for simplicity), here we show that application of strong external magnetic fields by virtue of producing a \emph{finite} density of states near the zero energy triggers the condensation of the CDW order even for \emph{infinitesimal} $V$. The proposed curved space magnetic catalysis mechanism is operative for uniform and inhomogeneous (bell-shaped) magnetic fields. We present scaling of the CDW order with the total flux enclosed by hyperbolic Dirac materials for a wide range of (especially subcritical) $V$.

arXiv commentPublished version in PRB: 10 Pages, 7 Figures (change in authorship)

References in corpus (30)

• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Fermi-Hubbard physics with atoms in an optical lattice
• Interactions and phase transitions on graphene's honeycomb lattice
• Artificial graphene as a tunable Dirac material
• Observation of Spatial Charge and Spin Correlations in the 2D Fermi-Hubbard Model
• Theory of interacting electrons on the honeycomb lattice
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• Magnetic field-induced insulating behavior in highly oriented pyrolitic graphite
• Design and characterization of electronic fractals
• Excitonic gap, phase transition, and quantum Hall effect in graphene
• Crystallography of Hyperbolic Lattices
• Hyperbolic band theory
• Dirty Weyl semimetals: Stability, phase transition and quantum criticality
• Automorphic Bloch theorems for hyperbolic lattices
• Magnetic catalysis and axionic charge-density-wave in Weyl semimetals
• SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field
• Imaging Quasi-Periodic Electronic States in a Synthetic Penrose Tiling
• Interacting line-node semimetal: Proximity effect and spontaneous symmetry breaking
• Antiferromagnetism in the Hubbard Model on the Bernal-stacked Honeycomb Bilayer
• Universality of Hofstadter butterflies on hyperbolic lattices
• Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals
• Band theory and boundary modes of high-dimensional representations of infinite hyperbolic lattices
• Chiral Symmetry Breaking and the Quantum Hall Effect in Monolayer Graphene
• Fermion Condensate and Vacuum Current Density Induced by Homogeneous and Inhomogeneous Magnetic Fields in (2+1)-Dimensions
• Selberg trace formula in hyperbolic band theory
• Inhomogeneous magnetic catalysis on graphene's honeycomb lattice
• Inhomogeneous Condensates in Planar QED
• Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry
• Competing charge-density-wave, magnetic and topological ground states at and near Dirac points in graphene in axial magnetic fields

Cited by in corpus (6)

• Dynamic mass generation on two-dimensional electronic hyperbolic lattices
• Hyperbolic Spin Liquids
• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Quantum geometric tensors from sub-bundle geometry
• Zero modes and index theorems for non-Hermitian Dirac fermions
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices