Emergent geometry experienced by fermions in graphene in the presence of dislocations
arXiv:1412.2683 · doi:10.1016/j.aop.2015.03.005
Abstract
In graphene in the presence of strain the elasticity theory metric naturally appears. However, this is not the one experienced by fermionic quasiparticles. Fermions propagate in curved space, whose metric is defined by expansion of the effective Hamiltonian near the topologically protected Fermi point. We discuss relation between both types of metric for different parametrizations of graphene surface. Next, we extend our consideration to the case, when the dislocations are present. We consider the situation, when the deformation is described by elasticity theory and calculate both torsion and emergent magnetic field carried by the dislocation. The dislocation carries singular torsion in addition to the quantized flux of emergent magnetic field. Both may be observed in the scattering of quasiparticles on the dislocation. Emergent magnetic field flux manifests itself in the Aharonov - Bohm effect while the torsion singularity results in Stodolsky effect.
arXiv commentAccepted for publication in Annals of Physics
References in corpus (21)
- Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
- Weyl Semimetal in a Topological Insulator Multilayer
- Topological nodal semimetals
- Experimental Realization of a Three-Dimensional Dirac Semimetal
- Gauge fields in graphene
- Stability of Fermi Surfaces and K-Theory
- Topological Phases in Graphitic Cones
- Low-energy effective theory in the bulk for transport in a topological phase
- On the coupling of Galilean-invariant field theories to curved spacetime
- Understanding electron behavior in strained graphene as a reciprocal space distortion
- Density-curvature response and gravitational anomaly
- Generalizing the Fermi velocity of strained graphene from uniform to nonuniform strain
- Dislocations and torsion in graphene and related systems
- Parallel Transport of Electrons in Graphene Parallels Gravity
- World Nematic Crystal Model of Gravity Explaining the Absence of Torsion
- Emergent Horava gravity in graphene
- Effective theory of two-dimensional chiral superfluids: gauge duality and Newton-Cartan formulation
- The Berry phase of dislocations in graphene and valley conserving decoherence
- More On Nonrelativistic Diffeomorphism Invariance
- World Nematic Crystal Model of Gravity Explaining the Absence of Torsion
- Emergent gravity in graphene
Cited by in corpus (20)
- Electronic and optical properties of strained graphene and other strained 2D materials: a review
- Current splitting and valley polarization in elastically deformed graphene
- Current flow paths in deformed graphene: from quantum transport to classical trajectories in curved space
- Magnetic description of the Fermi arc in type-I and type-II Weyl semimetals
- Chiral anomaly in Dirac semimetals due to dislocations
- Torsional Landau levels and geometric anomalies in condensed matter Weyl systems
- Effective Dirac Hamiltonian for anisotropic honeycomb lattices: optical properties
- Emergent gravity in the cubic tight-binding model of Weyl semimetal in the presence of elastic deformations
- Low-energy theory for strained graphene: an approach up to second-order in the strain tensor
- Fermionic vacuum currents in topologically nontrivial braneworlds: Two-brane geometry
- Fermionic currents in topologically nontrivial braneworlds
- The Casimir effect for fermionic currents in conical rings with applications to graphene ribbons
- Effective magnetic field induced by inhomogeneous Fermi velocity in strained honeycomb structures
- Quantum chaos associated with emergent ergosurface in transition layer between type-I and type-II Weyl semimetals
- Landau Levels in graphene in the presence of emergent gravity
- Deformation of graphene sheet: Interaction of fermions with phonons
- The type II Weyl semimetals at low temperatures: chiral anomaly, elastic deformations, zero sound
- Multifractal wave functions of charge carriers in graphene with folded deformations, ripples or uniaxial flexural modes: analogies to the quantum Hall effect under random pseudomagnetic fields
- Effects of a uniform magnetic field on twisted graphene nanoribbons
- Dirac's spectrum from Newton laws in graphene