Publisher’s Note: Berry Phase Correction to Electron Density of States in Solids [Phys. Rev. Lett.<b>95</b>, 137204 (2005)]

Xiao, Di; Shi, Junren; Niu, Qian

doi:10.1103/physrevlett.95.169903

Cited by 202 publications

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“…We note that the factor D arises from a field-induced change of the volume of the phase space 22 . In the following, we focus on the uniform system.…”

Section: Semiclassical Formulas For Nonlinear Optical Effectsmentioning

confidence: 99%

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

et al. 2016

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We study nonlinear magneto-optical responses of metals by a semiclassical Boltzmann equation approach. We derive general formulas for linear and second order nonlinear optical effects in the presence of magnetic fields that include both Berry curvature and orbital magnetic moment. Applied to Weyl fermions, the semiclassical approach (i) captures the directional anisotropy of linear conductivity under magnetic field as a consequence of an anisotropic B 2 contribution, which may explain the low-field regime of recent experiments; (ii) predicts strong second harmonic generation proportional to B that is enhanced as the Fermi energy approaches the Weyl point, leading to large nonlinear Kerr rotation. Moreover, we show that the semiclassical formula for the circular photogalvanic effect arising from the Berry curvature dipole is reproduced by a full quantum calculation using a Floquet approach.

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“…We note that the factor D arises from a field-induced change of the volume of the phase space 22 . In the following, we focus on the uniform system.…”

Section: Semiclassical Formulas For Nonlinear Optical Effectsmentioning

confidence: 99%

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

et al. 2016

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“…[2][3][4][5][6][7] The polarization P measures the position differences between the band electrons and the lattice ions, which is in general nonzero in a crystal without inversion symmetry. In an open system, it results in boundary charges, which gives rise to the energy density ∆E = −P · E in an external electric field.…”

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confidence: 99%

Unified formalism for calculating polarization, magnetization, and more in a periodic insulator

Chen

Lee

2011

Phys. Rev. B

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In this paper, we propose a unified formalism, using Green's functions, to integrate out the electrons in an insulator under uniform electromagnetic fields. We derive a perturbative formula for the Green's function in the presence of uniform magnetic or electric fields. Applying the formula, we derive the formula for the polarization, the orbital magnetization, and the orbital magnetopolarizability, without assuming time reversal symmetry. Specifically, we realize that the terms linear in the electric field can only be expressed in terms of the Green's functions in one extra dimension. This observation directly leads to the result that the coefficient of the θ-term in any dimensions is given by a Wess-Zumino-Witten like term, integrated in the extended space whose boundary is the original physical Brillouin zone, with the group element replaced by the Green's function. This generalizes an earlier result for the case of time reversal invariance. 1

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“…In the Supplemental Material [14] we describe a procedure to estimate the required upper limit for g for a specific experimental procedure based on a SQUID measurement of the magnetic flux created by an external charge placed near a topological surface. After the external charge screening process has been completed, we find that the azimuthal current response has two contributions, one proportional to the Hall conductivity and treated previously by Zang and Nagaosa, [8] and one proportional to an external potential induced change in the internal orbital magnetization [19] of the surface states. For the particular case of a massive Dirac model the two contributions cancel exactly in the clean T = 0 limit when the carrier density is finite.…”

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confidence: 63%

“…Below we show that this happens because gradients in the density of carriers, all of which generally carry intrinsic magnetic moments [13,19], also yield an azimuthal current.…”

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confidence: 78%

Topological Magnetoelectric Effect Decay

Pesin

MacDonald

2013

Phys. Rev. Lett.

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We address the influence of realistic disorder and finite doping on the effective magnetic monopole induced near the surface of an ideal topological insulator (TI) by currents that flow in response to a suddenly introduced external electric charge. We show that when the longitudinal conductivity σxx = g(e 2 /h) = 0, the apparent position of a magnetic monopole initially retreats from the TI surface at speed vM = αcg, where α is the fine structure constant and c is the speed of light. For the particular case of TI surface states described by a massive Dirac model, we further find that the temperature T = 0 Hall currents vanish when the external potential is screened. Introduction-When a time-reversal-symmetry breaking perturbation opens a gap in the surface state spectrum of a three-dimensional topological insulator (TI) [1,2], surface Hall currents and orbital magnetism are induced by electrical perturbations. This magneto-electric coupling effect can be attractively described [3] by adding a E · B term to the electromagnetic Lagrangian. The duality of the resulting axion electrodynamics model[4] leads to a curious topological magneto-electric effect [5,11,12] in which an electric charge placed above the TI surface induces Hall currents and associated orbital magnetization that appears to emanate from a magnetic monopole below the surface.

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Publisher’s Note: Berry Phase Correction to Electron Density of States in Solids [Phys. Rev. Lett.95, 137204 (2005)]

Cited by 202 publications

References 0 publications

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals

Unified formalism for calculating polarization, magnetization, and more in a periodic insulator

Topological Magnetoelectric Effect Decay

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