Gauge-invariant Green function dynamics: A unified approach

Swiecicki, Sylvia D.; Sipe, J. E.

doi:10.1016/j.aop.2013.09.014

Cited by 3 publications

(14 citation statements)

References 18 publications

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“…Therefore, rather than simply using (3), we perform a generalized Peierls transformation introduced earlier [25] to arrive at the gauge-invariant Green function…”

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

“…For simplicity we take z(u; x, y) = z(u final − u + u initial ; y,x); that is, we assume that the path from y to x is a reverse of the path from x to y; this will be true of the paths used in this paper. The dynamics of the gauge-invariant Green function (4) is described in the independent particle approximation by a kinetic equation [25],…”

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

“…In the simplest case the straight line paths between points are chosen. but they can be shown to be gauge invariant as they can be rewritten in terms of the electromagnetic fields [25],…”

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

“…The dynamical equation (6), as well as the expressions for the microscopic charge and current densities [25] ρ…”

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

“…1). For the paths from this category the Peierls phase is of the form (x, y; T ) = γ R (x,T ) − γ R ( y,T ), and the Green function (4) is formed from the transformed field operators [25,26] …”

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

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Linear response of crystals to electromagnetic fields: Microscopic charge-current density, polarization, and magnetization

Swiecicki

Sipe

2014

Phys. Rev. B

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We present an electrodynamic approach to the description of the linear response of solids to electromagnetic fields. For time and spatially varying applied fields we solve the dynamical equations satisfied by the gaugeinvariant Green function and find microscopic charge and current densities that result in a form allowing for an easy construction of the multipole expansion of applied fields. Restricting ourselves to static and uniform electric and magnetic fields, we construct microscopic expressions for polarization and magnetization fields associated with each lattice site. The approach is in the spirit of the Power-Zienau-Wooley (PZW) treatment but generalized to account for the motion of the charge between lattice sites. We show that the macroscopic polarization and magnetization can be understood as the spatial average of the generalized PZW microscopic fields.

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“…Therefore, rather than simply using (3), we perform a generalized Peierls transformation introduced earlier [25] to arrive at the gauge-invariant Green function…”

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

“…In the simplest case the straight line paths between points are chosen. but they can be shown to be gauge invariant as they can be rewritten in terms of the electromagnetic fields [25],…”

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

“…The dynamical equation (6), as well as the expressions for the microscopic charge and current densities [25] ρ…”

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

Section: A Gauge-invariant Green Function and The Pzw Transformationmentioning

confidence: 99%

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Linear response of crystals to electromagnetic fields: Microscopic charge-current density, polarization, and magnetization

Swiecicki

Sipe

2014

Phys. Rev. B

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Microscopic polarization and magnetization fields in extended systems

2019

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We introduce microscopic polarization and magnetization fields at each site of an extended system, as well as free charge and current density fields associated with charge movement from site to site, by employing a lattice gauge approach based on a set of orthogonal orbitals associated with each site. These microscopic fields are defined using a single-particle electron Green function, and the equations governing its evolution under excitation by an electromagnetic field at arbitrary frequency involve the electric and magnetic fields rather than the scalar and vector potentials. If the sites are taken to be far from each other, we recover the limit of isolated atoms. For an infinite crystal we choose the orbitals to be maximally-localized Wannier functions, and in the long-wavelength limit we recover the expected linear response of an insulator, including the zero frequency transverse conductivity of a topologically nontrivial insulator. For a topologically trivial insulator we recover the expected expressions for the macroscopic polarization and magnetization in the ground state, and find that the linear response to excitation at arbitrary frequency is described solely by the microscopic polarization and magnetization fields. For very general optical response calculations the microscopic fields necessarily satisfy charge conservation, even under basis truncation, and do not suffer from the false divergences at zero frequency that can plague response calculations using other approaches.

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Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect

Mahon,

Lei,

MacDonald

2024

Phys. Rev. Research

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A delicate tension complicates the relationship between the topological magnetoelectric effect (TME) in three-dimensional (3D) Z2 topological insulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular Z2 topological classification of the electronic ground state of crystalline band insulators and the associated quantization of the magnetoelectric response coefficient calculated using bulk linear-response theory but, according to standard symmetry arguments, simultaneously forbids a nonzero magnetoelectric coefficient in any physical finite-size system. This contrast between theories of magnetoelectric response in formal bulk models and in real finite-sized materials originates from the distinct approaches required to introduce notions of (electronic) polarization and orbital magnetization in these fundamentally different environments. In this work we argue for a modified interpretation of the bulk linear-response calculations in nonmagnetic Z2 TIs that is more plainly consistent with TRS and use this interpretation to discuss the effect's observation—still absent over a decade after its prediction. Our analysis is reinforced by microscopic bulk and thin-film calculations carried out using a simplified but still realistic effective model for the well established V2VI3 [V=(Sb,Bi) and VI=(Se,Te)] family of nonmagnetic Z2 TIs. When a uniform dc magnetic field is included in this model, the anomalous n=0 Landau levels (LLs) play the central role, both in thin films and in bulk. In the former case, only the n=0 LL eigenfunctions can support a dipole moment, which vanishes if there are no magnetic surface dopants and is quantized in the thick-film limit if magnetic dopants at the top and bottom surfaces have opposite orientation. In the latter case, the Hamiltonian projected into the n=0 LL subspace is a one-dimensional Su-Schrieffer-Heeger model with ground-state polarization that is quantized in accordance with the bulk linear-response coefficient calculated for (a lattice regularization of) the starting 3D model. Motivated by analytical results, we conjecture a type of microscopic bulk-boundary correspondence: a bulk insulator with (generalized) TRS supports a magnetoelectric coefficient that is purely itinerant (which is generically related to the geometry of the ground state) if and only if magnetic surface dopants are required for the TME to manifest in finite samples thereof. We conclude that in nonmagnetic Z2 TIs the TME is activated by magnetic surface dopants, that the charge-density response to a uniform dc magnetic field is localized at the surface and specified by the configuration of those dopants, and that the TME is qualitatively less robust against disorder than the integer quantum Hall effect. Published by the American Physical Society 2024

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Gauge-invariant Green function dynamics: A unified approach

Cited by 3 publications

References 18 publications

Linear response of crystals to electromagnetic fields: Microscopic charge-current density, polarization, and magnetization

Linear response of crystals to electromagnetic fields: Microscopic charge-current density, polarization, and magnetization

Microscopic polarization and magnetization fields in extended systems

Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect

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