488
A. Martín-Ruiz et al.
by means of axion-like extended electrodynamics with a non-dynamical axion field
θ . Among the benefits of such effective field theory approach is that we can exploit a
Green’s function formulation to solve for the electromagnetic fields with rather arbitrary configuration of charges, currents, boundary conditions and/or combination of
these. Our tools and techniques have been applied to linear isotropic and homogeneous magnetoelectric media with mild coordinate restrictions that are, however,
plausible from an experimental point of view. Other benefit of the GF formulation is
that the method can be extended to the case of anisotropic media. To illustrate our tools
and techniques, we summarize some previously reported results that include: (i) a
detailed assessment of the boundary value problem of axion electrodynamics and the
modified boundary conditions for the electromagnetic fields across the magnetoelectric interface; (ii) the application to the case of a topological insulator with planar
geometry located between two parallel conducting plates to compute the ensuing
modification to the Casimir effect; (iii) as an example on how to extend the formulation beyond the static cases, we review some results showing that this technique
can be applied to the case of an electric charge traversing from one magnetoelectric
medium to another at a constant speed and perpendicular to the interface between
them to reveal that, besides the usual forward-directed Vavilov-Cherenkov emission
of radiation, a novel feature due entirely to the magnetoelectric effect is an additional
backward-directed radiation, termed reversed Vavilov-Cherenkov radiation. Last (iv)
we employ the same approach to study the induced electromagnetic fields due to a
static electric charge near the surface of a Weyl semimetal in the equilibrium state
and at neutrality point to find that inside the WSM medium the induced electric field
is nothing like inside a conductor nor insulator and the induced magnetic field outside the WSM has among its multipole contributions one term that corresponds to a
magnetic dipole field, as if below the surface of the WSM the electric charge induced
a stack of alternating axisymmetric circulating currents centered at the projection of
the electric charge. Two different experimental setups are proposed to measure distinctive characteristics of the induced magnetic field as smoking-gun signals of the
magnetoelectric effect in WSM and we argue that these observable signals could be
measured given the present-day experimental sensitivities available.
As mentioned in the beginning, the study of topological phases of matter is both
a fundamental and technological challenge. We think that with our exposition we
contributed in both fronts. Our approach allows to shed lights on the understanding
of the interaction of these new states of matter with electromagnetic radiation. At
the same time, and as a corollary of our approach, we have provided new means to
eventually measure observable signals of the magnetoelectric effect using topological
insulators or Weyl semimetals. Though we have provided but a few examples, the
generality of the Green’s function method paves the way for new proposals to similar
ends.
Acknowledgements A.M.R. acknowledges support from DGAPA-UNAM project IA101320.
M.C. has been partially supported by UNAB DGID under Grant No. DI-33-17/RG. L.F.U. acknowledges support from DGAPA-UNAM Project No. IN103319. We thank to F.M.D. Pellegrino and A.
Santonocito for useful remarks.
A. Martín-Ruiz et al.
by means of axion-like extended electrodynamics with a non-dynamical axion field
θ . Among the benefits of such effective field theory approach is that we can exploit a
Green’s function formulation to solve for the electromagnetic fields with rather arbitrary configuration of charges, currents, boundary conditions and/or combination of
these. Our tools and techniques have been applied to linear isotropic and homogeneous magnetoelectric media with mild coordinate restrictions that are, however,
plausible from an experimental point of view. Other benefit of the GF formulation is
that the method can be extended to the case of anisotropic media. To illustrate our tools
and techniques, we summarize some previously reported results that include: (i) a
detailed assessment of the boundary value problem of axion electrodynamics and the
modified boundary conditions for the electromagnetic fields across the magnetoelectric interface; (ii) the application to the case of a topological insulator with planar
geometry located between two parallel conducting plates to compute the ensuing
modification to the Casimir effect; (iii) as an example on how to extend the formulation beyond the static cases, we review some results showing that this technique
can be applied to the case of an electric charge traversing from one magnetoelectric
medium to another at a constant speed and perpendicular to the interface between
them to reveal that, besides the usual forward-directed Vavilov-Cherenkov emission
of radiation, a novel feature due entirely to the magnetoelectric effect is an additional
backward-directed radiation, termed reversed Vavilov-Cherenkov radiation. Last (iv)
we employ the same approach to study the induced electromagnetic fields due to a
static electric charge near the surface of a Weyl semimetal in the equilibrium state
and at neutrality point to find that inside the WSM medium the induced electric field
is nothing like inside a conductor nor insulator and the induced magnetic field outside the WSM has among its multipole contributions one term that corresponds to a
magnetic dipole field, as if below the surface of the WSM the electric charge induced
a stack of alternating axisymmetric circulating currents centered at the projection of
the electric charge. Two different experimental setups are proposed to measure distinctive characteristics of the induced magnetic field as smoking-gun signals of the
magnetoelectric effect in WSM and we argue that these observable signals could be
measured given the present-day experimental sensitivities available.
As mentioned in the beginning, the study of topological phases of matter is both
a fundamental and technological challenge. We think that with our exposition we
contributed in both fronts. Our approach allows to shed lights on the understanding
of the interaction of these new states of matter with electromagnetic radiation. At
the same time, and as a corollary of our approach, we have provided new means to
eventually measure observable signals of the magnetoelectric effect using topological
insulators or Weyl semimetals. Though we have provided but a few examples, the
generality of the Green’s function method paves the way for new proposals to similar
ends.
Acknowledgements A.M.R. acknowledges support from DGAPA-UNAM project IA101320.
M.C. has been partially supported by UNAB DGID under Grant No. DI-33-17/RG. L.F.U. acknowledges support from DGAPA-UNAM Project No. IN103319. We thank to F.M.D. Pellegrino and A.
Santonocito for useful remarks.