Chapter 17
Axion Electrodynamics in
Magnetoelectric Media
A. Martín-Ruiz, M. Cambiaso, and L. F. Urrutia
Abstract Topologically ordered media demand a new understanding of the emergent properties of quantum matter. This is a fundamental and technological feat.
Topological insulators and Weyl semimetals are materials with topological order.
Here we will focus on how these materials interact with sources of the electromagnetic field. We start from the effective field theory of Maxwell’s electrodynamics
extended by a so-called magnetoelectric term, namely axion electrodynamics and
summarize some results we have found exploiting a Green’s function approach to
solve for the electromagnetic fields. Signals of the magnetolectric effect are minute
compared with other electromagnetic responses, therefore precision measurements
are required for its detection. Our formulation can be used for topological insulators
and Weyl semimetals with planar, cylindrical and spherical geometries interacting
with general charges, currents and boundary conditions. Our formulation is exemplified by: (i) the issue of Casimir effect involving a planar topological insulator, (ii)
Vavilov-Cherenkov radiation produced in the forward- and backward-direction of a
charged particle traversing a planar interface of two magnetoelectric media and (iii)
the electromagnetic fields induced by a static electric charge near the surface of a
Weyl semimetal. All three applications can yield observable signals that are within
experimental sensitivities.
A. Martín-Ruiz · L. F. Urrutia (B)
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 Ciudad de
México, Mexico
e-mail: urrutia@nucleares.unam.mx
A. Martín-Ruiz
e-mail: alberto.martin@nucleares.unam.mx
M. Cambiaso
Universidad Andres Bello, Departamento de Ciencias Fisicas, Facultad de Ciencias Exactas,
Avenida Republica 220, Santiago, Chile
e-mail: mcambiaso@unab.cl
© Springer Nature Switzerland AG 2021
E. Kamenetskii (ed.), Chirality, Magnetism and Magnetoelectricity,
Topics in Applied Physics 138,
https://doi.org/10.1007/978-3-030-62844-4_17
459
Axion Electrodynamics in
Magnetoelectric Media
A. Martín-Ruiz, M. Cambiaso, and L. F. Urrutia
Abstract Topologically ordered media demand a new understanding of the emergent properties of quantum matter. This is a fundamental and technological feat.
Topological insulators and Weyl semimetals are materials with topological order.
Here we will focus on how these materials interact with sources of the electromagnetic field. We start from the effective field theory of Maxwell’s electrodynamics
extended by a so-called magnetoelectric term, namely axion electrodynamics and
summarize some results we have found exploiting a Green’s function approach to
solve for the electromagnetic fields. Signals of the magnetolectric effect are minute
compared with other electromagnetic responses, therefore precision measurements
are required for its detection. Our formulation can be used for topological insulators
and Weyl semimetals with planar, cylindrical and spherical geometries interacting
with general charges, currents and boundary conditions. Our formulation is exemplified by: (i) the issue of Casimir effect involving a planar topological insulator, (ii)
Vavilov-Cherenkov radiation produced in the forward- and backward-direction of a
charged particle traversing a planar interface of two magnetoelectric media and (iii)
the electromagnetic fields induced by a static electric charge near the surface of a
Weyl semimetal. All three applications can yield observable signals that are within
experimental sensitivities.
A. Martín-Ruiz · L. F. Urrutia (B)
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510 Ciudad de
México, Mexico
e-mail: urrutia@nucleares.unam.mx
A. Martín-Ruiz
e-mail: alberto.martin@nucleares.unam.mx
M. Cambiaso
Universidad Andres Bello, Departamento de Ciencias Fisicas, Facultad de Ciencias Exactas,
Avenida Republica 220, Santiago, Chile
e-mail: mcambiaso@unab.cl
© Springer Nature Switzerland AG 2021
E. Kamenetskii (ed.), Chirality, Magnetism and Magnetoelectricity,
Topics in Applied Physics 138,
https://doi.org/10.1007/978-3-030-62844-4_17
459