Measuring a piecewise constant axion field in classical electrodynamics

We theoretically predict that the Casimir force in vacuum between two Chern insulator plates can be repulsive (attractive) at long distances whenever the sign of the Chern numbers characterizing the two plates are opposite (equal). A unique feature of this system is that the sign of the force can be tuned simply by turning over one of the plates or alternatively by electrostatic doping. We calculate and take into account the full optical response of the plates and argue that such repulsion is a general phenomena for these systems as it relies on the quantized zero frequency Hall conductivity. We show that achieving repulsion is possible with thin films of Cr-doped ðBi; SbÞ 2 Te 3 , that were recently discovered to be Chern insulators with quantized Hall conductivity. DOI: 10.1103/PhysRevLett.112.056804 PACS numbers: 73.23.-b, 03.70.+k, 41.20.-q, 72.20.-i More than half a century after its theoretical prediction, the Casimir effect [1] still stands among the most intriguing quantum phenomena. The relatively recent quantitative experimental access to the physics of this effect [2], the force experienced by objects due to quantum vacuum fluctuations, has revealed that it is still far from being completely understood. Despite the development of useful calculating tools in terms of the scattering formalism [3,4], the possibility of achieving repulsion in vacuum between two material plates is still so far unreachable experimentally. Two dielectrics can repel when immersed in a medium with very specific optical properties [5,6] and no mirror-symmetric situation can give rise to repulsion [7,8]. These restrictions turn the search for repulsion in vacuum into a difficult challenge that can potentially solve stiction issues [2,9]. Earlier proposals include magnetic materials [10], metamaterials [11,12], engineered geometries [13], and quantum Hall effect (QHE) systems [14], where the latter was subsequently generalized to a QHE system made out of doped graphene sheets [15]. In [16,17], the concept of a topological Casimir effect was explored using three-dimensional topological insulators (TI) [18,19], which owing to their topological electromagnetic (EM) response, opened the way to a tunable repulsion. In these works, the finite frequency part of the topological response [20] arising from the EM response encoded in the θ term [21,22] was assumed to be the quantized zero frequency response for all frequencies, which is only valid for certain distance scales depending on material parameters.In this Letter, we propose to achieve and manipulate repulsion by exploring the Casimir force arising due to the topological nature of Chern insulators (CI). These general class of two dimensional materials have a quantized Hall conductivity in the absence of external magnetic field due to the nontrivial topological structure of the Bloch bands [18,19,23]. The Chern number C ∈ Z is the topological attribute of each band that, if finite, indicates a quantized contribution to the Hall conductivity at zero frequency σ xy ð0Þ ¼ Ce 2 =h. ...

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“…In our convention, these are consistent with results for 3D TI [16,32,33] and are related to those of Ref. [15] by a basis transformation.…”

supporting

confidence: 89%

Repulsive Casimir Effect with Chern Insulators

Rodriguez-López

Grushin

2014

Phys. Rev. Lett.

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“…Cross polarized field components vanish for Mη 0 approaches to infinity and co polarized field intensity increases as Mη 0 increases till it approaches to results of two dimensional PEC Gregorian reflector antenna the field patterns of Equation (14). It may be noted that limits of the integrals in Equation (13) are selected using the following relations by…”

Section: Resultsmentioning

confidence: 99%

“…Focusing systems [5][6][7][8] and PEMC medium [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] have been discussed by many authors.…”

Section: Introductionmentioning

confidence: 99%

High-Frequency Expression for the Field in the Caustic Region of a Pemc Gregorian System Using Maslov's Method

Fiaz¹,

Aziz²,

Ghaffar³

et al. 2008

PIER

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Abstract-Method proposed by Maslov has been used, to remedy the problem of geometrical optics, for a two dimensional Perfect electromagnetic conductor (PEMC) Gregorian system. It generates an integral form of solution near the caustic that can be evaluated analytically/numerically, or with uniform asymptotic techniques. Away from the caustic it recovers the geometrical optics field. Numerical computations are made to calculate the field around the caustic of a Gregorian system.

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“…As to the axion, when α =const, it does not affect the wave propagation. However, as pointed out in [13,40], one may observe measurable effects at the interfaces between spacetime domains with different constant values of α.…”

Section: Discussionmentioning

confidence: 95%

Equivalence principle and electromagnetic field: no birefringence, no dilaton, and no axion

Hehl

Obukhov

2008

Gen Relativ Gravit

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The coupling of the electromagnetic field to gravity is discussed. In the premetric axiomatic approach based on the experimentally well established conservation laws of electric charge and magnetic flux, the Maxwell equations are the same irrespective of the presence or absence of gravity. In this sense, one can say that the charge "substratum" and the flux "substratum"are not influenced by the gravitational field directly. However, the interrelation between these fundamental substrata, formalized as the spacetime relation H = H(F ) between the 2-forms of the electromagnetic excitation H and the electromagnetic field strength F , is affected by gravity. Thus the validity of the equivalence principle for electromagnetism depends on the form of the spacetime relation. We discuss the nonlocal and local linear constitutive relations and demonstrate that the spacetime metric can be accompanied also by skewon, dilaton, and axion fields. All these premetric companions of the metric may eventually lead to a violation of the equivalence principle.

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Measuring a piecewise constant axion field in classical electrodynamics

Cited by 95 publications

References 17 publications

Repulsive Casimir Effect with Chern Insulators

Repulsive Casimir Effect with Chern Insulators

High-Frequency Expression for the Field in the Caustic Region of a Pemc Gregorian System Using Maslov's Method

Equivalence principle and electromagnetic field: no birefringence, no dilaton, and no axion

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