Repulsive Casimir Effect with Chern Insulators

Abstract

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. ...

Signatures of complex optical response in Casimir interactions of type I and II Weyl semimetals

“…Additionally, Casimir force phase transitions driven by external fields have been predicted in related 2D materials, such as silicene, germanene, and stanene [13]. Moreover, repulsive and force quantization effects have been described in other materials, such as 3D topological insulators and Chern insulators [14][15][16][17].…”

Long-Range Repulsion Between Spatially Confined van der Waals Dimers

“…Such interactions are important not only for many fundamental phenomena throughout the fields of biology, chemistry, and physics but also for the design and performance of micro-and nano-structured devices. While Casimir forces can be both attractive or repulsive, depending on the nature of the fluctuations (quantum and/or thermal) and the spatial structure (topology and/or geometry) of the interacting systems [5][6][7][8], it is undisputed common wisdom that nonretarded vdW interactions between two objects in vacuo are inherently attractive [9][10][11]. The universality of vdW attraction is attributed to the ubiquitous zero-point energy lowering, induced by dipolar coupling between fluctuating electron charge densities [9,10].…”

Vacuum polarization at the boundary of a topological insulator

“…(5), since this charge will correct the vacuum energy found in the literature, given by Eq. (9). Such a charge is responsible for the dynamical effect that we are looking for and it does not occur when ordinary charges alone are considered.…”