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Register a new userCasimir forces in the flatland: interplay between photo-induced phase transitions and quantum Hall physics
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Added by
Yuri Muniz De Souza
Publication date
2021
fields
Physics
and research's language is
English
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We investigate how photo-induced topological phase transitions and the magnetic-field-induced quantum Hall effect simultaneously influence the Casimir force between two parallel sheets of staggered two-dimensional (2D) materials of the graphene family. We show that the interplay between these two effects enables on-demand switching of the force between attractive and repulsive regimes while keeping its quantized characteristics. We also show that doping these 2D materials below their first Landau level allows one to probe the photoinduced topology in the Casimir force without the difficulties imposed by a circularly polarized laser. We demonstrate that the magnetic field has a huge impact on the thermal Casimir effect for dissipationless materials, where the quantized aspect of the energy levels leads to a strong repulsion that could be measured even at room temperature.
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In magnetic topological phases of matter, the quantum anomalous Hall (QAH) effect is an emergent phenomenon driven by ferromagnetic doping, magnetic proximity effects and strain engineering. The realization of QAH states with multiple dissipationless edge and surface conduction channels defined by a Chern number $mathcal{C}geq1$ was foreseen for the ferromagnetically ordered SnTe class of topological crystalline insulators (TCIs). From magnetotransport measurements on Sn$_{1-x}$Mn$_{x}$Te ($0.00leq{x}leq{0.08}$)(111) epitaxial thin films grown by molecular beam epitaxy on BaF$_{2}$ substrates, hole mediated ferromagnetism is observed in samples with $xgeq0.06$ and the highest $T_mathrm{c}sim7.5,mathrm{K}$ is inferred from an anomalous Hall behavior in Sn$_{0.92}$Mn$_{0.08}$Te. The sizable anomalous Hall angle $sim$0.3 obtained for Sn$_{0.92}$Mn$_{0.08}$Te is one of the greatest reported for magnetic topological materials. The ferromagnetic ordering with perpendicular magnetic anisotropy, complemented by the inception of anomalous Hall effect in the Sn$_{1-x}$Mn$_{x}$Te layers for a thickness commensurate with the decay length of the top and bottom surface states, points at Sn$_{1-x}$Mn$_{x}$Te as a preferential platform for the realization of QAH states in ferromagnetic TCIs.
Using general scaling arguments combined with mean-field theory we investigate the critical ($T simeq T_c$) and off-critical ($T e T_c$) behavior of the Casimir forces in fluid films of thickness $L$ governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of $T$ and of the chemical potential $mu$. We find that the total force is attractive both below and above $T_c$. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point $(T_c,mu_c)$, where critical density fluctuations arise, or except at low temperatures and $(L/a) (betaDelta mu) =O(1)$, with $Delta mu=mu-mu_c <0$ and $a$ the characteristic distance between the molecules of the fluid, i.e., in the capillary condensation regime. While near the critical point the maximal amplitude of the attractive force if of order of $L^{-d}$ in the capillary condensation regime the force is much stronger with maximal amplitude decaying as $L^{-1}$. Essential deviations from the standard finite-size scaling behavior are observed within the finite-size critical region $L/xi=O(1)$ for films with thicknesses $L lesssim L_{rm crit}$, where $L_{rm crit}=xi_0^pm (16 |s|)^{ u/beta}$, with $ u$ and $beta$ as the standard bulk critical exponents and with $s=O(1)$ as the dimensionless parameter that characterizes the relative strength of the long-ranged tail of the substrate-fluid over the fluid-fluid interaction. We present the modified finite-size scaling pertinent for such a case and analyze in detail the finite-size behavior in this region.
We predict the existence of lateral drag forces near the flat surface of an absorbing slab of an anisotropic material. The forces originate from the fluctuations of the electromagnetic field, when the anisotropy axis of the material forms a certain angle with the surface. In this situation, the spatial spectra of the fluctuating electromagnetic fields becomes asymmetric, different for positive and negative transverse wave vectors components. Differently from the case of van der Waals interactions in which the forward-backward symmetry is broken due to the particle movement or in quantum noncontact friction where it is caused by the mutual motion of the bodies, in our case the lateral motion results merely from the anisotropy of the slab. This new effect, of particular significance in hyperbolic materials, could be used for the manipulation of nanoparticles.
We calculate exactly the Casimir force between a spherical particle and a plane, both with arbitrary dielectric properties, in the non-retarded limit. Using a Spectral Representation formalism, we show that the Casimir force of a sphere made of a material A and a plane made of a material B, differ from the case when the sphere is made of B, and the plane is made of A. The differences in energy and force show the importance of the geometry, and make evident the necessity of realistic descriptions of the sphere-plane system beyond the Proximity Theorem approximation.
Lateral Casimir force near a laterally-inhomogeneous plate is first revealed by both rigorous simulations and proximity approximations. The inhomogeneity-induced lateral Casimir force provides a novel method to control the lateral motion of nano-objects above the plate, and makes source-free manipulations of them possible. When incorporated with the Casimir repulsion in a fluid, the lateral Casimir force is shown to dominate over Brownian motion and enables long-distance quantum propulsion and firm quantum trapping of nano-objects. Gratings of varying filling factors to mimic micro-scale inhomogeneity also confirm those effects. The idea to design asymmetric distributions of nano-structures paves the way to sophisticated tailoring of the lateral Casimir force.
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