Casimir force phase transitions in the graphene family

Abstract

The Casimir force is a universal interaction induced by electromagnetic quantum fluctuations between any types of objects. The expansion of the graphene family by adding silicene, germanene and stanene (2D allotropes of Si, Ge, and Sn), lends itself as a platform to probe Dirac-like physics in honeycomb staggered systems in such a ubiquitous interaction. We discover Casimir force phase transitions between these staggered 2D materials induced by the complex interplay between Dirac physics, spin-orbit coupling and externally applied fields. In particular, we find that the interaction energy experiences different power law distance decays, magnitudes and dependences on characteristic physical constants. Furthermore, due to the topological properties of these materials, repulsive and quantized Casimir interactions become possible.

Topological Phase Transitions in the Photonic Spin Hall Effect

“…Unlike graphene [21], these materials are nonplanar and possess intrinsic spin-orbit coupling that results in the opening of a gap in their electronic band structure. Under the influence of external static and circularly polarized electromagnetic fields the four Dirac gaps are in general nondegenerate and the monolayer may be driven through several phase transitions involving topologically non-trivial states [22][23][24][25][26]. Previous studies on SHEL in the graphene family have been restricted to graphene [27][28][29], therefore overlooking the role of finite staggering, spin-orbit coupling, and spin/valley dynamics.…”

How to observe the giant thermal effect in the Casimir force for graphene systems

“…The van der Waals and Casimir forces in microsystems involving graphene have already been studied using a variety of theoretical approaches [24][25][26][27][28][29][30][31][32][33][34]. In the framework of the Dirac model [1][2][3][4], the natural description of the Casimir force in graphene systems, based on the first principles of quantum electrodynamics at nonzero temperature, is provided by the formalism of the polarization tensor in (2+1)-dimensional space-time [35][36][37][38][39][40][41].…”

Topological phase transitions and quantum Hall effect in the graphene family

“…1). The spin-orbit couplings for silicene, germanene, stanene, and plumbene are λ SO ≈ 3.9,43,100,200 meV [8,[16][17][18], respectively. Terms originating from Rashba physics are ignored because of their comparatively small effect [16,17].…”

“…Let us begin with the Hamiltonian for members of the graphene family, found through the use of a tightbinding model and subsequent low-energy expansion, including the effects of a circularly polarized laser and electric field [16][17][18] SO + e E z + η is half the mass gap. Here,τ i are Pauli matrices, p = (p x ,p y ) is the momentum for particles around points K (η = +1) and K (η = −1), spin s = ±1, and v F = √ 3dt/2h is the Fermi velocity, where d is the lattice constant and t is the nearest-neighbor coupling.…”

“…They are also nonplanar, with their two inequivalent sublattices lying in two distinct parallel planes, and thus respond to the presence of an out-of-plane static electric field [12][13][14][15]. Together with a circularly polarized laser, these external fields allow one to tune the gap for each spin and valley, allowing the materials to be driven through several phase transitions [16][17][18][19]. Many of the achievable phases possess topologically nontrivial features that can be characterized by a topological invariant, namely, the charge Chern number.…”