Quantum spin Hall effect of light

Abstract

Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect, i.e., surface modes with strong spin-momentum locking. These modes are evanescent waves that form, e.g., surface plasmonpolaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments demonstrating the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces.Solid-state physics exhibits a family of Hall effects with remarkable physical properties. The usual Hall effect (HE) and quantum Hall effect (QHE) appear in the presence of an external magnetic field, which breaks the time-reversal ( T ) symmetry of the system. The HE induces charge current orthogonal to both the magnetic field and an applied electric field, whereas the QHE [1] involves distinct topological electron states, with unidirectional edge modes (chargemomentum locking), characterized by the topological Chern number [2].The intrinsic spin Hall effect (SHE) can occur in T -symmetric electron systems with spinorbit interactions. It produces a spin-dependent transport of electrons orthogonal to the external driving force [3,4]. There is also the quantum spin Hall effect (QSHE) [5,6], which is characterized by unidirectional edge spin transport, i.e., edge states with opposite spins propagating in opposite directions. Such topological states with spin-momentum locking gave rise to a new class of materials: topological insulators [7,8].Alongside the extensive condensed-matter studies of electron Hall effects, their photonic counterparts have been found in various optical systems. In particular, both the HE [9] the QHE with unidirectional edge propagation [10,11] have been reported in magneto-optical systems with broken T -symmetry. Furthermore, because photons are relativistic spin-1 particles, they naturally exhibit intrinsic spin-orbit interaction effects, including Berry phase [12] and the SHE [13][14][15] stemming from fundamental spin properties of Maxwell equations [16].The only missing part in the above optical Hall effects is the QSHE for photons. Recently, it was suggested that photonic topological insulators can be created in complex metamaterials structures [17][18][19]. Here we show that pure free-space light already possesses intrinsic QSHE, and simple natural materials (such as metals supporting surface plasmon-polariton modes) exhibit some features resembling topological insulators. We show that the recently discovered transverse spin in evanescent wav...

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