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Symmetry-protected photonic topological insulator exhibiting robust pseudo-spin-dependent transportation, analogous to quantum spin Hall (QSH) phases and topological insulators, are of great importance in fundamental physics. Such transportation robustness is protected by time-reversal symmetry. Since electrons (fermion) and photons (boson) obey different statistics rules and associate with different time-reversal operators (i.e., Tf and Tb, respectively), whether photonic counterpart of Kramers degeneracy is topologically protected by bosonic Tb remains unidentified. Here, we construct the degenerate gapless edge states of two photonic pseudo-spins (left/right circular polarizations) in the band gap of a two-dimensional photonic crystal with strong magneto-electric coupling. We further demonstrated that the topological edge states are in fact protected by Tf rather than commonly believed Tb and their pseudo-spin dependent transportation is robust against Tf invariant impurities, discovering for the first time the topological nature of photons. Our results will pave a way towards novel photonic topological insulators and revolutionize our understandings in topological physics of fundamental particles.
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We propose an optical counterpart of the quantum spin Hall (QSH) effect in a two-dimensional photonic crystal composed of a gyrotropic medium exhibiting both gyroelectric and gyromagnetic properties simultaneously. Such QSH effect shows unidirectional polarization-dependent transportation of photonic topological edged states, which is robust against certain disorders and impurities. More importantly, we find that such unique property is not protected by conventional time-reversal symmetry of photons obeying the Bosonic statistics but rather by the same symmetry, as electrons time-reversal symmetry. Based on the tight-binding approximation approach, we construct an effective Hamiltonian for this photonic structure, which is shown to have a similar form to that of an electronic QSH system. Furthermore, the invariant of such model is calculated in order to unify its topological non-trivial character. Our finding provides a viable way to exploit the optical topological property, and also can be leveraged to develop a photonic platform to mimic the spin properties of electrons.
The formation of a superstructure - with a related Moire pattern - plays a crucial role in the extraordinary optical and electronic properties of twisted bilayer graphene, including the recently observed unconventional superconductivity. Here we put forward a novel, interdisciplinary approach to determine the Moire angle in twisted bilayer graphene based on the photonic spin Hall effect. We show that the photonic spin Hall effect exhibits clear fingerprints of the underlying Moire pattern, and the associated light beam shifts are well beyond current experimental sensitivities in the near-infrared and visible ranges. By discovering the dependence of the frequency position of the maximal photonic spin Hall effect shift on the Moire angle, we argue that the latter could be unequivocally accessed via all-optical far-field measurements. We also disclose that, when combined with the Goos-Hanchen effect, the spin Hall effect of light enables the complete determination of the electronic conductivity of the bilayer. Altogether our findings demonstrate that sub-wavelength spin-orbit interactions of light provide a unprecedented toolset for investigating optoelectronic properties of multilayer two-dimensional van der Waals materials.
Effective magnetic fields have enabled unprecedented manipulation of neutral particles including photons. In most studied cases, the effective gauge fields are defined through the phase of mode coupling between spatially discrete elements, such as optical resonators and waveguides in the case for photons. Here, in the paradigm of Bloch-wave modulated photonic crystals, we show creation of effective magnetic fields for photons in conventional dielectric continua for the first time, via Floquet band engineering. By controlling the phase and wavevector of Bloch waves, we demonstrated anomalous quantum Hall effect for light with distinct topological band features due to delocalized wave interference. Based on a cavity-free architecture, in which Bloch-wave modulations can be enhanced using guided-resonances in photonic crystals, the study here opens the door to the realization of effective magnetic fields at large scales for optical beam steering and topological light-matter phases with broken time-reversal symmetry.
How to measure the optical conductivity of atomically thin crystals is an important but challenging issue due to the weak light-matter interaction at the atomic scale. Photonic spin Hall effect, as a fundamental physical effect in light-matter interaction, is extremely sensitive to the optical conductivity of atomically thin crystals. Here, we report a precision measurement of the optical conductivity of graphene, where the photonic spin Hall effect acts as a measurement pointer. By incorporating with the weak-value amplification technique, the optical conductivity of monolayer graphene taken as a universal constant of $(0.993pm0.005)sigma_0$ is detected, and a high measuring resolution with $1.5times10^{-8}Omega^{-1}$ is obtained. For few-layer graphene without twist, we find that the conductivities increase linearly with layer number. Our idea could provide an important measurement technique for probing other parameters of atomically thin crystals, such as magneto-optical constant, circular dichroism, and optical nonlinear coefficient.
We experimentally realize a photonic analogue of the anomalous quantum Hall insulator using a two-dimensional (2D) array of coupled ring resonators. Similar to the Haldane model, our 2D array is translation invariant, has zero net gauge flux threading the lattice, and exploits next-nearest neighbor couplings to achieve a topologically non-trivial bandgap. Using direct imaging and on-chip transmission measurements, we show that the bandgap hosts topologically robust edge states. We demonstrate a topological phase transition to a conventional insulator by frequency detuning the ring resonators and thereby breaking the inversion symmetry of the lattice. Furthermore, the clockwise or the counter-clockwise circulation of photons in the ring resonators constitutes a pseudospin degree of freedom. We show that the two pseudospins acquire opposite hopping phases and their respective edge states propagate in opposite directions. These results are promising for the development of robust reconfigurable integrated nanophotonic devices for applications in classical and quantum information processing.
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