Abstract
The bulk-edge correspondence links the Chern-topological numbers with the net number of unidirectional states supported at an interface of the relevant materials. This fundamental principle is perhaps the most consequential result of topological photonics, as it determines the precise physical manifestations of nontrivial topological features. Even though the bulk-edge correspondence has been extensively discussed and used in the literature, it seems that in the general photonic case with dispersive materials it has no solid mathematical foundation and is essentially a conjecture. Here, I present a rigorous demonstration of this fundamental principle by showing that the thermal fluctuation-induced light-angular momentum spectral density in a closed cavity can be expressed in terms of the photonic gap Chern number, as well as in terms of the net number of unidirectional edge states. In particular, I highlight the rather fundamental connections between topological numbers in Chern-type photonic insulators and the fluctuation-induced light-momentum
Highlights
Topological matter and topological systems can have rather exotic properties and very unusual physics
In the recent work Ref. [23], I showed that the thermal fluctuation-induced light-angular momentum density per unit of area is precisely quantized in the photonic-insulator cavity, and that its “quantum” is determined by the net number of unidirectional edge states circulating around the cavity
From the continuum results (Fig. 3), one may expect that for low frequencies this system supports (i) one unidirectional edge state propagating along the lateral walls and (ii) two distinct unidirectional edge states propagating along the interface (y 1⁄4 0) of the two gyrotropic photonic crystals
Summary
Topological matter and topological systems can have rather exotic properties and very unusual physics. [23], I showed that the thermal fluctuation-induced light-angular momentum density per unit of area is precisely quantized in the photonic-insulator cavity, and that its “quantum” is determined by the net number of unidirectional edge states circulating around the cavity This rather universal property holds even when the system has no topological classification. It is demonstrated—never making use of the bulk-edge correspondence–—that there is an intimate connection between the Chern number and the fluctuation-induced Abraham angular momentum Both the Chern number and the angular momentum spectral density can be expressed in terms of an integral of the photonic Green function along a semistraight line parallel to the imaginary frequency axis [28].
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