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Photonic simulation of topological superconductor edge state and zero-energy mode at a vortex.

Tan W, Chen L, Ji X, Lin HQ - Sci Rep (2014)

Bottom Line: Two essential characteristics of topological superconductor, particle-hole symmetry and p(x) + ip(y) pairing potentials, are well emulated in photonic systems.Its topological features are presented by chiral edge state and zero-energy mode at a vortex.This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.

View Article: PubMed Central - PubMed

Affiliation: Beijing Computational Science Research Center, Beijing 100084, China.

ABSTRACT
Photonic simulations of quantum Hall edge states and topological insulators have inspired considerable interest in recent years. Interestingly, there are theoretical predictions for another type of topological states in topological superconductors, but debates over their experimental observations still remain. Here we investigate the photonic analogue of the p(x) + ip(y) model of topological superconductor. Two essential characteristics of topological superconductor, particle-hole symmetry and p(x) + ip(y) pairing potentials, are well emulated in photonic systems. Its topological features are presented by chiral edge state and zero-energy mode at a vortex. This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.

No MeSH data available.


Manifestation of chiral edge state in both reciprocal and real space.(a,b) Perfect analogy of TSC Hamiltonian and edge state with ideal material parameters. (a) Projected band diagram of infinite TSC-like photonic structure (shaded areas) and edge state at the interface between a semi-finite TSC-like medium in the region x > 0 and a semi-finite opaque medium in the region x < 0 (red line). (b) Magnetic field (Hz) distributions of edge state for a finite TSC-like medium. (c,d) Non-perfect TSC-like edge state with reduced material parameters. The results in (a) and (c) are analytically calculated by solving Maxwell's equations, and those in (b) and (d) are numerically simulated by employing FDFD method.
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f2: Manifestation of chiral edge state in both reciprocal and real space.(a,b) Perfect analogy of TSC Hamiltonian and edge state with ideal material parameters. (a) Projected band diagram of infinite TSC-like photonic structure (shaded areas) and edge state at the interface between a semi-finite TSC-like medium in the region x > 0 and a semi-finite opaque medium in the region x < 0 (red line). (b) Magnetic field (Hz) distributions of edge state for a finite TSC-like medium. (c,d) Non-perfect TSC-like edge state with reduced material parameters. The results in (a) and (c) are analytically calculated by solving Maxwell's equations, and those in (b) and (d) are numerically simulated by employing FDFD method.

Mentions: The non-zero winding number promises a chiral edge state localized at the interface between the TSC-like medium and another opaque medium. Let the interface be at x = 0, and the opaque medium be located in the region x < 0. The dispersion relation of the edge state is illustrated by the red line in figure 2a, where the shaded areas indicate the projected band diagram of infinite TSC-like medium. The material parameters of the TSC-like medium are taken as ε⊥0 = 0.8, εz0 = 1.1, μ⊥0 = 1.2, μz0 = 0.9, (which lead to δε⊥ = −δμ⊥ = −0.2, δεz = −δμz = 0.1), ωp = 89, and κ = 0.04 (with the unit of GHz). These parameters ensure the particle-hole-like symmetry of the effective Hamiltonian. From figure 2a, one can see a single branch of edge state with positive group velocity, which suggests broken TR symmetry and is expected to support one-way propagation. Note that another branch with negative group velocity can be realized by changing the permittivity and permeability tensors described by equation (6) into their conjugations, which makes the winding number flip its sign. To demonstrate the edge state intuitively, we also perform numerical calculations in real space by employing finite-difference frequency-domain (FDFD) method. As shown in figure 2b, the edge state distributes almost uniformly along the interface between two media and can pass through sharp bends at the corner without scattering.


Photonic simulation of topological superconductor edge state and zero-energy mode at a vortex.

Tan W, Chen L, Ji X, Lin HQ - Sci Rep (2014)

Manifestation of chiral edge state in both reciprocal and real space.(a,b) Perfect analogy of TSC Hamiltonian and edge state with ideal material parameters. (a) Projected band diagram of infinite TSC-like photonic structure (shaded areas) and edge state at the interface between a semi-finite TSC-like medium in the region x > 0 and a semi-finite opaque medium in the region x < 0 (red line). (b) Magnetic field (Hz) distributions of edge state for a finite TSC-like medium. (c,d) Non-perfect TSC-like edge state with reduced material parameters. The results in (a) and (c) are analytically calculated by solving Maxwell's equations, and those in (b) and (d) are numerically simulated by employing FDFD method.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4260229&req=5

f2: Manifestation of chiral edge state in both reciprocal and real space.(a,b) Perfect analogy of TSC Hamiltonian and edge state with ideal material parameters. (a) Projected band diagram of infinite TSC-like photonic structure (shaded areas) and edge state at the interface between a semi-finite TSC-like medium in the region x > 0 and a semi-finite opaque medium in the region x < 0 (red line). (b) Magnetic field (Hz) distributions of edge state for a finite TSC-like medium. (c,d) Non-perfect TSC-like edge state with reduced material parameters. The results in (a) and (c) are analytically calculated by solving Maxwell's equations, and those in (b) and (d) are numerically simulated by employing FDFD method.
Mentions: The non-zero winding number promises a chiral edge state localized at the interface between the TSC-like medium and another opaque medium. Let the interface be at x = 0, and the opaque medium be located in the region x < 0. The dispersion relation of the edge state is illustrated by the red line in figure 2a, where the shaded areas indicate the projected band diagram of infinite TSC-like medium. The material parameters of the TSC-like medium are taken as ε⊥0 = 0.8, εz0 = 1.1, μ⊥0 = 1.2, μz0 = 0.9, (which lead to δε⊥ = −δμ⊥ = −0.2, δεz = −δμz = 0.1), ωp = 89, and κ = 0.04 (with the unit of GHz). These parameters ensure the particle-hole-like symmetry of the effective Hamiltonian. From figure 2a, one can see a single branch of edge state with positive group velocity, which suggests broken TR symmetry and is expected to support one-way propagation. Note that another branch with negative group velocity can be realized by changing the permittivity and permeability tensors described by equation (6) into their conjugations, which makes the winding number flip its sign. To demonstrate the edge state intuitively, we also perform numerical calculations in real space by employing finite-difference frequency-domain (FDFD) method. As shown in figure 2b, the edge state distributes almost uniformly along the interface between two media and can pass through sharp bends at the corner without scattering.

Bottom Line: Two essential characteristics of topological superconductor, particle-hole symmetry and p(x) + ip(y) pairing potentials, are well emulated in photonic systems.Its topological features are presented by chiral edge state and zero-energy mode at a vortex.This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.

View Article: PubMed Central - PubMed

Affiliation: Beijing Computational Science Research Center, Beijing 100084, China.

ABSTRACT
Photonic simulations of quantum Hall edge states and topological insulators have inspired considerable interest in recent years. Interestingly, there are theoretical predictions for another type of topological states in topological superconductors, but debates over their experimental observations still remain. Here we investigate the photonic analogue of the p(x) + ip(y) model of topological superconductor. Two essential characteristics of topological superconductor, particle-hole symmetry and p(x) + ip(y) pairing potentials, are well emulated in photonic systems. Its topological features are presented by chiral edge state and zero-energy mode at a vortex. This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.

No MeSH data available.