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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 photonic zero-energy modes at a vortex and at edges.The mode at the vortex propagates counter-clockwise around the center vortex core, while the mode at the edge propagates clockwise. Azimuth-dependent off-diagonal elements in permittivity and permeability tensors are introduced to mimic a vortex with a singularity at the center.
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f3: Manifestation of photonic zero-energy modes at a vortex and at edges.The mode at the vortex propagates counter-clockwise around the center vortex core, while the mode at the edge propagates clockwise. Azimuth-dependent off-diagonal elements in permittivity and permeability tensors are introduced to mimic a vortex with a singularity at the center.

Mentions: Another prominent feature of px + ipy superconductor is zero-energy mode at a vortex1734353637. It is a solution of the Bogoliubov-de Gennes (BdG) equation in polar coordinates with Δ(r,θ) = Δ0(r)exp(±iθ), characterized by a bound state at zero energy at a vortex core which can be roughly considered as a small circular edge with vanishing density at the center17. Zero-energy mode is another important topological excitation, but earlier works in photonics only concentrated on edge states. Here we introduce azimuth-dependent off-diagonal elements in permittivity and permeability tensors with cylindrical symmetry, for example, κ1 = κ2 = κ exp(−iθ) and κ3 = κ4 = κ exp(+iθ). This design mimics a counter-clockwise vortex with a singularity at the center. FDFD method is employed to numerically calculate the field distributions in a finite medium at zero energy (ω0). The results are shown in figure 3. Two types of bound states are clearly seen: one appears at the edge and the other locates at the center “vortex core”. We have also confirmed that the bound state at the vortex only exists at ω0, which is indeed a “zero-energy” mode. It is known that the zero-energy modes at the vortex and at the edge can be described as the Jackiw-Rebbi solution in the 1D Dirac equation at the domain wall3839. Here we reproduce them in photonic structures. Further calculations illustrate that the mode around the center rotates counter-clockwise around the vortex core, while the other rotates clockwise along the edge. The electric and magnetic fields also show different patterns between these two modes: in one mode Ez and Hz oscillate in phase, while in the other Ez and Hz oscillate out of phase.


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 photonic zero-energy modes at a vortex and at edges.The mode at the vortex propagates counter-clockwise around the center vortex core, while the mode at the edge propagates clockwise. Azimuth-dependent off-diagonal elements in permittivity and permeability tensors are introduced to mimic a vortex with a singularity at the center.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Manifestation of photonic zero-energy modes at a vortex and at edges.The mode at the vortex propagates counter-clockwise around the center vortex core, while the mode at the edge propagates clockwise. Azimuth-dependent off-diagonal elements in permittivity and permeability tensors are introduced to mimic a vortex with a singularity at the center.
Mentions: Another prominent feature of px + ipy superconductor is zero-energy mode at a vortex1734353637. It is a solution of the Bogoliubov-de Gennes (BdG) equation in polar coordinates with Δ(r,θ) = Δ0(r)exp(±iθ), characterized by a bound state at zero energy at a vortex core which can be roughly considered as a small circular edge with vanishing density at the center17. Zero-energy mode is another important topological excitation, but earlier works in photonics only concentrated on edge states. Here we introduce azimuth-dependent off-diagonal elements in permittivity and permeability tensors with cylindrical symmetry, for example, κ1 = κ2 = κ exp(−iθ) and κ3 = κ4 = κ exp(+iθ). This design mimics a counter-clockwise vortex with a singularity at the center. FDFD method is employed to numerically calculate the field distributions in a finite medium at zero energy (ω0). The results are shown in figure 3. Two types of bound states are clearly seen: one appears at the edge and the other locates at the center “vortex core”. We have also confirmed that the bound state at the vortex only exists at ω0, which is indeed a “zero-energy” mode. It is known that the zero-energy modes at the vortex and at the edge can be described as the Jackiw-Rebbi solution in the 1D Dirac equation at the domain wall3839. Here we reproduce them in photonic structures. Further calculations illustrate that the mode around the center rotates counter-clockwise around the vortex core, while the other rotates clockwise along the edge. The electric and magnetic fields also show different patterns between these two modes: in one mode Ez and Hz oscillate in phase, while in the other Ez and Hz oscillate out of phase.

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.