The role of charge conjugation symmetry in topological photonics · 2016. 7. 7. · The role of...
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The role of charge conjugation symmetry in topological photonics
Henning Schomerus, Lancaster UniversityHeraklion, 16 June 2016
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Classification of electronic topological systems
Time reversal symmetry T : T HT = H reciprocity
Chiral symmetry X : X HX = -H sublattices, Dirac systems
Charge conj. symmetry C=XT : C HC = -H superconductors
→ 10 universality classes with different response to defects, e.g. • edge and defect states • parity/chiral anomaly • charge fractionalization…
Here: extend to optical systems with loss and gain:
consequence of topological defects and anomalies?
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Topological modes have finite : can manipulate selectively
anti-PT (Ge&Tureci PRA2013)
PT symm.: (map between equivalent subspaces)
topological variant: (Z2 gauge transformation)
charge-conjugate
|N-M| protected zero modes
+ reciprocity:
PT
chiral
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mode selection via topological anomalies in 1D and 2D
complex SSH chainhoneycomb lattices
dimerised Lieb lattice
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complex SSH chain
… because of chiral anomaly: sublattice-symmetry is broken
Top. characterization survives PT-sym. loss and gain
Midgap state … … selectively amplified …
Midgap state breaks thissymmetry: Sz=±1
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Microwave realization
Nature Communications 2015, with Nice group (Poli, Bellec, Kuhl, Mortessagne)
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Density of states
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Compare to nontopological defect
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Mode profiles
Robustness to structural disorder
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Pulse propagation
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PT lasers YD Chong et al PRL 2011; S Longhi PRA 2010; HS, PRL 2010; Guo, Sim, HS PRA 2011
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Topological Lasers
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2D version of SSH model: dimerised Lieb lattice
Flat band competes with point-defect states• generate isolated point defect state• NNN coupling: remove flat band
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corner centre
zeromode
flatband
Experiment
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disorder
staggered absorption … + disorder
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Pseudo-landau levels
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pseudo-Landau level laser
Parity anomaly: strained honeycomb lattices with gain and loss
Low-energy theory: SUSY
0th LL: sublattice polarized, thresholdlessamplification
higher LLs: not polarized and amplified until PT symmetry spontaneously broken
HS, N Yunger Halpern, PRL 2013
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Finite sys:sublatticepolarizationof 0th pseudo-LL is geometry-dependent
[C Poli, J Arkinstall and HS, PRB 2014]
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Open sys: ‘nontopological’ defect…| Flipped around
…via EPs on real and imaginary axis:
…becomes topological
HS & J Wiersig, PRA 2014; Malzard, Poli, HS, PRL 2015
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Final notes: beyond reciprocity
Instead of PT:
X HX=H* → X S(E)*X =[S-1(E*)]
can also do magneto-optics with PTT’:
X HX=H† → X S(E)†X =[S-1(E*)]
[or even ‘skew-Hamiltonian’ J HJ=H† where JT =-J ]
which all have no electronic analogue
HS PRL 2010, PRA 2012, Phil. Trans. R. Soc. A 2013
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Summary: topological anomalies → selectively amplified states
Landau levels
Complex SSH model
HS, Opt Lett 2013; C Poli, HS, M Bellec, U Kuhl, F Mortessagne, Nat Commun 2015; +subm.HS & N Yunger Halpern, PRL 2013; Malzard, Poli, HS, PRL 2015
lasers
Point defects