Institute for Theoretical Physics III | University of Stuttgart...motivation: diculties 4...
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Transcript of Institute for Theoretical Physics III | University of Stuttgart...motivation: diculties 4...
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team
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Hans Peter BüchlerNicolai Lang
Mikhail LukinNorman Yao
Sebastian Huber
motivation: topological states of matter
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topological bands
fermions
topological insulatorsinteger quantum Hall effect (QHE)
(edge states, quantized σxy)
non-interacting,filled band(single particle physics)
interacting+ flat bands
FQHE with anyonic excitationsopen question: non-Abelian states?
bosonic FQHE states
bosons
interacting+ flat bands
motivation: topological states of matter
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topological bands
fermions
topological insulatorsinteger quantum Hall effect (QHE)
(edge states, quantized σxy)
non-interacting,filled band(single particle physics)
interacting+ flat bands
FQHE with anyonic excitationsopen question: non-Abelian states?
bosonic FQHE states
bosons
interacting+ flat bands
motivation: difficulties
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topological bands
tunneling phases for neutral particles?
F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988)
Y. Wang. Phys. Rev. B 86, 201101 (2012)
motivation: experimental requirements
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"natural" realization with dipoles on lattices
▷ Two-dimensional lattice
▷ Three-level dipole
▷ Strong dipole-dipole interactions
squaretriangular
honeycomb...
polar moleculesRydberg atoms
NV centers
(not necessarily perfect)
setup with polar molecules
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one moleculepinned at each lattice site
setup with polar molecules
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one moleculepinned at each lattice site
Three level dipole from rotational structure:
rotationalconstant
angularmomentum
dipolemoment
externalfields
eigenstates without electric field:
see also:N. Yao, Phys. Rev. Lett. 109, 266804 (2012)N. Yao, Phys. Rev. Lett. 110, 185302 (2013)S. Syzranov, arXiv:1406.0570
setup with polar molecules
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one moleculepinned at each lattice site
Three level dipole from rotational structure:
rotationalconstant
angularmomentum
dipolemoment
externalfields
eigenstates without electric field:
eigenstates with electric field:
m is still a good quantum number
see also:N. Yao, Phys. Rev. Lett. 109, 266804 (2012)N. Yao, Phys. Rev. Lett. 110, 185302 (2013)S. Syzranov, arXiv:1406.0570
setup with polar molecules
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one moleculepinned at each lattice site
Three level dipole from rotational structure:
rotationalconstant
angularmomentum
dipolemoment
externalfields
eigenstates without electric field:
eigenstates with electric field:
m is still a good quantum number
see also:N. Yao, Phys. Rev. Lett. 109, 266804 (2012)N. Yao, Phys. Rev. Lett. 110, 185302 (2013)S. Syzranov, arXiv:1406.0570
dipolar exchange interactions
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dipole-dipole interactions in the plane
dipolar exchange interactions
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energy conserving processes:
dipole-dipole interactions in the plane
dipolar exchange interactions
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energy conserving processes:
dipole-dipole interactions in the plane
tunneling model
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interaction term, not relevantfor single excitation dynamics
tunneling phases
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tunneling phases
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tunneling phases
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tunneling phases
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bosonic model
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Describe excitations as effective particles (hardcore bosons)
spin-orbit couplinglong-range tunneling
Tunneling Hamiltonian
bosonic model
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Describe excitations as effective particles (hardcore bosons)
Tunneling Hamiltonian
momentum space
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momentum space
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spin-orbit coupling with:
momentum space
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spin-orbit coupling with:
band structure
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band structure
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band structure
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are these bands topological?
after tuning parameters
topological invariants
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Review on topological insulators:M. Hasan and C. Kane, Rev. Mod. Phys. 82, 3045 (2010)
topological invariants
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Review on topological insulators:M. Hasan and C. Kane, Rev. Mod. Phys. 82, 3045 (2010)
Chern number
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Chern number
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Chern number
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Chern number as a winding number
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Chern number as a winding number
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Chern number as a winding number
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Chern number as a winding number
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Chern number as a winding number
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topological phase diagram
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C as winding number
edge states
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edge states
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edge states
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edge states
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Hatsugai, Phys. Rev. Lett. 71, 3697 (1993)
edge states
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Chern number in the disordered system
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density of defects
sample-averaged Chern number
Chern number in the disordered system
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density of defects
sample-averaged Chern number
honeycomb lattice: flat bands
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conclusion
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1Y. Wang, Phys. Rev. B 86, 201101 (2012)2G. Möller, Phys. Rev. Lett. 103, 105303 (2009)
white
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Halperin state
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honeycomb lattice: topological phase diagram
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disordered system
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dispersion relation x/1 model
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Landau levels
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double-layer picture
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C=1 C=1
full BZ
C=2C=1
C=1
full BZ
C=1
1 + 1 = 2 x 11 + 1 = 2
outline
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edge states: disorder
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