title

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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

3

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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1

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tunneling phases

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1

2

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tunneling phases

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1

2

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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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