topological valley currents in gapped graphene · 2015-06-15 · 11.06.2015 45 nonlocal response in...
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TOPOLOGICAL VALLEY CURRENTS IN GAPPED GRAPHENE
Leonid Levitov (MIT)
● Berry phase in gapped graphene● Valley Hall effect without edge states● Detecting valley currents in G/hBN
superlattices: an all-electrical approach
NPSMP2015 symposium, ISSP, Tokyo University
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Berry curvature and topological currents
Electrons in crystals have charge, energy, momentum and Berry's curvature (built-in vorticity)
Semiclassical eqs of motion:
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Berry curvature and topological currents
Electrons in crystals have charge, energy, momentum and Berry's curvature (built-in vorticity)
Semiclassical eqs of motion:
Hall currents at B=0
Gorbachev, Song, et. al. , Science (2014)
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History and context
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History and context
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History and context
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Schematic derivation of anomalous velocity
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Analogy w/ Magnus effect
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Berry phase, Berry curvature and gap opening in graphene
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Berry phase in hexagonal lattice
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Massive/gapped Dirac particles
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Massive/gapped Dirac particles
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Massive/gapped Dirac particles
Magnetic AHE
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Massive/gapped Dirac particlesA/B sublattice asymmetry a gap-opening perturbation
Valley or spin AHE
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Massive/gapped Dirac particlesA/B sublattice asymmetry a gap-opening perturbationBerry curvature hot spots above and below the gap
D. Xiao, W. Yao, and Q. Niu, PRL 99, 236809 (2007)
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Create topological bands in graphene?
(and play curveball)
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Manchester
Justin Song
MIT
Song, Shytov, LL PRL 111, 266801 (2013)Song, Samutpraphoot, LL arXiv:1404.4019 (2014)Gorbachev, Song et al arXiv:1409.0113 (2014)Lensky, Song, Samuthrapoot, LL, arXiv:1412.1808 (2014)
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Stacked Van der Waals heterostructures
Stacked atomically thin layers: van der Waals crystals, atomic precision, axes alignment Image from: Geim & Grigorieva,
Nature 499, 419 (2013)
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Gap opening for G/hBN
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Gap opening for G/hBN
Activated behavior: gap ~200-400 K
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Gap opening for G/hBN
Activated behavior: gap ~200-400 KValley currents: Gorbachev, Song, et. al. , Science (2014)
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Valley index
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Dual gated bilayer graphene: field-tunable gap and Berry curvature
Broken A/B sublattice symmetry
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Dual gated bilayer graphene: field-tunable gap and Berry curvature
Broken A/B sublattice symmetryBerry curvature hot spots above and below the gap
Valley currents: Shimazaki et al. arxiv:1501.04776 (2015)
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Optical control of valleys
PL (MoS2) after shining σ-
Optical selection rules: addressing valleys individually
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Optical control of valleys
PL (MoS2) after shining σ-
Electrically switchable chiral light-emitting transistor
Zhang et. al. , Science (2014)
Optical selection rules: addressing valleys individually
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Optical control of valleys
PL (MoS2) after shining σ-
Electrically switchable chiral light-emitting transistor
Zhang et. al. , Science (2014)
Optical selection rules: addressing valleys individually
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Valley transport in the gap?
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Valley transport in the gap?
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Currents for an edgeless setting
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Currents peak in the gap
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Currents peak in the gap
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Valley Hall conductivity
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Microscopic particle trajectories
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Fully gapped system under bias
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Valley transport in a fully gapped system
Systems: graphene/hBN and bilayer graphene:Gorbachev, Song, et. al. , Science (2014)Shimazaki et al. Arxiv:1501.04776 (2015)
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Use Berry curvature to electrically manipulate valleys
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Use Berry curvature to electrically manipulate valleys
Valley Hall effect:Transverse charge-neutral currents
J⃗ v= J⃗K− J⃗K '
J⃗ v=σ xyv z⃗×E⃗
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Valley currents
Valleys in Bulk SiValleys in Graphene Valleys in MoS2
Berry curvature No Berry curvature
σ xyv=0σ xy
v≠0
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1
2
3
4Pump valley imbalance
Valley Current (Neutral)
Detecting valley currents
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Detecting valley currents
1
2
3
4Pump valley imbalance
Valley Current (Neutral)
Reverse Valley Hall Effect (RVHE):
Valley Hall Effect (VHE):
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Detecting valley currents
1
2
3
4Pump valley imbalance
Image credit: wikipedia.com
Valley Current (Neutral)
Reverse Valley Hall Effect (RVHE):
Valley Hall Effect (VHE):
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Nonlocal response in aligned G/hBN
Van der Pauw bound:
Berry hot spots
(VH
E)
(RV
HE
)Valley Current Collaboration:U Manchester
Gorbachev, Song, et. al. , Science (2014)
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Nonlocal response in aligned G/hBN
Van der Pauw bound:
Berry hot spots
(VH
E)
(RV
HE
)Valley Current Collaboration:U Manchester
Gorbachev, Song, et. al. , Science (2014)
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Nonlocal response in aligned G/hBN
Van der Pauw bound:
Berry hot spots Distance dependence
(VH
E)
(RV
HE
)Valley Current Collaboration:U Manchester
Gorbachev, Song, et. al. , Science (2014) Valley currents in BLG: Shimazaki et al. arxiv:1501.04776
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Checklist1) Non-ohmic: stray charge currents too small, super-sharp density dependence; mediated by long-range neutral currents2) Observed at B=0, excludes energy and spin (prev work)3) Good quantitative agreement w/ topo valley currents for Berry curvature induced by gap opening4) Seen in aligned G/hBN devices, never in nonaligned devices5) Scales as cube of xx as expected for valley currents
ρxx3
ρxx
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Checklist1) Non-ohmic: stray charge currents too small, super-sharp density dependence; mediated by long-range neutral currents2) Observed at B=0, excludes energy and spin (prev work)3) Good quantitative agreement w/ topo valley currents for Berry curvature induced by gap opening4) Seen in aligned G/hBN devices, never in nonaligned devices5) Scales as cube of xx as expected for valley currents
ρxx3
ρxx
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Checklist1) Non-ohmic: stray charge currents too small, super-sharp density dependence; mediated by long-range neutral currents2) Observed at B=0, excludes energy and spin (prev work)3) Good quantitative agreement w/ topo valley currents for Berry curvature induced by gap opening4) Seen in aligned G/hBN devices, never in nonaligned devices5) Scales as cube of xx as expected for valley currents
ρxx3
ρxx
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Valley transistor: proof of concept1) Full separation of valley and charge current2) ~140 mV/decade3) Gate-tunable valley currentModulation > 100 fold
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Valley transistor: proof of concept1) Full separation of valley and charge current2) ~140 mV/decade3) Gate-tunable valley currentModulation > 100 fold
Spin Transistor?
Koo, et. al., Science (2009), see also Wunderlich, et. al. , Science (2010)
Original Proposal: Datta, Das, APL (1990)Gorbachev, Song, et. al. , Science (2014)
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Future
● Chargeless long-range currents: Dissipationless transport?
● Berry curvature spectroscopy (signs, Chern numbers)
● Waveguides for valley currents● Valley currents in 1D channels (graphene
edge, BLG domain walls, p-n junctions)
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Edge currents from Josephson interferometry (Yacoby group 2015)
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Edge currents from Josephson interferometry (Yacoby group 2015)
Away from DP Near DP
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Edge currents from Josephson interferometry (Yacoby group 2015)
Evidence for guided-wave states at the edge