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ELECTRONIC PROPERTIES OF TWISTED BILAYER GRAPHENE Johannes Lischner - - PowerPoint PPT Presentation
ELECTRONIC PROPERTIES OF TWISTED BILAYER GRAPHENE Johannes Lischner - - PowerPoint PPT Presentation
ELECTRONIC PROPERTIES OF TWISTED BILAYER GRAPHENE Johannes Lischner Imperial College London TWISTED BILAYER GRAPHENE a moire material AB AA 4 nm TWISTED BILAYER GRAPHENE theory predicts (2011): flat bands at magic angle 4 nm Bistrizer,
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TWISTED BILAYER GRAPHENE
4 nm theory predicts (2011): flat bands at magic angle
Bistrizer, MacDonald, PNAS 108, 412233(2011)
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TWISTED BILAYER GRAPHENE
4 nm experiment catches up (2018) 4 nm
Cao et al., Nature 556, 80 (2018)
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TWISTED BILAYER GRAPHENE
phase diagram similar to cuprates
Cao et al., Nature 556, 43 (2018)
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UNDERSTANDING MOIRE MATERIALS
4 nm
?
What is the role of electron-electron interactions?
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UNDERSTANDING THE NORMAL STATE
4 nm atomistic tight-binding based Hartree theory
H =
- ij
t(ri − rj)c†
icj +
- i
VH(ri)c†
ici
W(r) = e2 4πǫ0ǫbg|r|
Goodwin et al., arXiv:2004.14784
VH(r) =
- dr′W(r − r′)[n(r′) − n0(r′)]
Rademaker et al., Phys. Rev. B 100, 205114 (2019)
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UNDERSTANDING THE NORMAL STATE
4 nm band structure of electron doped tBLG
Goodwin et al., arXiv:2004.14784
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UNDERSTANDING THE NORMAL STATE
4 nm band structure of hole doped tBLG
Goodwin et al., arXiv:2004.14784
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UNDERSTANDING THE NORMAL STATE
4 nm charge density of doped tBLG
−3 −2 −1 1 2 3 δn × 10−3
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UNDERSTANDING THE NORMAL STATE
4 nm electron doped band structure as function of twist angle
Goodwin et al., arXiv:2004.14784
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UNDERSTANDING THE NORMAL STATE
4 nm How to define the magic angle?
Goodwin et al., arXiv:2004.14784
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UNDERSTANDING THE NORMAL STATE
4 nm band structure of hole doped tBLG as function of twisted angle
Goodwin et al., arXiv:2004.14784
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UNDERSTANDING THE NORMAL STATE
4 nm comparison to experiment: nano-ARPES
Lisi et al., arXiv:2002.02289
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UNDERSTANDING THE NORMAL STATE
4 nm comparison to experiment: STM
Kerelsky et al., Nature 572, 95 (2019)
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UNDERSTANDING THE NORMAL STATE
4 nm comparison to experiment: STM
Kerelsky et al., Nature 572, 95 (2019)
°10 10 20 E / meV Γ K K0 M LDOS
AA AB
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UNDERSTANDING THE NORMAL STATE
4 nm STM: evolution as spectrum as function of doping
Kerelsky et al., Nature 572, 95 (2019)
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UNDERSTANDING THE NORMAL STATE
4 nm STM: evolution as spectrum as function of doping
Xie et al., Nature 572, 101 (2019)
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UNDERSTANDING THE NORMAL STATE
4 nm STM: evolution as spectrum as function of doping
Choi et al., Nat. Phys. 15, 174 (2019)
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UNDERSTANDING THE NORMAL STATE
4 nm STM: evolution as spectrum as function of twist angle
Kerelsky et al., Nature 572, 95 (2019)
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UNDERSTANDING THE NORMAL STATE
4 nm Local density of states from atomistic Hartree theory
Goodwin et al., arXiv:2004.14784
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UNDERSTANDING MOIRE MATERIALS
4 nm
?
What is the role of electron-electron interactions?
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UNDERSTANDING MOIRE MATERIALS
4 nm Broken symmetry states and Hubbard Hamiltonian
H = t
- ijσ
c†
iσcjσ + U
- i
ni↑ni↓
What is U/t in twisted bilayer graphene?
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WANNIER FUNCTIONS
AA AB AB AB AB AB AB
AA AB AB AB AB AB AB Goodwin et al., Phys. Rev. B 100, 121106 (2019)
t = wnR′|HDF T |wnR
U = wnRwnR|W|wnRwnR
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PARAMETERS OF HUBBARD HAMILTONIAN
Goodwin et al., Phys. Rev. B 100, 121106 (2019) 1.0 1.2 1.4 1.6 1.8 2.0 2.2 θ / degree 40 60 80 100 120 U / meV
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1.0 1.2 1.4 1.6 1.8 2.0 2.2 θ / degree 5 10 15 20 25 U/t
THE STRENGTH OF ELECTRON CORRELATIONS
Goodwin et al., Phys. Rev. B 100, 121106 (2019)
critical U/t U/t as function of twist angle
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100 200 300 400 r / ˚ A 10 20 30 40 50 V / meV
1.7o 1.29o 1.05o
LONG RANGED INTERACTIONS
Goodwin et al., Phys. Rev. B 100, 121106 (2019)
Extended Hubbard interactions
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LONG RANGED INTERACTIONS
Mapping onto short-ranged Hubbard model
U ∗ = V00 − V01
Schueler et al., Phys. Rev. Lett. 111, 036601 (2013)
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LONG RANGED INTERACTIONS
Goodwin et al., Phys. Rev. B 100, 121106 (2019)
U/t as function of twist angle
1.0 1.2 1.4 1.6 1.8 2.0 2.2 θ / degree 5 10 15 20 25 U/t
Dielectric Substrate U∗
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SCREENING
External
100 200 300 400 r / ˚ A 5 10 15 20 25 V / meV
Goodwin et al., Phys. Rev. B 100, 121106 (2019)
1.7o 1.29o 1.05o
ξ = 10 nm
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SCREENING
Dependence on thickness of hBN layer
Goodwin et al., Phys. Rev. B 101, 165110 (2020)
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SCREENING
Magnetic phases and critical U/t
Klebl, Honerkamp, Phys. Rev. B 100, 155145 (2019)
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SCREENING
Phase diagrams as function of twist angle and hBN thickness
Goodwin et al., Phys. Rev. B 101, 165110 (2020)
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SCREENING
Experiment
Stepanov et al., arXiv:1911.09198
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SUPERCONDUCTIVITY
4 nm
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SCREENING
Internal
0.00 0.05 0.10 0.15 |q| °˚ A
−1¢
10 20 30 40 50 Πo ° keV−1˚ A
−2¢
θ (degree)
2.13 1.70 1.54 1.41 1.25 1.05
Goodwin et al., Phys. Rev. B 100, 235424 (2019)
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INTERNAL SCREENING
Attractive interactions
Goodwin et al., Phys. Rev. B 100, 235424 (2019)
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POLARIZATION GLUE?
Kohn, Luttinger, Phys. Rev. Lett. 15, 524 (1965)
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ELECTRONIC PROPERTIES OF TWISTED BILAYER GRAPHENE
Summary:
- importance of long-ranged interactions revealed in normal state
- new opportunities to probe electron correlations in two dimensions
- twisted bilayer graphene might be very different from the cuprates after all
- internal screening might provide superconducting glue
Zachary Goodwin Valerio Vitale Arash Mostofi Dmitri Efetov
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