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, MacDonald, PNAS 108, 412233(2011)

TWISTED BILAYER GRAPHENE experiment catches up (2018) 4 nm 4 nm Cao et al., Nature 556, 80 (2018)

TWISTED BILAYER GRAPHENE phase diagram similar to cuprates Cao et al., Nature 556, 43 (2018)

UNDERSTANDING MOIRE MATERIALS What is the role of electron-electron interactions? ? 4 nm

UNDERSTANDING THE NORMAL STATE atomistic tight-binding based Hartree theory t ( r i − r j ) c † V H ( r i ) c † � � H = i c j + i c i ij i � d r ′ W ( r − r ′ )[ n ( r ′ ) − n 0 ( r ′ )] V H ( r ) = e 2 W ( r ) = 4 πǫ 0 ǫ bg | r | 4 nm Rademaker et al., Phys. Rev. B 100, 205114 (2019) Goodwin et al., arXiv:2004.14784

UNDERSTANDING THE NORMAL STATE band structure of electron doped tBLG 4 nm Goodwin et al., arXiv:2004.14784

UNDERSTANDING THE NORMAL STATE band structure of hole doped tBLG 4 nm Goodwin et al., arXiv:2004.14784

UNDERSTANDING THE NORMAL STATE charge density of doped tBLG 3 2 1 δ n × 10 − 3 0 − 1 − 2 − 3 4 nm

UNDERSTANDING THE NORMAL STATE electron doped band structure as function of twist angle 4 nm Goodwin et al., arXiv:2004.14784

UNDERSTANDING THE NORMAL STATE How to define the magic angle? 4 nm Goodwin et al., arXiv:2004.14784

UNDERSTANDING THE NORMAL STATE band structure of hole doped tBLG as function of twisted angle 4 nm Goodwin et al., arXiv:2004.14784

UNDERSTANDING THE NORMAL STATE comparison to experiment: nano-ARPES 4 nm Lisi et al., arXiv:2002.02289

UNDERSTANDING THE NORMAL STATE comparison to experiment: STM 4 nm Kerelsky et al., Nature 572, 95 (2019)

UNDERSTANDING THE NORMAL STATE comparison to experiment: STM 20 10 E / meV 0 ° 10 AA AB LDOS K 0 K Γ M 4 nm Kerelsky et al., Nature 572, 95 (2019)

UNDERSTANDING THE NORMAL STATE STM: evolution as spectrum as function of doping 4 nm Kerelsky et al., Nature 572, 95 (2019)

UNDERSTANDING THE NORMAL STATE STM: evolution as spectrum as function of doping 4 nm Xie et al., Nature 572, 101 (2019)

UNDERSTANDING THE NORMAL STATE STM: evolution as spectrum as function of doping 4 nm Choi et al., Nat. Phys. 15, 174 (2019)

UNDERSTANDING THE NORMAL STATE STM: evolution as spectrum as function of twist angle 4 nm Kerelsky et al., Nature 572, 95 (2019)

UNDERSTANDING THE NORMAL STATE Local density of states from atomistic Hartree theory 4 nm Goodwin et al., arXiv:2004.14784

UNDERSTANDING MOIRE MATERIALS What is the role of electron-electron interactions? ? 4 nm

UNDERSTANDING MOIRE MATERIALS Broken symmetry states and Hubbard Hamiltonian � c † � H = t i σ c j σ + U n i ↑ n i ↓ � ij � σ i What is U/t in twisted bilayer graphene? 4 nm

WANNIER FUNCTIONS AB AB AB AB AA AB AB AB AB AB AA AB AB AB t = � w n R ′ | H DF T | w n R � U = � w n R w n R | W | w n R w n R � Goodwin et al., Phys. Rev. B 100, 121106 (2019)

PARAMETERS OF HUBBARD HAMILTONIAN 120 100 U / meV 80 60 40 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 θ / degree Goodwin et al., Phys. Rev. B 100, 121106 (2019)

THE STRENGTH OF ELECTRON CORRELATIONS U/t as function of twist angle 25 20 15 U/t 10 critical U/t 5 0 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 θ / degree Goodwin et al., Phys. Rev. B 100, 121106 (2019)

LONG RANGED INTERACTIONS Extended Hubbard interactions 50 40 V / meV 30 20 1.7 o 10 1.29 o 1.05 o 0 0 100 200 300 400 r / ˚ A Goodwin et al., Phys. Rev. B 100, 121106 (2019)

LONG RANGED INTERACTIONS Mapping onto short-ranged Hubbard model U ∗ = V 00 − V 01 Schueler et al., Phys. Rev. Lett. 111, 036601 (2013)

LONG RANGED INTERACTIONS U/t as function of twist angle 25 Dielectric Substrate U ∗ 20 15 U/t 10 5 0 1 . 0 1 . 2 1 . 4 1 . 6 1 . 8 2 . 0 2 . 2 θ / degree Goodwin et al., Phys. Rev. B 100, 121106 (2019)

SCREENING External 25 ξ = 10 nm 20 1.7 o 15 V / meV 1.29 o 1.05 o 10 5 0 0 100 200 300 400 r / ˚ A Goodwin et al., Phys. Rev. B 100, 121106 (2019)

SCREENING Dependence on thickness of hBN layer Goodwin et al., Phys. Rev. B 101, 165110 (2020)

SCREENING Magnetic phases and critical U/t Klebl, Honerkamp, Phys. Rev. B 100, 155145 (2019)

SCREENING Phase diagrams as function of twist angle and hBN thickness Goodwin et al., Phys. Rev. B 101, 165110 (2020)

SCREENING Experiment Stepanov et al., arXiv:1911.09198

SUPERCONDUCTIVITY 4 nm

SCREENING Internal 50 θ (degree) 2.13 1.41 40 − 2 ¢ 1.70 1.25 1.54 1.05 keV − 1 ˚ A 30 20 ° Π o 10 0 0 . 00 0 . 05 0 . 10 0 . 15 − 1 ¢ ° ˚ | q | A Goodwin et al., Phys. Rev. B 100, 235424 (2019)

INTERNAL SCREENING Attractive interactions Goodwin et al., Phys. Rev. B 100, 235424 (2019)

POLARIZATION GLUE? Kohn, Luttinger, Phys. Rev. Lett. 15, 524 (1965)

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