Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene
Source abstract
Abstract
Abstract We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance of samples with fixed width decreases with the system size in the longitudinal direction for incommensurate angles within the sub-ballistic regime. Our results show that incommensurability/quasiperiodicity effects are of crucial importance in the narrow-band regime. The incommensurate nature of a general twist angle must therefore be taken into account for an accurate description of magic-angle twisted bilayer graphene.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Graphene research and applications · Quantum and electron transport phenomena · Surface and Thin Film Phenomena
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (80)
Show source-provided references
1. Graphene bilayer with a twist: electronic structure10.1103/PhysRevLett.99.256802 ↗
2. Moiré bands in twisted double-layer graphene10.1073/pnas.1108174108 ↗
3. Continuum model of the twisted graphene bilayer10.1103/PhysRevB.86.155449 ↗
4. Localization of Dirac electrons in rotated graphene bilayers10.1021/nl902948m ↗
5. Flat bands in slightly twisted bilayer graphene: tight-binding calculations10.1103/PhysRevB.82.121407 ↗
6. Electronic structure of turbostratic graphene10.1103/PhysRevB.81.165105 ↗
7. Unconventional superconductivity in magic-angle graphene superlattices10.1038/nature26160 ↗
8. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices10.1038/nature26154 ↗
9. Superconductivity and strong correlations in moiré flat bands10.1038/s41567-020-0906-9 ↗
10. Possible high Tc superconductivity in the Ba-La-Cu-O system10.1007/BF01303701 ↗
11. Symmetry, maximally localized Wannier states and a low-energy model for twisted bilayer graphene narrow bands10.1103/PhysRevX.8.031088 ↗
12. Band structure of twisted bilayer graphene: emergent symmetries, commensurate approximants and Wannier obstructions10.1103/PhysRevB.98.085435 ↗
13. Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene10.1103/PhysRevX.8.031089 ↗
14. Origin of magic angles in twisted bilayer graphene10.1103/PhysRevLett.122.106405 ↗
15. Moiré flat bands in twisted double bilayer graphene10.1021/acs.nanolett.9b05117 ↗
16. All magic angles in twisted bilayer graphene are topological10.1103/PhysRevLett.123.036401 ↗
17. Pressure dependence of the magic twist angle in graphene superlattices10.1103/PhysRevB.98.085144 ↗
18. Correlated states of a triangular net of coupled quantum wires: implications for the phase diagram of marginally twisted bilayer graphene10.1103/PhysRevB.101.165431 ↗
19. Electronic band structure and pinning of fermi energy to van hove singularities in twisted bilayer graphene: a self-consistent approach10.1103/PhysRevB.100.205113 ↗
20. Fragile topology and Wannier obstructions10.1103/PhysRevLett.121.126402 ↗
21. Maximally localized Wannier orbitals and the extended Hubbard model for twisted bilayer graphene10.1103/PhysRevX.8.031087 ↗
22. Faithful tight-binding models and fragile topology of magic-angle bilayer graphene10.1103/PhysRevB.99.195455 ↗
23. Strong correlations and d + id superconductivity in twisted bilayer graphene10.1103/PhysRevB.98.241407 ↗
24. Mean-field theory for superconductivity in twisted bilayer graphene10.1103/PhysRevB.98.220504 ↗
25. Unconventional superconductivity and density waves in twisted bilayer graphene10.1103/PhysRevX.8.041041 ↗
26. Interactions in the 8-orbital model for twisted bilayer graphene10.1103/PhysRevB.102.155149 ↗
27. Band structure and insulating states driven by coulomb interaction in twisted bilayer graphene10.1103/PhysRevB.102.045107 ↗
28. Transport measurements in twisted bilayer graphene: electron-phonon coupling and Landau level crossing10.1103/PhysRevB.98.035425 ↗
29. Tuning superconductivity in twisted bilayer graphene10.1126/science.aav1910 ↗
30. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene10.1038/s41586-019-1695-0 ↗
31. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene10.1038/s41586-019-1460-4 ↗
32. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene10.1126/science.aaw3780 ↗
33. Maximized electron interactions at the magic angle in twisted bilayer graphene10.1038/s41586-019-1431-9 ↗
34. Electronic correlations in twisted bilayer graphene near the magic angle10.1038/s41567-019-0606-5 ↗
35. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene10.1038/s41586-019-1422-x ↗
36. Electronic compressibility of magic-angle graphene superlattices10.1103/PhysRevLett.123.046601 ↗
37. Intrinsic quantized anomalous Hall effect in a moiré heterostructure10.1126/science.aay5533 ↗
38. The Mott-semiconducting state in the magic angle bilayer graphene
39. Model for the metal-insulator transition in graphene superlattices and beyond10.1103/PhysRevB.98.045103 ↗
40. Microscopic electronic inhomogeneity in the high- Tc superconductor Bi2Sr2CaCu2O 8+x10.1038/35095012 ↗
41. Disorder raises the critical temperature of a cuprate superconductor10.1073/pnas.1817134116 ↗
42. Quasicrystalline electronic states in 30∘ rotated twisted bilayer graphene10.1103/PhysRevB.99.165430 ↗
43. Emergent localization in dodecagonal bilayer quasicrystals10.1103/PhysRevB.99.245401 ↗
44. Quasicrystalline 30∘ twisted bilayer graphene as an incommensurate superlattice with strong interlayer coupling10.1073/pnas.1720865115 ↗
45. Dirac electrons in a dodecagonal graphene quasicrystal10.1126/science.aar8412 ↗
46. Magic-angle semimetals10.1038/s41535-020-00271-9 ↗
47. Ballistic charge transport in twisted bilayer graphene
48. Moiré localization in two-dimensional quasiperiodic systems10.1103/PhysRevB.100.144202 ↗
49. Mixed spectra and partially extended states in a two-dimensional quasiperiodic model10.1103/PhysRevB.101.014205 ↗
50. Localization transitions and mobility edges in coupled Aubry–André chains10.1103/PhysRevB.99.054211 ↗
51. We also tested models with intralayer hoppings up to third nearest neighbors and observed that the results remained qualitatively unaffected up to the expected shift in the energy of the Dirac points and a slight change in the narrow band angle θ ft
52. Localization of Dirac electrons in rotated graphene bilayers10.1021/nl902948m ↗
53. Numerical studies of confined states in rotated bilayers of graphene10.1103/PhysRevB.86.125413 ↗
54. DC conductivity of twisted bilayer graphene: angle-dependent transport properties and effects of disorder10.1103/PhysRevMaterials.2.034004 ↗
55. See supplemental material, which includes [63 79 80], for: details on finite-size scaling method used for exact diagonalization results and additional information on these results; Results on band inversion; technical details on the computation of momentum-space inverse participation ratio; technical details and additional results on conductance
56. This method was originally proposed in [77]. See also [78] for an example of a recent application
57. It is important to advert that the study of momentum-space localization in finite systems requires closed boundary conditions, which motivates the construction of approximant structures previously described. For open boundaries, one-dimensional edge defects are sufficient to induce momentum-space delocalization even for commensurate structures
58. SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems10.1145/1089014.1089019 ↗
59. Balay · 2019
60. From ballistic motion to localization: a phase space analysis10.1140/epjb/e20020125 ↗
61. In fact, L is the linear size of the rhombus used to compute Ik , which is proportional to N1/2 : this size is what sets the resolution for the computation of Ik , see SM [55] for details
62. Distribution of the ratio of consecutive level spacings in random matrix ensembles10.1103/PhysRevLett.110.084101 ↗
63. Kwant: a software package for quantum transport10.1088/1367-2630/16/6/063065 ↗
64. Large linear-in-temperature resistivity in twisted bilayer graphene10.1038/s41567-019-0596-3 ↗
65. Strange metal in magic-angle graphene with near Planckian dissipation10.1103/PhysRevLett.124.076801 ↗
66. Emergent Geometric Frustration and Flat Band in Moiré Bilayer Graphene10.1103/PhysRevLett.123.186402 ↗
67. Observation of superconductivity with Tc onset at 12 K in electrically tunable twisted double bilayer graphene
68. Tunable spin-polarized correlated states in twisted double bilayer graphene10.1038/s41586-020-2458-7 ↗
69. Electric field tunable correlated states and magnetic phase transitions in twisted bilayer-bilayer graphene
70. Topological insulators in twisted transition metal dichalcogenide homobilayers10.1103/PhysRevLett.122.086402 ↗
71. Magic continuum in twisted bilayer WSe2
72. Tunable lattice reconstruction, triangular network of chiral one-dimensional states and bandwidth of flat bands in magic angle twisted bilayer graphene10.1103/PhysRevLett.125.236102 ↗
73. Continuum models for twisted bilayer graphene: effect of lattice deformation and hopping parameters10.1103/PhysRevB.99.205134 ↗
74. Lattice relaxation and energy band modulation in twisted bilayer graphene10.1103/PhysRevB.96.075311 ↗
75. Many-body localization in a quasiperiodic system10.1103/PhysRevB.87.134202 ↗
76. Observation of many-body localization of interacting fermions in a quasirandom optical lattice10.1126/science.aaa7432 ↗
77. Quantum particle in one-dimensional potentials with incommensurate periods10.1103/PhysRevLett.43.1954 ↗
78. Non-power-law universality in one-dimensional quasicrystals10.1103/PhysRevB.98.134201 ↗
79. Weyl semimetal to metal phase transitions driven by quasiperiodic potentials10.1103/PhysRevLett.120.207604 ↗
80. Scaling theory of localization: absence of quantum diffusion in two dimensions10.1103/PhysRevLett.42.673 ↗