We argue that the unusually strong electron–electron interactions in the narrow bands in moiré superlattices originate from compact Wannier orbitals. Enhanced overlaps of electronic wavefunctions, enabled by such orbitals, result in a strong el–el superlattice umklapp scattering. We identify the umklapp scattering processes as a source of the strong temperature-dependent resistivity observed in these systems. In a simple model, the umklapp scattering predicts a
Magic-angle twisted bilayer graphene (MATBG) exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well-isolated electronic bands. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron–electron (phonon) interactions and nontrivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus on two independent quantities that are considerably modified by Coulomb interaction-driven band renormalization, namely the density of states and the minimal spatial extent associated with the Wannier functions. First, we show that a filling-dependent enhancement of the density of states, caused by band flattening, in combination with phonon-mediated attraction due to electron-phonon umklapp processes, increases the tendency towards superconducting pairing in a range of angles around magic-angle. Second, we demonstrate that the minimal spatial extent associated with the Wannier functions, which contributes towards increasing the superconducting phase stiffness, also develops a nontrivial enhancement due to the interaction-induced renormalization of the Bloch wavefunctions. While our modeling of superconductivity (SC) assumes a weak electron-phonon coupling and does not consider many of the likely relevant correlation effects, it explains simply the experimentally observed robustness of SC in the wide range of angles that occurs in the relevant range of fillings.
more » « less- Award ID(s):
- 1753306
- NSF-PAR ID:
- 10304836
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Quantum Materials
- Volume:
- 6
- Issue:
- 1
- ISSN:
- 2397-4648
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract T -dependent resistivity that grows asT 2with a numerical prefactor that grows as the Wannier orbital radius decreases. We quantify the enhancement in el–el scattering by the Kadowaki–Woods (KW) ratio, a quantity that is sensitive to umklapp scattering but, helpfully, insensitive to the effects due to the high density of electronic states. Our analysis predicts anomalously large KW ratio values that clearly indicate the importance of the umklapp el–el processes and their impact on theT -dependent resistivity. -
null (Ed.)Moiré superlattices in two-dimensional van der Waals heterostructures provide an efficient way to engineer electron band properties. The recent discovery of exotic quantum phases and their interplay in twisted bilayer graphene (tBLG) has made this moiré system one of the most renowned condensed matter platforms. So far studies of tBLG have been mostly focused on the lowest two flat moiré bands at the first magic angle θ m1 ∼ 1.1°, leaving high-order moiré bands and magic angles largely unexplored. Here we report an observation of multiple well-isolated flat moiré bands in tBLG close to the second magic angle θ m2 ∼ 0.5°, which cannot be explained without considering electron–election interactions. With high magnetic field magnetotransport measurements we further reveal an energetically unbound Hofstadter butterfly spectrum in which continuously extended quantized Landau level gaps cross all trivial band gaps. The connected Hofstadter butterfly strongly evidences the topologically nontrivial textures of the multiple moiré bands. Overall, our work provides a perspective for understanding the quantum phases in tBLG and the fractal Hofstadter spectra of multiple topological bands.more » « less
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