Internal screening and dielectric engineering in magic-angle twisted bilayer graphene

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Internal screening and dielectric engineering in magic-angle twisted bilayer graphene

J. M. Pizarro, M. Rösner, R. Thomale, R. Valentí, and T. O. Wehling

Phys. Rev. B 100, 161102(R) – Published 3 October 2019

Abstract

Magic-angle twisted bilayer graphene (MA-tBLG) has appeared as a tunable testing ground to investigate the conspiracy of electronic interactions, band structure, and lattice degrees of freedom to yield exotic quantum many-body ground states in a two-dimensional (2D) Dirac material framework. While the impact of external parameters such as doping or magnetic field can be conveniently modified and analyzed, the all-surface nature of the quasi-2D electron gas combined with its intricate internal properties pose a challenging task to characterize the quintessential nature of the different insulating and superconducting states found in experiments. We analyze the interplay of internal screening and dielectric environment on the intrinsic electronic interaction profile of MA-tBLG. We find that interlayer coupling generically enhances the internal screening. The influence of the dielectric environment on the effective interaction strength depends decisively on the electronic state of MA-tBLG. Thus, we propose the experimental tailoring of the dielectric environment, e.g., by varying the capping layer composition and thickness, as a promising pursuit to provide further evidence for resolving the hidden nature of the quantum many-body states in MA-tBLG.

Received 9 May 2019

DOI:https://doi.org/10.1103/PhysRevB.100.161102

Physics Subject Headings (PhySH)

Density of states Dielectric properties Electric polarization

2-dimensional systems Bilayer films Graphene Strongly correlated systems Superconductors Topological materials Two-dimensional electron gas

Band structure methods Many-body techniques Plane-wave expansion

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. M. Pizarro ^1,2,*, M. Rösner³, R. Thomale⁴, R. Valentí⁵, and T. O. Wehling^1,2,†

¹Institute for Theoretical Physics, University of Bremen, Otto-Hahn-Allee 1, D-28359 Bremen, Germany
²Bremen Center for Computational Material Sciences, University of Bremen, Am Fallturm 1a, D-28359 Bremen, Germany
³Institute for Molecules and Materials, Radbound University, NL-6525 AJ Nijmegen, The Netherlands
⁴Institute for Theoretical Physics and Astrophysics, University of Würzburg, Am Hubland, D-97074 Würzburg, Germany
⁵Institute of Theoretical Physics, Goethe University Frankfurt am Main, D-60438 Frankfurt am Main, Germany

^*jpizarro@uni-bremen.de
^†twehling@uni-bremen.de

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Issue

Vol. 100, Iss. 16 — 15 October 2019

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Images

Figure 1
Setups for dielectric engineering of MA-tBLG: (a) MA-tBLG encapsulated in hBN, where the dielectric function $ɛ_{1} \approx 4$ encodes both the contribution from hBN (gray) and from the $σ$ -band higher-energy background of MA-tBLG (red). $ɛ_{2}$ describes the dielectric surrounding (blue) at a distance $d$ from the center of MA-tBLG. MA-tBLG with a metallic gate at a distance $d$ is realized for $ɛ_{2} \to \infty$ . (b) Dielectric $ɛ_{2}$ in direct contact with MA-tBLG as described by $d = 3.35 Å$ , which is the interlayer distance of BLG and hBN [34]. (c) In the moiré pattern of MA-tBLG, $A A$ and $A B / B A$ regions can be recognized according to the stacking of the atoms in each graphene layer. The moiré lattice constant $λ$ corresponds to the distance between adjacent $A A$ regions, and is $134 Å$ for the first magic angle. (d) The reciprocal space is broken up into the hexagonal mini Brillouin zones (BZs) associated with the moiré real-space superlattice. The reciprocal lattice is spanned by the reciprocal lattice vectors $G_{1}^{M}$ and $G_{2}^{M}$ [8]. Neighboring mini-BZs are included in the low-energy continuum description of MA-tBLG up to a certain cutoff $G_{c}$ .
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Figure 2
Static polarization function of MA-tBLG in comparison to uncoupled tBLG $(Π_{0}^{Dirac}$ , orange line) from Eq. (3), the model of quasilocalized states plus Dirac background $(Π_{0}^{D + H}$ , green dashed line) from Eq. (4), and the DOS of commensurate $A A$ (brown dashed-dotted line) and $A B$ BLG (pink dashed-dotted line). For MA-tBLG, polarizabilities from RPA (red line) assuming a metallic state and cRPA (blue line), i.e., excluding polarization processes within the flat bands similarly to a Mott insulator, are shown. $G_{M} = 0.057 Å^{- 1}$ marks the length of the reciprocal lattice vectors.
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Figure 3
Dielectric engineering of MA-tBLG with an external dielectric $ɛ_{2}$ at a distance $d$ . (a) Effective local interaction $U$ as a function of the dielectric constant $ɛ_{2}$ of the environment in direct contact with MA-tBLG. The RPA (red line) mimicking metallic screening and cRPA (blue line) numerical results assuming suppressed low-energy screening for MA-tBLG are compared with the analytical estimates from the $A B$ BLG model (pink dashed-dotted line) and the quasiatomic model with a Dirac background $(D + H$ , green dashed line) from Eq. (4). (b) Influence of a metallic gate $(ɛ_{2} \to \infty)$ at a distance $d$ from MA-tBLG on $U$ . (c) Effective cRPA screened local interaction $U$ (color coded) as a function of the dielectric surrounding $ɛ_{2}$ and its distance $d$ from MA-tBLG.
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