Effects of lithium intercalation in twisted bilayer graphene

Daniel T. Larson, Stephen Carr, Georgios A. Tritsaris, and Efthimios Kaxiras

Phys. Rev. B 101, 075407 – Published 5 February 2020

Abstract

We investigate the effects of lithium intercalation in twisted bilayers of graphene, using first-principles electronic structure calculations. To model this system we employ commensurate supercells that correspond to twist angles of $7 . 34^{\circ}$ and $2 . 45^{\circ}$ . From the energetics of lithium absorption we demonstrate that for low Li concentration the intercalants cluster in the AA regions with double the density of a uniform distribution. The charge donated by the Li atoms to the graphene layers results in modifications to the band structure that can be qualitatively captured using a continuum model with modified interlayer couplings in a region of parameter space that has yet to be explored either experimentally or theoretically. Thus, the combination of intercalation and twisted layers simultaneously provides the means for spatial control over material properties and an additional knob with which to tune moiré physics in twisted bilayers of graphene, with potential applications ranging from energy storage and conversion to quantum information.

Received 15 November 2019
Accepted 23 January 2020

DOI:https://doi.org/10.1103/PhysRevB.101.075407

Physics Subject Headings (PhySH)

First-principles calculations

2-dimensional systems Electronic structure Graphene

Density functional theory k dot p method

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Daniel T. Larson ¹, Stephen Carr ¹, Georgios A. Tritsaris², and Efthimios Kaxiras ^1,2

¹Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
²John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

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Issue

Vol. 101, Iss. 7 — 15 February 2020

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Images

Figure 1
(a) Intercalation energy $E_{I}$ for single Li intercalants in the $2 . 45^{\circ}$ cell (solid circles) and $7 . 34^{\circ}$ cell (open green circles). Blue points represent intercalants along the line connecting AA and AB regions, shown with a blue arrow in (b); orange points are along the domain wall connecting AA regions, shown with an orange arrow in (b). The green points have been shifted by $- 100$ meV for ease of comparison. (b) Configurations of six Li atoms arranged in a circle around a seventh Li atom (black) located at the center of an AA region in the relaxed $2 . 45^{\circ}$ graphene cell. The Li-Li distances $d_{7}$ are 4.3 (blue), 9.8 (green), 12.3 (cyan), 14.7 (yellow), and 19.7 (purple) Å. For $d_{7} = 19.7 Å$ the Li atoms from neighboring AA regions are almost as close as the neighbors centered around the same AA region, as indicated by the dashed purple circle. The red circle represents a configuration with $d_{7} = 9.8 Å$ , centered at an AB region. (c) Average intercalation energy per atom $E_{I}$ for pairs of Li intercalants as a function of the distance between the Li atoms $d_{2}$ . The orange circles represent configurations where one Li atom is very close to the center of the AA region but the other atom is much farther away, whereas the blue points represent configurations where the two Li atoms are more evenly spaced about the center of the AA region. The lines are simple fits as guides to the eye. (d) $E_{I}$ vs $d_{7}$ for the configurations of seven Li atoms shown in (b). The colors of the data points match the colors of the atoms and circles in (b). The line is a simple polynomial fit.
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Figure 2
Average separation $h$ (Å) between graphene layers in a 5-Å circle centered at points a distance $r$ (Å) along a line between AA and AB regions. Colored curves show the separation in a cell with a Li intercalant located a fixed distance from the AA region, marked with a matching colored arrow above. The gray curve shows the separation when seven Li atoms are concentrated within 5 Å of the AA region. The dashed black curve shows the layer separation at the same locations in the empty bilayer.
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Figure 3
(a)–(c) DFT band structures of the $2 . 45^{\circ}$ twisted bilayer graphene cell with zero, one, and seven Li intercalants in the AA region. The locations of the Li atoms have been chosen to minimize the total energy, with Li-Li distances of approximately 15 Å. (d) Continuum model with 30% increase (decrease) in the AA (AB) interlayer coupling. In each case the Fermi level is indicated by a dashed line of the same color.
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Figure 4
Top and side views of the charge density difference for the $7 . 34^{\circ}$ cell with three Li atoms located near the AA region. Yellow clouds represent excess electrons.
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