PHYSICAL REVIEW MATERIALS
8
, L051001 (2024)
Letter
First-principles electron-phonon interactions and electronic
transport in large-angle twisted bilayer graphene
Shiyuan Gao
,
1
,
2
Jin-Jian Zhou
,
3
Yao Luo
,
1
and Marco Bernardi
1
,
*
1
Department of Applied Physics and Materials Science, and Department of Physics,
California Institute of Technology
, Pasadena, California 91125, USA
2
Department of Physics and Astronomy, Institute for Quantum Matter,
Johns Hopkins University
, Baltimore, Maryland 21218, USA
3
School of Physics,
Beijing Institute of Technology
, Beijing 100081, China
(Received 3 March 2024; revised 22 April 2024; accepted 7 May 2024; published 22 May 2024)
Twisted bilayer graphene (tBLG) has emerged as an exciting platform for novel condensed matter physics.
However, electron-phonon (
e
-ph) interactions in tBLG and their effects on electronic transport are not completely
understood. Here we show first-principles calculations of
e
-ph interactions and resistivity in commensurate
tBLG with large twist angles of 13.2 and 21.8 degrees. These calculations overcome key technical barriers,
including large unit cells of up to 76 atoms, Brillouin-zone folding of the
e
-ph interactions, and unstable lattice
vibrations due to the AA-stacked domains. We show that
e
-ph interactions due to layer-breathing phonons
enhance intervalley scattering in large-angle tBLG. This interaction effectively couples the two layers, which
are otherwise electronically decoupled at such large twist angles. As a result, the phonon-limited resistivity in
tBLG deviates from the temperature-linear trend characteristic of monolayer graphene and tBLG near the magic
angle. Taken together, our work quantifies
e
-ph interactions and scattering mechanisms in tBLG, revealing subtle
interlayer coupling effects at large twist angles.
DOI:
10.1103/PhysRevMaterials.8.L051001
Electronic transport in graphene is a rich subject [
1
].
Theory showed that the carrier mobility in graphene is lim-
ited by acoustic phonons [
2
], and then focused on bilayer
graphene [
3
] and the role of flexural phonons [
4
–
6
]. First-
principles calculations based on density functional theory
(DFT) have also been employed to study phonon-limited
transport in graphene, initially using the deformation potential
approximation [
7
–
10
] and later with first-principles electron-
phonon (
e
-ph) interactions [
11
,
12
], which take into account all
phonon modes and electronic states on equal footing, enabling
quantitative predictions.
Twisted bilayer graphene (tBLG) is now attracting intense
interest due to the emergence of correlated insulating and
superconducting states near the magic angle [
13
,
14
]. While
the origin of these phases is still debated,
e
-ph interactions
are thought to play an important role in the rich physics of
tBLG [
15
–
19
]. For example, electronic transport is intimately
linked to the
e
-ph interactions in tBLG, and experiments
have observed a large linear-in-temperature resistivity near the
magic angle [
20
], whose origin remains unclear.
Theoretical work has focused on analytic and tight-binding
models of
e
-ph interactions and phonon-limited resistivity
in tBLG [
15
,
21
–
24
]. The effects of lattice relaxation on the
electronic structure of tBLG have also been studied using both
tight-binding and continuum models [
25
–
27
]. However, ex-
plicit first-principles calculations of
e
-ph interactions in tBLG
have remained prohibitive due to the large unit cell sizes,
particularly at small twist angles.
*
bmarco@caltech.edu
Here, we show first-principles calculations of
e
-ph inter-
actions and transport properties in large-angle tBLG. Our
approach allows us to quantify the contributions to electron
scattering and transport from different acoustic and opti-
cal modes and from intravalley and intervalley processes.
Similar to monolayer graphene, we find that the resistiv-
ity in large-angle tBLG is controlled by acoustic phonon
scattering at low temperature and optical phonon scattering
near and above room temperature. Yet, the phonon-limited
resistivity in tBLG is found to deviate significantly from
two decoupled layers, with a faster-than-linear temperature
dependence due to intervalley scattering mediated by layer-
breathing phonons. These results reveal subtle interactions
emerging from the twist-angle degree of freedom, high-
lighting the promise of first-principles calculations to study
tBLG.
The commensurate moiré superlattice of tBLG is gener-
ated by rotating the superlattice vector of one graphene layer,
a
(1)
S
=
m
a
1
+
n
a
2
,into
a
(2)
S
=
n
a
1
+
m
a
2
, where
a
1
and
a
2
are graphene lattice vectors and (
m
,
n
) is a pair of coprime
integers [
28
,
29
]. We focus on the two smallest tBLG unit
cells, a 28-atom unit cell with (
m
,
n
)
=
(2
,
1) and a 76-atom
unit cell with (
m
,
n
)
=
(3
,
2), which correspond to twist an-
gles of 21
.
8
◦
and 13
.
2
◦
respectively. We compute the ground
state electronic structure of these tBLG systems using DFT
in a plane-wave basis with the
QUANTUM ESPRESSO
pack-
age [
30
,
31
]. We employ the local density approximation with
a plane-wave kinetic energy cutoff of 90 Ry, using the exper-
imental lattice constant of 2.46 Å for graphene. The resulting
electronic band structures of 21
.
8
◦
and 13
.
2
◦
tBLG are given
in the Supplemental Material (SM) [
32
].
2475-9953/2024/8(5)/L051001(7)
L051001-1
©2024 American Physical Society