1
BNL-111779-2016-JA
Direct measurement of the tunable electronic
structure of bilayer MoS2 by interlayer twist
Po-Chun Yeh, Wencan Jin, Nader Zaki,
Jens
Kunstmann, Daniel Chenet, Ghidewon Arefe,
Jerzy T. Sadowski, Jerry I. Dadap, Peter Sutter,
James Hone, and Richard M. Osgood, Jr.
Submitted to Nano Letters
January 2016
Center For Functional Nanomaterials
Brookhaven National Laboratory
U.S. Department of Energy
USDOE Office of Science (SC),
Basic Energy Sciences (BES) (SC-22)
Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under
Contract No. DE- SC0012704 with the U.S. Department of Energy. The publisher by accepting the
manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up,
irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others
to do so, for United States Government purposes.
2
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the
United States Government. Neither the United States Government nor any
agency thereof, nor any of their employees, nor any of their contractors,
subcontractors, or their employees, makes any warranty, express or implied, or
assumes any legal liability or responsibility for the accuracy, completeness, or any
third party’s use or the results of such use of any information, apparatus, product,
or process disclosed, or represents that its use would not infringe privately owned
rights. Reference herein to any specific commercial product, process, or service
by trade name, trademark, manufacturer, or otherwise, does not necessarily
constitute or imply its endorsement, recommendation, or favoring by the United
States Government or any agency thereof or its contractors or subcontractors.
The views and opinions of authors expressed herein do not necessarily state or
reflect those of the United States Government or any agency thereof.
1
Direct measurement of the tunable electronic structure of bilayer MoS
2
by interlayer
twist
Po-Chun Yeh,
1
Wencan Jin,
2
Nader Zaki,
2
Jens Kunstmann
3,4
,Daniel Chenet
5
, Ghidewon Arefe
5
, Jerzy T. Sadowski,
6
Jerry I.
Dadap,
2
Peter Sutter,
7
James Hone
5
, and Richard M. Osgood, Jr.
1,2,*
1
Department of Electrical Engineering, Columbia University, New York, New York 10027, USA
2
Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
3
Department of Chemistry, Columbia University, New York, New York 10027, USA
4
Theoretical Chemistry, TU Dresden, 01062 Dresden, Germany
5
Department of Mechanical Engineering, Columbia University, New York, New York 10027, USA
6
Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA
7
Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA
Keywords: Stacked van der Waals Structures, Photoemission, Twisted van der Waals Materials, Spectromicroscopy, Low
Energy Electron Microscopy (LEEM), MoS
2
Abstract
Usin
g angle-resolved photoemission on
micrometer-scale sample areas, we directly measure
the interlayer twist angle-dependent electronic band
structure of bilayer molybdenum-disulfide (MoS
2
).
Our measurements, performed on arbitrarily stacked
bilayer MoS
2
flakes prepared by chemical vapor
de
position, provide direct evidence for a downshift of
the quasiparticle energy of the valence-band at the
Brillouin zone center (Γ
point) with the interlayer twist angle, up to a maximum of 120 meV at a twist
angle of ~40°. Our direct measurements of the valence band structure enable the extraction of the
hole effective mass as a function of the interlayer twist angle. While our results at Γ
agree with
recently published photoluminescence data, our measurements of the quasiparticle spectrum over the
full 2D Brillouin zone reveal a richer and more complicated change in the electronic structure than
previously theoretically predicted. The electronic structure measurements reported here, including the
evolution of the effective mass with twist-angle, provide new insight into the physics of twisted
transition-metal dichalcogenide bilayers and serve as a guide for the practical design of MoS
2
op
toelectronic and spin-/valley-tronic devices.
Van der Waals layered materials, especially the transition-metal dichalcogenides (TMDs), can
be prepared as atomically thin semiconductors
1
with high-quality homo- or hetero-junction interfaces.
These interfaces can be formed without the restrictions faced by conventional 3D semiconductors in
terms of lattice matching or interlayer crystallographic alignment. The utilization of layered materials
opens up potential applications for bandgap engineering by using strain
2
, stacking of layers
3, 4
, or
bu
ilding of heterojunctions
5, 6
. For TMDs such as MoS
2
, MoSe
2
, WS
2
, and WSe
2
, the electrical, optical
1, 7
,
and vibrational properties
8
are also known to be significantly dependent on interlayer coupling. One of
the well-known consequences of interlayer coupling in TMDs is the direct-to-indirect bandgap
transition from monolayer to multilayer films. The size of the indirect band gap has also been predicted
Page 1 of 12
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
BNL-111779-2016-JA
2
to vary with both the number of layers and the interlayer distance
8
, due to associated changes in
interlayer electronic coupling. To date, however, experimental efforts directed toward understanding
the interlayer interaction in TMDs, via direct measurements of the electronic band structure, have only
been conducted for the case of crystallographically-aligned layers, as found in samples exfoliated from
bulk materials
1, 7, 8, 9, 10
. Recently, photoluminescence (PL)
11, 12, 13, 14
and density functional theory
(DFT)
11, 12, 13, 15,16
studies on arbitrarily-aligned bilayer MoS
2
flakes (with variable interlayer twist angle)
have been reported. In PL measurements, the bilayer MoS
2
flakes are prepared by stacking two
chemical-vapor-deposition (CVD) prepared monolayer MoS
2
flakes.
Based on these recent PL results and Raman measurements of the characteristic phonon modes
(E
2g
and A
1g
) for twisted-bilayer MoS
2
11, 12, 13, 14
, one can conclude that (1) the interlayer coupling has a
global maximum for 0-degree twist angle, (2) the interlayer coupling of bilayer MoS
2
has a local
maximum for 60-degree twist angle (bilayer MoS
2
per se), and (3) the interlayer coupling is at a
minimum when the twist angle lies between 30-40 degrees. Density functional theory studies attribute
these results to a twist-angle-dependent change of the layer separation, which consequently
determines the degree of energy splitting of the highest occupied states around Γ
. The extent of this
energy splitting is reflected indirectly in the evolution of the relative energy difference between the
photoluminescence Γ
− K
∗
and K
− K
∗
transitions, where K
and K
∗
denote the highest occupied
valence band and the lowest unoccupied conduction band states at the high symmetry point K,
respectively. As deduced from theoretical calculations
11, 15
and photoluminescence measurements
11, 12,
13, 14
, the evolution of the uppermost valence band and the lowest conduction band (or conduction
band minimum, CBM) with respect to interlayer twist in bilayer MoS
2
changes the valence band
maximum (VBM) at Γ
, while leaving the energy gap at K
almost intact (the direct gap changes by ≤ 80
meV between 0° and 60° twist angle
11
). In light of these recent reports, there is a pressing need to
examine these findings using a more direct probe, and thus to verify the current theoretical predictions
via direct experimental measurements of the energy-momentum dispersion, which is not accessible
through photoluminescence studies. Furthermore, given the current intense interest in the field to the
fabrication and electronic engineering of heterostructures composed of two-dimensional/monolayer
materials, it is important to characterize the electronic structure via a direct band structure probing
technique, such as angle resolved photoemission (ARPES).
In this paper, we directly measure the energy-momentum-dispersion of CVD-grown and dry-
transferred twisted bilayer MoS
2
(TB-MoS
2
) for several twist angles ranging from 0° to 60° using micro-
spot angle-resolved photoemission spectroscopy (µ-ARPES). By utilizing bright-field (BF) low-energy
electron microscopy (LEEM), we locate twisted bilayer regions of interest, and determine their relative
twist angle and their region boundaries by in-situ micro-spot low-energy electron diffraction (µ-LEED)
and dark-field (DF) LEEM imaging. Our µ-ARPES measurements over the entire surface-Brillouin zone
reveal that the valence band maximum at Γ
is indeed the highest occupied state for all twist angles,
affirming the indirect nature of the bilayer MoS
2
bandgap, irrespective of twist angle, as suggested on
the basis of photoluminescence spectroscopy
11
,
12
,
13
. We directly quantify the energy difference
between the high symmetry points at Γ
and K
in the valence basnd, which is a function of twist angle,
Page 2 of 12
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
and observe the same trend reported in the above-mentioned photoluminescence and Raman studies.
We confirm that this trend is a result of the energy shifting of the topmost occupied state at Γ
, which
was previously predicted by DFT calculations (in part in Ref. 11-15 and associated supplemental
materials
). While our results at Γ
agree with recently published photoluminescence data, our
measurements of the quasiparticle spectrum over the full 2D Brillouin zone reveal a richer and more
complicated twist angle dependence of the electronic structure than is captured by DFT calculations of
isolated bilayers. For example, our measurements over the entire 2D Brillouin zone allows us to
determine variations of the hole effective mass at
as a function of twist angle.
Fig. 1 Bright field (BF) and dark field (DF) LEEM images of monolayer/twisted bilayer MoS
2
flakes with
twist angles of 47° ((a), (b)) and ~0° ((e), (f)), respectively. The CVD growth process yields both isolated
islands and connected patches of MoS
2
. Both were used in our experiment. The markers in (a) and (e)
indicate the location of measurements used to determine the twist angle. In (a), spot 1 is located on
the bilayer (with triangular upper flake) and spot 2 lies on the larger bottom flake that extends beyond
the top flake. (b) DF-LEEM imaging of (a) using a LEED spot originating from the top layer shows a
bright bilayer and a dark monolayer section, confirming a non-zero twist angle between the two flakes
(spot 1 was used in the DF-LEEM). An analogous placement of measurement spots was chosen in (e),
where both the top and bottom flakes are triangular. Since their twist angle is nearly zero, there is
minimal contrast in their DF-LEEM image (f). (c) and (d), (g) and (h) are LEED patterns of the bilayer and
monolayer segments of flake (a) and (e), respectively showing the same orientation of the diffraction
spots. The electron energies used here were (a) 3.5 eV, (b) 40 eV, (c)-(d) 40 eV, (e) 4.6 eV, (f) 36.4 eV,
(g)-(h) 40 eV.
Sample quality (see also Supplementary Information) and crystal orientation (i.e., interlayer
twist) of our TB-MoS
2
samples were examined using both BF- and DF-LEEM and µ-LEED (Fig. 1). DF-
LEEM using LEED spots originating from different MoS
2
layers shows clear contrast between ML MoS
2
flakes of different crystal orientations (Fig. 1(b) and 1(f)), which makes it preferable over BF-LEEM to
identify twisted bilayers (Fig. 1(a) and 1(e)). DF-LEEM also allows us to identify the boundary of a
region of interest. Note that in Fig. 1(b), for the case of the 47° twist angle, the DF-LEEM image shows a
distinct contrast between the top (bilayer) and the bottom (exposed monolayer). As for Fig. 1(f), in the
case of the ~0° twist angle, the DF-LEEM image shows almost no contrast between the top (red line)
and bottom (yellow line) layer, as expected for identically oriented layers. The corresponding electron
diffraction patterns (at a primary electron energy of 40 eV) of the top and bottom layer of the 47-
Page 3 of 12
3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60