Crystalline solids assembled from superatomic building blocks are attractive functional materials due to their hierarchical structure, multifunctionality, and tunability. An interesting example is Re6Se8Cl2, in which the Re6Se8 building blocks are covalently linked into two-dimensional (2D) sheets that are stacked into a layered van der Waals solid. It is an indirect gap semiconductor that, when heavily doped, becomes a superconductor at low temperatures. Given the finite electronic bandwidths (300–400 meV), carrier properties in this material are expected to be strongly influenced by coupling to phonons. Here, we apply angle-resolved photoemission spectroscopy to probe the valence band edge (VBE) of Re6Se8Cl2. We find that dispersion of the VBE is a strong function of temperature. The bandwidth is W = 120 ± 30 meV at 70 K and decreases by one order of magnitude to W ∼ 10 ± 20 meV as temperature is increased to 300 K. This observation reveals the dominant polaronic effects in Re6Se8Cl2, consistent with the Holstein polaron model commonly used to describe molecular solids.

Assembling nanoscale building blocks into functional materials has been a longstanding goal in nanoscience. Prominent examples include crystalline solids assembled from nanoparticles (NPs) via van der Waals interactions or DNA hybridization.1,2 Both approaches are limited by intrinsic disorder resulting from variations in NP size, shape, surface chemistry, and inter-NP interaction and by weak inter-NP electronic coupling due to intervening capping ligands. The recent development of superatomic crystals overcomes both limitations as the building blocks are atomically precise clusters and inter-cluster interaction can be sufficiently strong from intimate van der Waals, electrostatic, or covalent interactions.3–5 The replacement of atoms in conventional solids by superatomic units offers the enticing prospect of combining multifunctionality and tunability.

Here, we investigate the polaronic properties of a model superatomic semiconductor, Re6Se8Cl2. In this solid, the [Re6Se8] clusters are covalently linked in-plane through Re–Se bonds to form two-dimensional (2D) sheets terminated with Cl atoms; the 2D sheets are stacked to form a layered van der Waals structure [Fig. 1(a)].6 This semiconductor has an indirect bandgap of 1.58 eV.7 Its hierarchical atomic structure translates into a hierarchical phonon landscape, including zero-dimensional (0D) cluster breathing modes, 2D inter-cluster twisting modes, and three-dimensional (3D) inter-sheet acoustic modes, with the 2D modes found to strongly couple to electronic transitions.8 Interestingly, a recent theoretical analysis9 of a related 3D cluster solid PbMo6S8 suggests that strong coupling of electrons to the inter-cluster twisting modes is critical to superconductivity,10,11 and superconductivity was observed in electron-doped 2D layered Re6Se8Cl2 crystals.12 Besides superconductivity, electron–phonon coupling can affect conventional carrier properties via polaron formation. Density functional theory (DFT) calculation shows that the valence bandwidth of Re6Se8Cl2 is 300–400 meV.7 This is smaller than those in typical 2D atomic semiconductors such as MoSe2, making electron–phonon coupling more important to carrier properties in the superatomic crystal.

FIG. 1.

(a) Top (left) and side (right) views of the layered superatomic crystal Re6Se8Cl2. Color code: Cl, green; Re, blue; and Se, maroon. (b) Optical microscope image of a cleaved Re6Se8Cl2 single crystal. (c) Schematic of the reciprocal lattice (blue) and the first Brillouin zone (black) along the ab plane of Re6Se8Cl2. (d) Schematic of angle-resolved photoemission spectroscopy (ARPES) measurement. EUV, extreme ultraviolet pulse; θ, photoelectron ejection polar angle; and k//, photoelectron parallel momentum along the Γ–Y direction.

FIG. 1.

(a) Top (left) and side (right) views of the layered superatomic crystal Re6Se8Cl2. Color code: Cl, green; Re, blue; and Se, maroon. (b) Optical microscope image of a cleaved Re6Se8Cl2 single crystal. (c) Schematic of the reciprocal lattice (blue) and the first Brillouin zone (black) along the ab plane of Re6Se8Cl2. (d) Schematic of angle-resolved photoemission spectroscopy (ARPES) measurement. EUV, extreme ultraviolet pulse; θ, photoelectron ejection polar angle; and k//, photoelectron parallel momentum along the Γ–Y direction.

Close modal

In this work, we apply angle-resolved photoemission spectroscopy (ARPES) to determine the valence band dispersion in Re6Se8Cl2. ARPES is particularly powerful in probing electron–phonon coupling, as it directly measures the spectral function, which, in the commonly accepted “sudden approximation,” describes the quasiparticle of an electron interacting with phonons and other electrons.13 Our ARPES measurements show that the valence bandwidth (W) is a strong function of temperature; it is 120 ± 30 meV at 70 K and decreases by one order of magnitude to W ∼ 10 ± 20 meV as temperature is increased to 300 K. This band narrowing with increasing temperature is consistent with strong electron–phonon coupling, as described by the Holstein polaron model.14 For comparison, we show that the valence bandwidth in the traditional atomic 2D semiconductor, MoSe2, is independent of temperature (100–300 K).

Re6Se8Cl2 single crystals were synthesized by chemical vapor transport following reported procedures, as detailed elsewhere.7Figure 1(b) shows an optical image of a cleaved single crystal. The nearly square but anisotropic structure in the ab plane is confirmed by indexing the crystal edges.7Figure 1(c) illustrates the reciprocal lattice (blue) and the first Brillouin zone (BZ, black) in the a–b plane. We performed ARPES experiment using a setup that features an extreme ultraviolet (EUV) laser source (21.6 eV, 35 fs, 10 kHz) and a hemispherical analyzer with angular (θ) resolution.15 We carried out ARPES measurement along the Γ–Y direction [Fig. 1(d)]. The kinetic energy of photoelectrons as a function of the parallel momentum k// directly probes the hole dispersion in the valence band.

Figure 2(a) shows room temperature ARPES of Re6Se8Cl2 along the Γ–Y direction; the corresponding energy distribution curve (EDC) at the Γ point is shown in Fig. 2(b). The observations of the valence band edge (VBE) and midgap defect states are in agreement with previous photoemission and scanning tunneling spectroscopy measurements.7 The large number (16) of atoms in the unit cell of the Re6Se8Cl2 superatomic solid results in a dense manifold of valence bands.7 In contrast to atomic solids such as MoSe2 (see Fig. 3), the individual valence bands of Re6Se8Cl2 are not resolved. The most surprising and important finding from Fig. 2(a) is that the experimental dispersion over the momentum range (Γ → Y) is nearly flat (±20 meV). For comparison, DFT calculation for a rigid lattice gives a valence band dispersion of ∼300 meV in the Γ → Y direction.7 

FIG. 2.

(a) Room temperature ARPES of the Re6Se8Cl2 single crystal along the Γ–Y direction. EF: Fermi level. (b) Energy distribution curve (EDC) at the Γ point from a vertical cut at k// = 0.0 Å−1. VBE, valence band edge; D, defects. (c) ARPES of Re6Se8Cl2 along the Γ–Y direction around the VBE at three temperatures: 70 K (bottom), 108 K (middle), and 300 K (top). The red dashed lines are fits to a tight-binding model. (d) EDC at the Γ point (black dots) and the Y point (blue dots) obtained from vertical cuts in (c) at k// = 0.0 Å−1 and 0.6 Å−1, respectively. Solid lines: linear fits of the VBEs.

FIG. 2.

(a) Room temperature ARPES of the Re6Se8Cl2 single crystal along the Γ–Y direction. EF: Fermi level. (b) Energy distribution curve (EDC) at the Γ point from a vertical cut at k// = 0.0 Å−1. VBE, valence band edge; D, defects. (c) ARPES of Re6Se8Cl2 along the Γ–Y direction around the VBE at three temperatures: 70 K (bottom), 108 K (middle), and 300 K (top). The red dashed lines are fits to a tight-binding model. (d) EDC at the Γ point (black dots) and the Y point (blue dots) obtained from vertical cuts in (c) at k// = 0.0 Å−1 and 0.6 Å−1, respectively. Solid lines: linear fits of the VBEs.

Close modal
FIG. 3.

(a) Temperature dependent valence bandwidth of the Re6Se8Cl2 superatomic crystal (solid circles), pentacene single crystal (triangles), and MoSe2 single crystal monolayer (open circles). Solid and dashed curves are fits to Eq. (2) for Re6Se8Cl2 and pentacene, respectively. The dotted–dashed line is a constant to represent the negligible temperature dependence in the bandwidth of the MoSe2 monolayer. The pentacene results are reproduced with permission from Nakayama et al., J. Phys. Chem. Lett. 8, 1259 (2017).18 Copyright 2017 American Chemical Society. [(b) and (c)] ARPES obtained at 300 K and 106 K, respectively, from the MoSe2 single crystal monolayer on SiO2/Si.

FIG. 3.

(a) Temperature dependent valence bandwidth of the Re6Se8Cl2 superatomic crystal (solid circles), pentacene single crystal (triangles), and MoSe2 single crystal monolayer (open circles). Solid and dashed curves are fits to Eq. (2) for Re6Se8Cl2 and pentacene, respectively. The dotted–dashed line is a constant to represent the negligible temperature dependence in the bandwidth of the MoSe2 monolayer. The pentacene results are reproduced with permission from Nakayama et al., J. Phys. Chem. Lett. 8, 1259 (2017).18 Copyright 2017 American Chemical Society. [(b) and (c)] ARPES obtained at 300 K and 106 K, respectively, from the MoSe2 single crystal monolayer on SiO2/Si.

Close modal

The valence band dispersion is a strong function of temperature. Figure 2(c) shows the ARPES of Re6Se8Cl2 along the Γ–Y direction near the VBE at three temperatures: T = 70 K (bottom), 108 K (middle), and 300 K (top). It is obvious that the valence band dispersion increases as temperature decreases. If we approximate Re6Se8Cl2 in the ab plane as consisting of a square lattice and use the tight-binding model, we can describe the band dispersion E in the Γ–Y direction as E = E0 + W/2 · cos(k · b) at k = 0; E0 is a constant offset, and b is the lattice constant. Fits to this approximation [red dashed curves in Fig. 2(c)] yield valence bandwidths of W = 120 ± 30 meV, 80 ± 25 meV, and 10 ± 20 meV at T = 70 K, 108 K, and 300 K, respectively. Similar results on the temperature dependent valence bandwidth can be obtained by comparing the VBE at the Γ point (k// = 0 Å−1) and the Y point (k// = 0.6 Å−1), as shown by the EDCs in Fig. 2(d).

The observed band narrowing with increasing temperature is a signature of strong electron–phonon coupling, as is implicit in the Holstein polaron theory.14 The nearly flat valence band at 300 K suggests that the photo-hole forms a small polaron. Theoretical analysis of the experimentally observed band narrowing with temperature in molecular crystals16–18 has been described in the Holstein–Peierls model.19,20 In the simple case when one considers local electron–phonon coupling (Holstein model) and assumes no energy or polarization dispersion of phonon modes, W is given by19 

W=W0Expλ12+Nλgλmm2+gλnn2,
(1)

where Nλ = [exp(ωλ/kBT) − 1]−1 is the phonon occupation number for phonon mode λ, ωλ is the phonon energy, gλmm and gλnn are the electron-lattice coupling constants for on-site and nearest neighbor, respectively, and W0 is the asymptotic bandwidth at 0 K. Lacking a detailed knowledge of the coupling of each individual phonon to the hole, we fit the temperature dependent bandwidth using the effective phonon occupation number (Neff) and coupling strength (geff),

W=W0Exp12+Neffgeff2,
(2)

with Neff = [exp(ωeff/kBT) − 1]−1 given by the effective phonon frequency ωeff. A recent study based on coherent phonon spectroscopy has suggested that the coupling of electrons to the inter-cluster twisting mode at ω = 10.8 meV is particularly strong, while those to other modes are much weaker,8 and we take this as the effective phonon mode. By fitting the experimental data in Fig. 3(a) (solid circles) to Eq. (2), we obtain W0 = 280 ± 50 meV and geff = 1.2 ± 0.2. This asymptotic W0 value is in excellent agreement with the DFT valence bandwidth for a rigid Re6Se8Cl2 crystal without electron–phonon coupling.7 

The decrease in electronic bandwidth with temperature is related to the well-known phenomenon of decrease in semiconductor bandgap, and both can be traced to the decrease in exchange integral. The decrease in semiconductor bandgap with temperature has been described by the semi-empirical Varshni equation20,21 and attributed also to electron–phonon coupling.22 Note that thermal expansion increases the bond length and decreases the exchange integral, but this effect is much smaller than that of electron–phonon coupling. The thermal expansion coefficient of Re6Se8Cl2 is not known but is close to ∼9 × 10−6 K−1, which is related to the super-atom solid of PbMo6S8.23 This corresponds to a thermal expansion of only ∼0.2% in the temperature range of 70–300 K. Note that the Re6Se8Cl2 crystal remains in the same phase in this temperature range and there are no structural changes.12,23,24

To put the observed band narrowing of Re6Se8Cl2 in perspective, we compare these results in Fig. 3(a) to the temperature dependent bandwidths in a monolayer atomic solid, MoSe2, and a layered van der Waals molecular semiconductor, pentacene. The two MoSe2 data points (open circles) are from ARPES spectra [Figs. 3(b) and 3(c)] measured on a mm-size MoSe2 single crystal monolayer exfoliated onto a SiO2/Si substrate by a gold tape method.25 The spectra in Figs. 3(b) and 3(c) are in excellent agreement with the previous ARPES measurement on monolayer MoSe2.26 As temperature is decreased from 300 K to 106 K, we observe a rigid downward shift in the band structure due to an increase in surface workfunction, but no changes in band dispersion or valence bandwidth. We conclude that the polaronic effect is negligible in the 2D atomic solid of MoSe2.

For crystalline pentacene, we reproduce the ARPES results of Nakayama et al.18 as open triangles in Fig. 3(a). Hatch et al. reported that an effective phonon energy of ω = 11 meV, corresponding to an intermolecular vibration mode in pentacene crystal, is strongly coupled to the hole.17 Fitting to Eq. (2) using this effective phonon energy yields W0 = 240 ± 40 meV and geff = 0.4 ± 0.1. While the asymptotic bandwidth in the molecular solid of pentacene is close to that in the superatomic solid Re6Se8Cl2, the effective hole–phonon coupling constant in the former is three times smaller than that in the latter. The larger geff in Re6Se8Cl2 than that in pentacene may be attributed to the covalent nature of inter-cluster interaction in the former.

In summary, we have quantified the temperature dependent valence bandwidth in the layered Re6Se8Cl2 superatomic semiconductor using ARPES. We observe a band-narrowing effect with increasing temperature. The bandwidth is W = 120 ± 30 meV at 70 K and decreases by one order of magnitude to W ∼ 10 ± 20 meV as the temperature is increased to 300 K. This observation is consistent with a dominant polaronic effect. Fitting the temperature-dependent bandwidth to the Holstein polaron model gives an asymptotic low temperature valence bandwidth of 280 ± 50 meV, in excellent agreement with the DFT bandwidth for the rigid Re6Se8Cl2 structure. A comparison to the well-known layered molecular semiconductors, pentacene, and the layered atomic semiconductor, MoSe2, suggests that the Re6Se8Cl2 superatomic semiconductor is closer to the former in terms of polaronic characters.

All data needed to evaluate the conclusions are present in this paper.

This work was supported by the Center for Precision Assembly of Superstratic and Superatomic Solids, a Materials Science and Engineering Research Center (MRSEC), through NSF Grant No. DMR-1420634. F.L. acknowledges support from the Department of Energy (DOE) Office of Energy Efficiency and Renewable Energy (EERE) Postdoctoral Research Award under the EERE Solar Energy Technologies Office administered by the Oak Ridge Institute for Science and Education (ORISE). ORISE is managed by Oak Ridge Associated Universities (ORAU) under DOE Contract No. DE-SC00014664. All opinions expressed in this paper are the authors’ and do not necessarily reflect the policies and views of DOE, ORAU, or ORISE.

1.
C. B.
Murray
,
C. R.
Kagan
, and
M. G.
Bawendi
,
Science
270
,
1335
(
1995
).
2.
S. Y.
Park
,
A. K. R.
Lytton-Jean
,
B.
Lee
,
S.
Weigand
,
G. C.
Schatz
, and
C. A.
Mirkin
,
Nature
451
,
553
(
2008
).
3.
S. A.
Claridge
,
A. W.
Castleman
,
S. N.
Khanna
,
C. B.
Murray
,
A.
Sen
, and
P. S.
Weiss
,
ACS Nano
3
,
244
(
2009
).
4.
D.-L.
Long
,
E.
Burkholder
, and
L.
Cronin
,
Chem. Soc. Rev.
36
,
105
(
2007
).
5.
A.
Pinkard
,
A. M.
Champsaur
, and
X.
Roy
,
Acc. Chem. Res.
51
,
919
(
2018
).
6.
L.
Leduc
,
A.
Perrin
, and
M.
Sergent
,
Acta Crystallogr., Sect. C: Cryst. Struct. Commun.
39
,
1503
(
1983
).
7.
X.
Zhong
,
K.
Lee
,
B.
Choi
,
D.
Meggiolaro
,
F.
Liu
,
C.
Nuckolls
,
A.
Pasupathy
,
F.
De Angelis
,
P.
Batail
,
X.
Roy
, and
X.
Zhu
,
Nano Lett.
18
,
1483
(
2018
).
8.
K.
Lee
,
S. F.
Maehrlein
,
X.
Zhong
,
D.
Meggiolaro
,
J. C.
Russell
,
D. A.
Reed
,
B.
Choi
,
F.
De Angelis
,
X.
Roy
, and
X.
Zhu
,
Adv. Mater.
31
,
1903209
(
2019
).
9.
J.
Chen
,
A. J.
Millis
, and
D. R.
Reichman
,
Phys. Rev. Mater.
2
,
114801
(
2018
).
10.
B. T.
Matthias
,
M.
Marezio
,
E.
Corenzwit
,
A. S.
Cooper
, and
H. E.
Barz
,
Science
175
,
1465
(
1972
).
11.
Ø.
Fischer
,
R.
Odermatt
,
G.
Bongi
,
H.
Jones
,
R.
Chevrel
, and
M.
Sergent
,
Phys. Lett. A
45
,
87
(
1973
).
12.
E. J.
Telford
,
J. C.
Russell
,
J. R.
Swann
,
B.
Fowler
,
X.
Wang
,
K.
Lee
,
A.
Zangiabadi
,
K.
Watanabe
,
T.
Taniguchi
,
C.
Nuckolls
,
P.
Batail
,
X.
Zhu
,
J. A.
Malen
,
C. R.
Dean
, and
X.
Roy
,
Nano Lett.
20
,
1718
(
2020
).
13.
T.
Cuk
,
D. H.
Lu
,
X. J.
Zhou
,
Z.-X.
Shen
,
T. P.
Devereaux
, and
N.
Nagaosa
,
Phys. Status Solidi B
242
,
11
(
2005
).
14.
T.
Holstein
,
Ann. Phys.
8
,
325
(
1959
).
15.
F.
Liu
,
M.
Ziffer
,
K. R.
Hansen
,
J.
Wang
, and
X. -Y.
Zhu
,
Phys. Rev. Lett.
122
,
246803
(
2019
).
16.
N.
Koch
,
A.
Vollmer
,
I.
Salzmann
,
B.
Nickel
,
H.
Weiss
, and
J. P.
Rabe
,
Phys. Rev. Lett.
96
,
156803
(
2006
).
17.
R. C.
Hatch
,
D. L.
Huber
, and
H.
Höchst
,
Phys. Rev. Lett.
104
,
047601
(
2010
).
18.
Y.
Nakayama
,
Y.
Mizuno
,
M.
Hikasa
,
M.
Yamamoto
,
M.
Matsunami
,
S.
Ideta
,
K.
Tanaka
,
H.
Ishii
, and
N.
Ueno
,
J. Phys. Chem. Lett.
8
,
1259
(
2017
).
19.
K.
Hannewald
,
V. M.
Stojanović
,
J. M. T.
Schellekens
,
P. A.
Bobbert
,
G.
Kresse
, and
J.
Hafner
,
Phys. Rev. B
69
,
075211
(
2004
).
20.
F.
Ortmann
,
K.
Hannewald
, and
F.
Bechstedt
,
Appl. Phys. Lett.
93
,
222105
(
2008
).
21.
Y. P.
Varshni
,
Physica
34
,
149
(
1967
).
22.
K. P.
O’Donnell
and
X.
Chen
,
Appl. Phys. Lett.
58
,
2924
(
1991
).
23.
S.
Miraglia
,
W.
Goldacker
,
R.
Flükiger
,
B.
Seeber
, and
Ø.
Fischer
,
Mater. Res. Bull.
22
,
795
(
1987
).
24.
N.
Le Nagard
,
A.
Perrin
,
M.
Sergent
, and
C.
Levy-Clement
,
Mater. Res. Bull.
20
,
835
(
1985
).
25.
F.
Liu
,
W.
Wu
,
Y.
Bai
,
S. H.
Chae
,
Q.
Li
,
J.
Wang
,
J.
Hone
, and
X.-Y.
Zhu
,
Science
367
,
903
(
2020
).
26.
Y.
Zhang
,
T.-R.
Chang
,
B.
Zhou
,
Y.-T.
Cui
,
H.
Yan
,
Z.
Liu
,
F.
Schmitt
,
J.
Lee
,
R.
Moore
,
Y.
Chen
,
H.
Lin
,
H.-T.
Jeng
,
S.-K.
Mo
,
Z.
Hussain
,
A.
Bansil
, and
Z.-X.
Shen
,
Nat. Nanotechnol.
9
,
111
(
2014
).