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Indirect to Direct Gap Crossover in Two-Dimensional InSe Revealed by Angle-Resolved Photoemission Spectroscopy Matthew J. Hamer, Johanna Zultak, Anastasia V. Tyurnina, Viktor Zólyomi, Daniel Terry, Alexei Barinov, Alistair Garner, Jack Donoghue, Aidan P. Rooney, Viktor Kandyba, Alessio Giampietri, Abigail Graham, Natalie Teutsch, Xue Xia, Maciej Koperski, Sarah J. Haigh, Vladimir I. Fal'ko, Roman Vladislavovich Gorbachev, and Neil Richard Wilson ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b08726 • Publication Date (Web): 24 Jan 2019 Downloaded from http://pubs.acs.org on January 26, 2019
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Indirect to Direct Gap Crossover in Two-Dimensional InSe Revealed by Angle-Resolved Photoemission Spectroscopy Matthew J. Hamer,
†,‡
Zólyomi,
Daniel Terry,
Aidan P. Rooney,
Natalie Teutsch,
Fal'ko,
†School
†,‡
k
§
†,‡
Johanna Zultak,
†,‡
Alexei Barinov,
Viktor Kandyba,
k
Xue Xia,
∗,†,‡,⊥
¶
¶
Anastasia V. Tyurnina,
Alistair Garner,
¶
Alessio Giampietri,
Maciej Koperski,
†,‡
∗,†,‡,⊥
Roman V. Gorbachev,
§
†,‡
Viktor
§
Jack Donoghue,
k
Abigail Graham,
§,‡
Sarah J. Haigh,
Vladimir I.
and Neil R. Wilson
∗,k
of Physics and Astronomy, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
‡National
Graphene Institute, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
¶Elettra §School
- Sincrotrone Trieste, S.C.p.A., Basovizza (TS), 34149, Italy
of Materials, University of Manchester, Oxford Road, Manchester, M13 9PL, UK
kDepartment
of Physics, University of Warwick, Coventry, CV4 7AL, UK
⊥Henry
Royce Institute, Oxford Road, Manchester, M13 9PL
E-mail: *
[email protected]; *
[email protected]; *
[email protected] Abstract Atomically thin lms of III-VI post-transition metal chalcogenides (InSe and GaSe) form an interesting class of two-dimensional semiconductor that feature a strong varia1
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tion of their band gap as a function of the number of layers in the crystal and, speci cally for InSe, an expected crossover from a direct gap in the bulk to a weakly indirect band gap in monolayers and bilayers. Here, we apply angle resolved photoemission spectroscopy with submicrometer spatial resolution (µARPES) to visualise the layerdependent valence band structure of mechanically exfoliated crystals of InSe. We show that for 1 layer and 2 layer InSe the valence band maxima are away from the Γ-point, forming an indirect gap, with the conduction band edge known to be at the Γ-point. In contrast, for six or more layers the bandgap becomes direct, in good agreement with theoretical predictions. The high-quality monolayer and bilayer samples enable us to resolve, in the photoluminescence spectra, the band-edge exciton (A) from the exciton (B) involving holes in a pair of deeper valence bands, degenerate at Γ, with a splitting that agrees with both µARPES data and the results of DFT modelling. Due to the dierence in symmetry between these two valence bands, light emitted by the A-exciton should be predominantly polarised perpendicular to the plane of the two-dimensional crystal, which we have veri ed for few-layer InSe crystals.
Keywords ARPES, indium selenide, 2D materials, density functional theory, photoluminescence, spinorbit coupling
Two-dimensional materials (2DM) and their van der Waals heterostructures, constructed by the mechanical assembly of individual 2D crystals, have great potential for optoelectronic applications.
1
The fast growing family of 2DM
2
includes 2D insulators, 2D semiconductors
with various band gaps, 2D metals and even 2D superconductors, with electronic and optical properties that often dier from their bulk allotropes.
3
In this family, post-transition metal
monochalcogenides (PTMC), III-VI compounds such as GaSe and InSe, are emerging as important materials to study, due to their interesting layer-dependent optical properties and exceptionally high carrier mobility.
410
Both GaSe and InSe display a pronounced quantum
2
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con nement eect: an increase of the band gap upon decreasing the number of layers, which is stronger in InSe
6,11
than in GaSe
12
L,
lms as revealed recently by photoluminescence
(PL) spectroscopy of atomically thin lms of these compounds. The latter eect is partly due to the interlayer hybridisation of S-orbitals of metal atoms and Pz -orbitals of Se dominating among the states at the edge of the conduction band at the a light in-plane mass whose
L-dependent values,
of Shubnikov de Haas oscillations,
6
Γ-point, where electrons also have
determined from the temperature variation
coincide with the theoretically predicted masses.
11
Such a
spectral evolution is accompanied by the theoretically predicted attening of the top valence band dispersion, which has the potential to lead to a phase transition of p-doped GaSe monolayer lms into,
e.g., a ferromagnetic state, 13,14 but is more likely to localise holes, as
observed by high (MΩ range) resistances measured in p-doped InSe.
15
Moreover, for both
InSe and GaSe the valence band edge in monolayer and bilayer lms was predicted to shift away from the
Γ-point,
as recently con rmed for GaSe by angle resolved photoemission
spectroscopy (ARPES) studies.
16,17
Here, we use ARPES to determine the valence band structure of monolayer and few-layer crystals of intrinsic Bridgman method).
γ -InSe
(purchased from 2D Semiconductors, grown using the vertical
Conventional ARPES is limited to large (typically
>100 µm)
atomi-
cally at samples, which for most atomically thin materials necessitates epitaxial growth on single crystal substrates.
For this reason, previous ARPES experiments on monolayer
metal monochalcogenides have used materials grown by molecular beam epitaxy.
1619
Most
transport and optical investigations instead use mechanically exfoliated akes which, though higher-quality, are typically only a few
µm
across.
We have recently demonstrated that
sub-micrometer spatially resolved ARPES (µARPES) enables high resolution measurements from mechanically exfoliated akes.
20
In this way we can directly determine the valence band
electronic structure in the same samples as were used for electrical and optical studies in these 2DM. Here, we combine
µARPES
with optical spectroscopy and
ab initio calculations
to directly demonstrate the crossover from direct to indirect gap and gain insight into the
3
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Figure 1:
InSe sample structure.
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Crystal structure, (a), and Brillouin zone, (b), of
γ-
InSe. The blue shaded regions in (a) indicate the unit cell, lattice vectors are shown in blue. (c) Optical microscope image of a mechanically exfoliated InSe ake, regions of dierent optical contrast correspond to regions of dierent thickness as labelled (scale bar
5 µm).(d)
Schematic of the 2D heterostructure used for ARPES measurements.
peculiar layer-number-dependent electronic structure of atomic lms of InSe.
Results and Discussion Layers of InSe have a honeycomb atomic arrangement produced by four planes of atoms, Se-In-In-Se. Stacked in the most commonly observed thick InSe has a hexagonal 2D Brillouin zone, Fig.
γ -InSe 1b.
polytype, Fig. 1a, few-layer-
An optical microscope image of
a typical InSe crystal produced by mechanical exfoliation onto an oxidised silicon wafer is shown in Fig. 1c, where individual
1
to
7L
terraces were identi ed by their optical contrast,
con rmed by atomic force microscopy. Individual regions within the ake were identi ed by
4
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scanning photoemission microscopy (SPEM) each uniform few
µm area.
20
before performing detailed ARPES studies of
To acquire high-resolution spectra, akes must be transferred onto
an atomically at substrate, be electrically grounded to dissipate the photoemission current, and display a clean surface.
20
To meet these criteria, mechanically exfoliated InSe akes were
sandwiched between a substrate made of hexagonal boron nitride or graphite (see Methods) and a capping layer of graphene, as shown schematically in Figure 1d. The graphene layer provides charge dissipation and protects the material from decomposition during air exposure and subsequent vacuum annealing necessary to clean the surface. The stack was constructed in a puri ed Ar environment using a remotely controlled micromanipulation system
21
that
enabled us to preserve the pristine crystalline structure by avoiding the oxidation of InSe.
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Figure 2:
γ -InSe
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valence band dispersion. µARPES measurement of the valence band
structure of mechanically exfoliated 1L, (a), and bulk, (d), InSe along the high symmetry directions as labelled. DFT band structures are overlaid as white (black) dashed lines for the valence (conduction) band; in (d) the blue dotted lines correspond to the theoretical predictions for
kz = 0.5
lattice constant.
and the white / black to
kz = 0
The red dashed lines are guides to the eye for the graphene bands as
labelled. The experimental data has been re ected about with theory. (blue).
in units of out-of-plane reciprocal
Γ
in each case to aid comparison
Optical transitions corresponding to the A (B) exciton are labelled in red
The photoluminescence spectrum of the monolayer is also shown, (b), along with
the dependence of the optical transition energies in PL on the number of layers, (c). The photoluminescence spectra for thicker layers are shown in the Supplementary Information.
Figure 2 shows the results of
µARPES
measurements of the valence band dispersion of
monolayer and bulk InSe, both compared to the results of DFT modelling (white dashed lines). The energy-momentum
I E, kk
spectra are plotted along the high-symmetry direc-
tions, as marked. In the monolayer data, Fig. 2a, graphene's
π
and
σ
bands are highlighted
by red dashed lines. For all samples measured, the Dirac point energy,
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ED ,
of the graphene
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on top of the InSe was within
50 meV of the Fermi energy, EF , indicating little charge transfer
between InSe and graphene. The binding energy of
v
then gives the layer-dependent valence
band oset between InSe and graphene, Table 2. The large band oset for monolayer InSe con rms a signi cant Schottky barrier would be formed if graphene were used as a contact to InSe, explaining the high resistance previously reported
6
(however, as we discuss below, the
band oset is smaller for few-layer crystals, in agreement with high quality tunable contacts observed in Ref.
10
). The measured monolayer InSe bands appear to be in a good agreement
with valence band spectra calculated using VASP code
22
with experimentally measured lat-
tice parameters, as overlaid in Figure 2a. The upper valence band, labelled near
Γ,
v,
is almost at
dispersing to higher binding energy at the Brillouin zone boundaries. Our DFT cal-
culations (see Methods) take into account spin-orbit coupling (SOC), which is necessary for the accurate description of two quadruplets of the lower-lying valence bands, dominated by the Px and Py orbitals of Se atoms.
z → −z
23
v1
bands and odd in
by atomic SOC into two doublets
±3
v1,22
and
the total (spin plus orbital) angular momentum projections onto the z-axis of energy) and
± 21 11
v2 ,
±1
v1,22
± 32
v2 ,
with
(higher
(lower energy), respectively. To further aid the discussion on optical prop-
erties, we also show the conduction band, implemented
and
These bands are distinguished by the
mirror symmetry of their wave functions, which are even in
and each of these quadruplets is split
v1
17,23
c,
as predicted by theory with a scissor correction
to counter the underestimation of the gap in DFT (see Methods).
The ARPES spectra in Fig. 2a can be compared to photoluminescence (PL) observed in monolayer InSe, shown in Fig.
2b, and in thicker layers, shown in Fig.
DFT prediction for the energy of the transitions. transition from the transition
c↔v
at
± 32
c ↔ v1
Γ,
6
2c alongside
Here, the A-exciton corresponds to the
as marked by the red arrow on Figure 2a, and the B-exciton to
, as marked by the blue arrow. Based on the PL spectrum shown in
Fig. 2b, we are, now, able to resolve A- and B-exciton lines in monolayer InSe (which was not
6
possible in the earlier optical studies of this system ) and compare those to the ARPES data in Table 1.(The photoluminescence spectrum and corresponding A-B peaks for thicker InSe
7
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Figure 3:
Valence band inversion in 1L InSe around Γ.
energy near
Γ as predicted by DFT with experimental data overlaid within the white dashed
(a) Upper valence band
rectangle, the color scale is identical for both and is given to the right. (b) Line pro les of the upper valence band dispersion close to
Γ
in the
M→Γ→K
directions as marked: the
red dashed and dotted lines are DFT predictions for spin up and down bands.
layers is shown in the Supplementary Information). From the ARPES spectra we determine the energy dierence between
300 ± 100 meV
v
and the upper doublets
120 ± 70 meV,
model (TBM).
of
v1
and
v2
quadruplets to be
(the uncertainty is large due to the weak photoemitted intensity for
the broad linewidth of the intense splitting,
±3
v1,22
23
v
v1
and
band). This appears to be larger than the A-B exciton
and the estimate,
170 meV,
of the earlier-developed tight-binding
Such a dierence can be attributed to the hybridisation of selenium's Pz
orbitals with carbon, which pushes the
v band upward, increasing its distance from v1,2 bands
whose Px,y orbitals are immune to the interlayer hybridisation. For monolayer InSe the ARPES spectra reveal a band inversion around
Γ,
as shown in
detail in Figure 3. The energy of the upper valence band, as predicted by DFT, is plotted as a function of
kx
and
ky
in the vicinity of
Γ in Figure 3a, where a lighter color corresponds to
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a lower binding energy. There are six valence band maxima (VBM), each center in the
K/K0
directions, with corresponding saddle points on the
∆kk
from the zone
Γ−M
line. Within
the white dashed box, experimental band energies extracted from the ARPES spectra (see Methods and Supporting Information, Section S1) are overlaid, and the VBM and saddle points can be discerned despite the noise of the measurements. Line pro les through both the experimental data and DFT simulations are shown in Fig. 3b, allowing the position of the VBM and the depth of the band inversion to be determined as
∆E1exp =50 ± 20 meV
∆kkexp =0.3 ± 0.1 Å
respectively. In addition, we nd that the saddle point is
−1
and
20 ± 20 meV
relative to the VBM. These values agree within uncertainty with our DFT predictions: VBM at
∆kkDF T =0.28 Å
7 meV
−1
from
Γ
and
∆E1DF T =69 meV,
with the saddle point in the
M
direction
higher in binding energy than the VBM, con rming that the monolayer is, indeed, an
indirect band gap semiconductor.
Table 1:
InSe monolayer valence band parameters at Γ.
Monolayer energy splittings
between the upper valence band and the lower valence bands, comparing the ARPES and PL data to previous
23
calculations and DFT modelling in the present work.
±3
InSe 1L TBM
23
DFT (this work) ARPES PL,
XB − X A
Unlike the monolayer, bulk
v − v1 2 (meV) 170 310 300 ± 100 120 ± 70
γ -InSe
agreement with the existing literature.
± 23
v1
±1
− v1 2 (meV) 380 360 400 ± 100
is clearly a direct band gap material, Fig.
2426
The ARPES spectra of a bulk crystal show broad
features with multiple states dispersed in the
kz
direction, perpendicular to the layers, since
µARPES detects photoemitted electrons with a wide (here,
undetermined) range of
white and blue dashed lines correspond to DFT band structure calculations with
kz = 0.5
2d, in
(in units of out-of-plane reciprocal lattice parameter) respectively.
kz .
The
kz = 0 and
Where these
overlay, and are similar to the monolayer data, the bands are typically 2D in nature with little dispersion in the
kz
direction.
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In Figure 4 we show how the valence band spectrum changes as a function of the number of layers in a lm.
In the centre of the Brillouin zone, the valence band
primarily of selenium Pz orbitals
11
v
is composed
which overlap and hybridize between the consecutive
layers, leading to the pronounced subband structure in the ARPES spectra (two subbands in a bilayer, three in a trilayer, and so on). Simultaneously, the VBM moves to a progressively lower binding energy and gets closer to the band inversion, with
∆kkexp =0.1 ± 0.1 Å
−1
Γ-point.
∆E2exp =30 ± 20 meV.
and
band inversion is no longer measurable with
For 2L InSe there remains a measurable
exp ∆EL≥3
