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Indirect to Direct Gap Crossover in Two Dimensional InSe Revealed by Angle-Resolved Photoemission Spectroscopy

Two dimensional (2D) van der Waals heterostructures, composed of layered stacks of different 2D atomic crystals, show fascinating potential for studying fundamental physics and for (opto)electronic applications. The electronic properties of the stacks depend on the electronic structure in the individual layers and on band alignments between them. With the ever-growing family of 2D materials (2DMs), there are now widely studied 2D metals, semiconductors, insulators, superconductors and more. Learning how to utilise these 2DMs requires that we gain a fundamental understanding of their properties which are often fundamentally different from the bulk layered materials from which they are derived. 
The metal monochalcogenide III-VI compound, InSe, is emerging as an important 2D semiconductor with interesting layer-dependent electronic structure. InSe changes from a direct gap semiconductor in its bulk form to an indirect gap in the monolayer or few-layer form, though still optically active due to weak dispersion in the valence band (VB). With strong quantum confinement effects, as the number of layers decreases, the VB around Γis predicted to take on a characteristic ‘inverted Mexican hat’. The weak dispersion of the VB has implications for the importance of many-body effects and could lead to a phase transition into a ferromagnetic state, or to a charge density wave due to electron-phonon coupling. Magneto-transport and optical measurements have determined the effective mass of conduction band electrons and excitons for L>1: both are small and only weakly layer dependent. However, due to the weak dispersion, the VB properties have proven difficult to determine experimentally.
Fortunately, angle resolved photoemission spectroscopy (ARPES) is a proven technique for studying VB structure of 2DMs. Conventional ARPES is limited to large (>100 µm) atomically flat samples, which for most 2DMs necessitates epitaxial growth on single crystal substrates. However, using the Spectromicroscopy beamline at Elettra, we have recently demonstrated that sub-micrometre spatially resolved ARPES (µ-ARPES) enables high resolution measurements from mechanically exfoliated flakes only a few µm across. Hence the same samples can be studied as widely used for fundamental studies of transport and optical phenomena in 2DMs. Here, using again the Spectromicroscopy beamline, we apply µ-ARPES to resolve the valence band structure of InSe, comparing the experimental results to ab initio calculations.
An optical micrograph of a mechanically exfoliated InSe flake is shown in Figure 1; regions of different thickness can be identified by their optical contrast, and the number of layers confirmed by atomic force microscopy. For µ-ARPES, InSe flakes were encapsulated with graphene on top and graphite underneath, to dissipate the photo-emission current and give an atomically flat substrate. Scanning photoemission microscopy was used to identify the flakes and regions of different thickness within them, and spectra acquired at fixed points. Energy-momentum slices, I(E,k//), showing the valence band dispersion around Γ, are given for 1L, 2L, 3L, 4L and bulk (>30L) InSe in Figure 1e, taken from the flake in the optical micrograph of Figure 1d. Density functional theory (DFT) predictions, using the VASP code, are overlaid on these spectra, with the valence (conduction) bands shown as white (black) dashed lines. The agreement between theory and experiment is clear: hybridization between the selenium porbitals decreases the binding energy of the upper VB as the number of layers increases, correlated to the increase in band gap. As decreases, the upper valence band becomes flatter around Γ and finally inverts. Correspondingly, for one and two-layer InSe the valence band maxima (VBM) move away from Γ, forming an indirect gap. For L>6, the VBM returns to Γ with a direct gap, in agreement with the DFT predictions. 

Figure 1.  Atomic structure (a), and Brillouin zone (b), of γ-InSe. The blue-shaded regions in (a) mark the unit cell. (c) Schematic of the 2D heterostructures used for µ-ARPES and (d) optical microscope of a mechanically exfoliated InSe flake, scale bar 5 µm. (e) Layer-dependent valence band dispersion around Г; energy momentum slices, I(E,K//), about Г for 1L, 2L, 3L, 4L and bulk InSe as marked. Overlaid are the corresponding DFT predictions.

A more detailed analysis of the ‘Mexican hat’ dispersion in 1L InSe is shown in Figure 2, where the upper valence band energy from the ab initio calculations is compared to values obtained from fitting the experimental spectra. Line profiles clearly show the band inversion, with the energy difference from Γ to the maxima agreeing within uncertainty for the experimental (ΔE1exp =50±20 meV) and theoretical (ΔE1DFT =69 meV meV) data. These results show how µ-ARPES has an important role to play in understanding and developing 2DMs.

Figure 2.  Valence band inversion in 1L InSe around Г. (a) DFT prediction of upper valence band energy near Г; overlaid within the white dashed rectangle are the experimental data. (b) Line profiles of the upper valence band dispersion in the directions as marked; DFT predictions for spin up and spin down bands are shown as dashed and dotted red lines.


This research was conducted by the following research team:

Matthew J. Hamer1, Johanna Zultak1, Anastasia V. Tyurnina1, Viktor Zólyomi1, Daniel Terry1, Maciej Koperski1, Vladimir I. Falko1, Roman V. Gorbachev1, Alistair Garner2, Jack Donoghue2, Aidan P. Rooney2, Sarah J. Haigh2, Alexei Barinov3, Viktor Kandyba3, Alessio Giampietri3, Abigail Graham4, Natalie Teutsch4, Xue Xia4and Neil R. Wilson41 


School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester and National Graphene Institute, University of Manchester, Oxford Road, Manchester, U.K.

School of Materials, University of Manchester, Oxford Road, Manchester, U.K.

Elettra - Sincrotrone Trieste, S.C.p.A., Basovizza (TS), Italy

Department of Physics, University of Warwick, Coventry, U.K.

Contact persons:

Neil R. Wilson e-mail: neil.wilson@warwick.ac.uk


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 V. Gorbachev, and Neil R. Wilson “Indirect to Direct Gap Crossover in Two Dimensional InSe Revealed by Angle-Resolved Photoemission Spectroscopy”ACS Nano 13, 2136 (2019), DOI: 10.1021/acsnano.8b08726.

Last Updated on Wednesday, 03 April 2019 15:36