Single-layer ${\text{MoS}}_{2}$ on Au(111): Band gap renormalization and substrate interaction

Single-layer ${MoS}_{2}$ on Au(111): Band gap renormalization and substrate interaction

Albert Bruix, Jill A. Miwa, Nadine Hauptmann, Daniel Wegner, Søren Ulstrup, Signe S. Grønborg, Charlotte E. Sanders, Maciej Dendzik, Antonija Grubišić Čabo, Marco Bianchi, Jeppe V. Lauritsen, Alexander A. Khajetoorians, Bjørk Hammer, and Philip Hofmann

Phys. Rev. B 93, 165422 – Published 18 April 2016

Abstract

The electronic structure of epitaxial single-layer ${MoS}_{2}$ on Au(111) is investigated by angle-resolved photoemission spectroscopy, scanning tunneling spectroscopy, and first-principles calculations. While the band dispersion of the supported single layer is close to a free-standing layer in the vicinity of the valence-band maximum at $\bar{K}$ and the calculated electronic band gap on Au(111) is similar to that calculated for the free-standing layer, significant modifications to the band structure are observed at other points of the two-dimensional Brillouin zone: at $\bar{Γ}$ , the valence-band maximum has a significantly higher binding energy than in the free ${MoS}_{2}$ layer and the expected spin-degeneracy of the uppermost valence band at the $\bar{M}$ point cannot be observed. These band structure changes are reproduced by the calculations and can be explained by the detailed interaction of the out-of-plane ${MoS}_{2}$ orbitals with the substrate.

Received 23 December 2015
Revised 24 March 2016

DOI:https://doi.org/10.1103/PhysRevB.93.165422

Physics Subject Headings (PhySH)

Electronic structure Surface states

Transition metal dichalcogenides

Angle-resolved photoemission spectroscopy Density functional theory Scanning tunneling microscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Albert Bruix¹, Jill A. Miwa¹, Nadine Hauptmann², Daniel Wegner², Søren Ulstrup¹, Signe S. Grønborg¹, Charlotte E. Sanders¹, Maciej Dendzik¹, Antonija Grubišić Čabo¹, Marco Bianchi¹, Jeppe V. Lauritsen¹, Alexander A. Khajetoorians², Bjørk Hammer¹, and Philip Hofmann^1,*

¹Department of Physics and Astronomy, Interdisciplinary Nanoscience Center (iNANO), Aarhus University, 8000 Aarhus C, Denmark
²Institute for Molecules and Materials, Radboud University, 6500 GL Nijmegen, The Netherlands

^*philip@phys.au.dk

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Vol. 93, Iss. 16 — 15 April 2016

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Figure 1
Models used for the DFT calculations. (a) Top views of the matched model consisting of a $(1 \times 1)$ unit cell of ${MoS}_{2}$ on a $(1 \times 1)$ cell of Au(111). The different positions considered of the bottom S atoms with respect to the underlying Au lattice (on-top, hcp, and fcc) are shown. (b) Top view of the mismatched model consisting of a $(\sqrt{13} \times \sqrt{13}) R 13 . 9^{\circ}$ cell of ${MoS}_{2}$ on a $(4 \times 4)$ cell of Au(111). (c) Side view of the ${MoS}_{2}$ /Au(111) interface indicating the relevant distance $r$ between the lower S layer and the outermost surface layer of Au(111). Turquoise, yellow, and brown spheres indicate the position of Mo, S, and Au atoms, respectively.
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Figure 2
(a) Photoemission intensity for epitaxial SL ${MoS}_{2}$ on Au(111) along different high-symmetry directions of the BZ, measured at a photon energy of 70 eV; inset: hexagonal BZ. (b) Data acquired at a photon energy of 49 eV in the energy region of the top valence band of ${MoS}_{2}$ . (c) The same data as in (b) but with the theoretical dispersion for a free-standing layer (solid yellow lines) and projected band gap edges of the (111) surface of Au (solid orange lines) [35] superimposed on the experimental data. The measured difference in the top of the valance band at $\bar{K}$ compared to $\bar{Γ}$ is noted to be 0.31 eV.
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Figure 3
(a) Constant-current STM image of 0.5 ML coverage of SL ${MoS}_{2}$ on Au(111). Image parameters: $V_{S} = - 1.5 V$ and $I_{t} = 0.2 nA$ . (b) Atomically resolved image of a SL ${MoS}_{2}$ island revealing the atomic lattice and moiré pattern. Image parameters: $V_{S} = - 0.12 V$ and $I_{t} = 0.1 nA$ . (c) Representative STS [current and differential conductance ( $d I / d V$ )] near the center of a SL ${MoS}_{2}$ island. The tip was stabilized at $V_{S} = 1.9 V$ and $I_{t} = 0.4 nA$ . A modulation amplitude of 42 mV was used.
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Figure 4
(a) Calculated projected density of states (pDOS) of the ${MoS}_{2}$ layer in the matched (on-top) and mismatched ${MoS}_{2}$ /Au(111) models and for the free-standing monolayer. (b) pDOS on ${MoS}_{2}$ for the on-top, hcp, and fcc positions for the matched model. (c) DOS projected on the different atom types of the mismatched model, i.e., Au, Mo, and S atoms from the upper and lower layers. The pDOS of the S atoms has been scaled $\times 3$ for clarity. Peaks in (c) have been labeled according to the assignments made in Fig. 3. The onsets of VB1 and CB1 are $- 1.05$ and 0.54 eV, respectively. The peaks of VB2, CB2, and CB3 are $- 1.83$ , 1.15, and 1.43 eV, respectively.
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Figure 5
Calculated band structures for free-standing SL ${MoS}_{2}$ and SL ${MoS}_{2}$ on Au(111) (matched model). The size of the green circles in the second panel indicate the weight for each state from ${MoS}_{2}$ orbitals. For the rest of panels, the blue (red) circles indicate the weight from in-plane (out-of-plane) orbitals for the Mo atom and for the sulfur atoms on the ${MoS}_{2}$ -vacuum (upper S) and ${MoS}_{2}$ -Au(111) interfaces (lower S). The weight for the S orbitals have been multiplied by two in order to visualize their contributions more clearly.
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Figure 6
Unfolded bandstructures for (a) a bare $(4 \times 4)$ Au(111) surface and (b) the mismatched model consisting of a $(\sqrt{13} \times \sqrt{13}) R 13 . 9^{\circ}$ cell of ${MoS}_{2}$ on a $(4 \times 4)$ cell of Au(111). The position of relevant ${MoS}_{2}$ bands (VB1, VB2, and CB1) has been indicated according to the labels in Figs. 3 and 4. The hybridization of ${MoS}_{2}$ states with $d$ -band continuum states of Au is illustrated in (c) for clarity.
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Physical Review B

covering condensed matter and materials physics

Single-layer ${MoS}_{2}$ on Au(111): Band gap renormalization and substrate interaction

Albert Bruix, Jill A. Miwa, Nadine Hauptmann, Daniel Wegner, Søren Ulstrup, Signe S. Grønborg, Charlotte E. Sanders, Maciej Dendzik, Antonija Grubišić Čabo, Marco Bianchi, Jeppe V. Lauritsen, Alexander A. Khajetoorians, Bjørk Hammer, and Philip Hofmann

Phys. Rev. B 93, 165422 – Published 18 April 2016

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Physical Review B

covering condensed matter and materials physics

Single-layer MoS2 on Au(111): Band gap renormalization and substrate interaction

Albert Bruix, Jill A. Miwa, Nadine Hauptmann, Daniel Wegner, Søren Ulstrup, Signe S. Grønborg, Charlotte E. Sanders, Maciej Dendzik, Antonija Grubišić Čabo, Marco Bianchi, Jeppe V. Lauritsen, Alexander A. Khajetoorians, Bjørk Hammer, and Philip Hofmann

Phys. Rev. B 93, 165422 – Published 18 April 2016

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Single-layer ${MoS}_{2}$ on Au(111): Band gap renormalization and substrate interaction