Layer-dependent electronic structure of an atomically heavy two-dimensional dichalcogenide

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Layer-dependent electronic structure of an atomically heavy two-dimensional dichalcogenide

Po-Chun Yeh, Wencan Jin, Nader Zaki, Datong Zhang, Jonathan T. Liou, Jerzy T. Sadowski, Abdullah Al-Mahboob, Jerry I. Dadap, Irving P. Herman, Peter Sutter, and Richard M. Osgood, Jr.

Phys. Rev. B 91, 041407(R) – Published 20 January 2015

Abstract

We report angle-resolved photoemission spectroscopic measurements of the evolution of the thickness-dependent electronic band structure of the atomically heavy two-dimensional layered dichalcogenide, tungsten diselenide $(WS e_{2})$ . Our data, taken on mechanically exfoliated $WS e_{2}$ single crystals, provide direct evidence for shifting of the valence-band maximum from $\bar{Γ}$ (multilayer $WS e_{2}$ ) to $\bar{K}$ (single-layer $WS e_{2}$ ). Further, our measurements also set a lower bound on the energy of the direct band gap and provide direct measurement of the hole effective mass.

Received 9 July 2014

DOI:https://doi.org/10.1103/PhysRevB.91.041407

Authors & Affiliations

Po-Chun Yeh¹, Wencan Jin², Nader Zaki², Datong Zhang², Jonathan T. Liou¹, Jerzy T. Sadowski³, Abdullah Al-Mahboob³, Jerry I. Dadap², Irving P. Herman², Peter Sutter³, and Richard M. Osgood, Jr.^1,2

¹Department of Electrical Engineering, Columbia University, New York, New York 10027, USA
²Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA
³Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA

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Vol. 91, Iss. 4 — 15 January 2015

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Images

Figure 1
(a) Side view and (b) top view of the trigonal prismatic coordination of the atoms in 2H- $WS e_{2}$ . (c) LEEM image of 1 ML $WS e_{2}$ after transfer (detector artifacts and background signal have been removed.) The inset is the corresponding optical microscope image of the same sample. LEEM images were taken at an electron energy of 1.8 eV.
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Figure 2
(a)–(d) LEED patterns at 48 eV electron energy on exfoliated $WS e_{2}$ (a) 1 ML, (b) 2 ML, (c) 3 ML, and (d) bulk after transfer to Si. The halo around the 1 ML (00) spot came from the edge deflection of electrons due to a limited sample size. (e) Measured FWHM of the (00) LEED spot for 1–3 ML $WS e_{2}$ flakes relative to that of bulk, measured at 20.5, 30, and 40 eV electron energy. The FWHM decreases with an increasing number of layers, since electrons elastically backscattered from the Si substrate are progressively decreased.
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Figure 3
(a) Brillouin zone and high-symmetry points of $WS e_{2}$ . (b) Atomic photoionization cross section for W $5 d$ and Se $4 p$ subshells as a function of ARPES photon energy [28]. At 33 eV, the cross section between W $5 d$ and Se $4 p$ has an order-of-magnitude difference. Therefore, the dominant features in our ARPES measurement are the contribution of the W $5 d$ subshell. Note that the Cooper minimum of the Se orbital is ∼50 eV. (c) Angle-integrated photoemission spectra of monolayer $WS e_{2}$ extracted from high-symmetry directions $K$ -Γ- $K$ and $M$ -Γ- $M$ , and over the full BZ, referenced with respect to the Fermi level.
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Figure 4
µ-ARPES band mapping of exfoliated $WS e_{2}$ for (a) 1 ML, (d) 2 ML, (c) 3 ML, and (f) bulk along the high-symmetry path $M - Γ - K$ in the Brillouin zone. $E = 0$ denotes the Fermi level. The overlaid white lines are our DFT-calculated band structures. The calculations do not include the effect of spin-orbit coupling. (b), (c) Corresponding EDCs and MDCs of 1 ML $WS e_{2}$ , respectively.
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Figure 5
(a)–(d) Second derivatives of the low-energy valence bands along high-symmetry points of exfoliated 1–3 ML and bulk $WS e_{2}$ , respectively, generated from the µ-ARPES band maps of Fig. 4. The white lines are the corresponding DFT-calculated bands as in Fig. 4. The dashed white lines refer to the top valence bands, which illustrate the layer-number dependence of the electronic structure near the VBM. Here the energy scale is set to zero at the VBM. (e) Layer-number-dependent VBM transition in terms of the energy difference between $K$ and Γ points. The error bars denote the standard deviation of the fittings from all six high-symmetry equivalent directions, and they are well under the detector error of ±0.10 eV. The theoretical and experimental results are plotted for comparison.
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