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Visualizing electrostatic gating effects in two-dimensional heterostructures


The ability to directly monitor the states of electrons in modern field-effect devices—for example, imaging local changes in the electrical potential, Fermi level and band structure as a gate voltage is applied—could transform our understanding of the physics and function of a device. Here we show that micrometre-scale, angle-resolved photoemission spectroscopy1,2,3 (microARPES) applied to two-dimensional van der Waals heterostructures4 affords this ability. In two-terminal graphene devices, we observe a shift of the Fermi level across the Dirac point, with no detectable change in the dispersion, as a gate voltage is applied. In two-dimensional semiconductor devices, we see the conduction-band edge appear as electrons accumulate, thereby firmly establishing the energy and momentum of the edge. In the case of monolayer tungsten diselenide, we observe that the bandgap is renormalized downwards by several hundreds of millielectronvolts—approaching the exciton energy—as the electrostatic doping increases. Both optical spectroscopy and microARPES can be carried out on a single device, allowing definitive studies of the relationship between gate-controlled electronic and optical properties. The technique provides a powerful way to study not only fundamental semiconductor physics, but also intriguing phenomena such as topological transitions5 and many-body spectral reconstructions under electrical control.

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Fig. 1: Visualizing electrostatic gating of monolayer graphene.
Fig. 2: Layer-number-dependent CBE in WSe2.
Fig. 3: Electrostatic gating of monolayer WSe2.
Fig. 4: Renormalization of the bandgap and comparison with optical spectroscopy.

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All data presented in this paper are available at Additional data related to this paper may be requested from the authors.


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Our research into monitoring gated electronic structure changes is supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. Initial development of the samples and technique was done under award DE-SC0002197 via D.H.C. and P.V.N. Optical spectroscopy and partial sample fabrication were supported by award DE-SC0018171 (via X. Xu and N.P.W.). P.V.N. and J.K. received partial support from NSF Materials Research Science and Engineering Centers (MRSEC) award 1719797. N.R.W. and N.D.M.H. were supported through UK Engineering and Physical Sciences Research Council (EPSRC) award EP/P01139X/1. N.C.T., N.Y. and A.J.G. were supported through EPSRC studentships (EP/M508184/1 and EP/R513374/1). X. Xia was supported by a University of Warwick studentship. N.D.M.H. and G.C.C. were supported by the Winton Programme for the Physics of Sustainability. G.C.C. was supported by the Cambridge Trust European Scholarship. Computing resources were provided by the Darwin Supercomputer of the University of Cambridge High Performance Computing Service, the Scientific Computing Research Technology Platform of the University of Warwick, and the UK national high-performance computing service, ARCHER, via the UKCP consortium (EP/P022561/1).

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Authors and Affiliations



N.R.W., X. Xu and D.H.C. conceived and supervised the project. P.V.N., J.K. and N.P.W. fabricated the samples. N.C.T., N.R.W., P.V.N., X. Xia, A.J.G., V.K., A.G. and A.B. collected µ-ARPES data. N.C.T., N.R.W. and P.V.N. analysed µ-ARPES data (with input from A.B.). N.P.W. acquired photoluminescence data. N.D.M.H., N.Y. and G.C.C. performed the band-structure calculations. D.H.C., N.R.W., P.V.N. and X. Xu wrote the paper with input from all authors.

Corresponding authors

Correspondence to Xiaodong Xu, David H. Cobden or Neil R. Wilson.

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Extended data figures and tables

Extended Data Fig. 1 Fabrication of a gated heterostructure.

Diagram showing the process for fabricating WSe2 device 1, with associated micrographs. Scale bars are 15 µm unless otherwise noted. PC, polycarbonate; PDMS, polydimethylsiloxane.

Extended Data Fig. 2 Distortion-free, uniform band shifting in electrostatically gated graphene.

ac, Constant energy slices through a graphene Dirac cone at the stated gated voltages and electron energies relative to the Dirac point (black dot). No substantial change is seen on varying VG, implying that the spectrum is not distorted by electrostatic/space charge effects. The width of each panel represents 4 Å−1. d, Bottom, slice of energy E versus in-plane momentum k|| along the zone boundary, through points K and K′ (shown at the top), in gated graphene at VG = +3.35 V. Scale bar, 0.5 Å−1. The spectrum is symmetric about point M, as illustrated by the consistent Dirac-point energy (dashed line) between K and K′. These measurements are from the same device as Fig. 3, from a region in which the graphene was on top of the 1L WSe2 (which produces the faint bands at binding energies of around 2 eV) but still electrostatically gated. This shows that the electric field from the gate does not distort the measured graphene spectrum in any direction in momentum space.

Extended Data Fig. 3 Extracted graphene Fermi velocity versus gate voltage.

We calculated the Dirac-point energy and Fermi velocity from E − k slices (some of which are shown in Fig. 1) near the graphene K point, by analysing the band dispersions. We extracted momentum-distribution curves (MDCs; that is, intensity as a function of momentum I(k) at constant energy), and found the positions of the branches on each side of the Dirac cone by fitting Gaussian peaks. After repeating this process for each MDC within |E − EF| < 1 eV, we fit a straight line of the same absolute slope to each side, yielding the Dirac point, ED, from where the lines cross and the Fermi velocity, vF, from their slope. In cases in which one side was much more intense than the other, we used only the more intense side to find vF. The extracted velocity is here plotted against gate voltage. Evidence has previously been reported36 of a reduction in vF of up to 20% near ED in graphene films at low doping levels (roughly 1 × 1012 cm−2). This corresponds to a subtle distortion of the bands at ED, which the spectrometer at Elettra does not as yet have the resolution to probe, and could not be detected by the above procedure which assumes purely linear dispersion. Note that the variations seen in this figure can be explained by systematic errors, taking into account experimental limitations such as the very weak emission from one branch and the sensitivity to the exact alignment of the momentum slice with the Dirac point.

Extended Data Fig. 4 Uniform band shifting in electrostatically gated 2L WSe2.

Constant energy maps of electrostatically gated 2L WSe2 at VG = +8 V: left, at a binding energy of 1.555 eV, which here corresponds to the valence-band maximum; and right, near the Fermi energy at a binding energy of 0.025 eV. It can be seen that the CBE is the same at points Q and Q′, implying that the gate field does not substantially distort the spectrum in this case either.

Extended Data Fig. 5 CBEs in monolayer MoS2, MoSe2 and WS2.

a, Diagram of a device, with graphene contact grounded and gate voltage applied to the graphite back gate, as in Fig. 2a. b, Diagram showing the bands near point K, at zero gate voltage (left) and at a gate voltage that exceeds the threshold voltage to bring the Fermi level to the CBE (right). CBM, conduction-band maximum; VBM, valence-band maximum. ce, Energy-momentum slices through point for monolayer MoS2, MoSe2 and WS2. Scale bars, 0.3 Å−1.

Extended Data Fig. 6 Photocurrent and SPEM maps of a WSe2 heterostructure device.

a, Diagram of the device, with the graphene contact grounded and a gate voltage applied to the graphite back gate. b, c, Optical (b) and SPEM (c) images of WSe2 device 1, with 1L, 2L and 3L regions identified. Dashed lines trace boundaries of the graphite gate (red) and the graphene contact (black). d, Photocurrent image acquired simultaneously with the SPEM image in panel c. Scale bars, 5 µm.

Extended Data Fig. 7 Gate-induced band shifts and photocurrent in monolayer WSe2.

a, ΔEΓ versus VG for WSe2 monolayer device 2. b, VG − ΔEΓ/e versus VG. c, Current from gate to ground versus VG. The grey shaded regions indicate the threshold regions in which the WSe2 becomes conducting. See Methods for discussion.

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Nguyen, P.V., Teutsch, N.C., Wilson, N.P. et al. Visualizing electrostatic gating effects in two-dimensional heterostructures. Nature 572, 220–223 (2019).

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