The ability to directly observe electronic band structure in modern nanoscale field-effect devices could transform understanding of their physics and function. One could, for example, visualize local changes in the electrical and chemical potentials as a gate voltage is applied. One could also study intriguing physical phenomena such as electrically induced topological transitions and many-body spectral reconstructions. Here we show that submicron angle-resolved photoemission (-ARPES) applied to two-dimensional (2D) van der Waals heterostructures affords this ability. In graphene devices, we observe a shift of the chemical potential by 0.6 eV across the Dirac point as a gate voltage is applied. In several 2D semiconductors we see the conduction band edge appear as electrons accumulate, establishing its energy and momentum, and observe significant band-gap renormalization at low densities. We also show that -ARPES and optical spectroscopy can be applied to a single device, allowing rigorous study of the relationship between gate-controlled electronic and excitonic properties.Angle resolved photoemission spectroscopy (ARPES), in which the energy and momentum of photoemitted electrons are measured from a sample subjected to a spectrally narrow ultraviolet or X-ray excitation, is a powerful technique that yields the momentum-dependent single-electron band structure and chemical potential in a solid with essentially no assumptions. It probes only electron states near the surface, and so cannot be applied to conventional semiconductor devices. It is, however, very effective when applied to 2D materials and has been used extensively to study the bands in graphene 1 , monolayer transition metal dichalcogenides 2-7 , and others 8,9 . Furthermore, µ-ARPES (with a micron-scale beam spot) can be performed 10 on 2D heterostructures (2DHSs) 11 made of stacked exfoliated 2D materials 12-14 , suggesting the possibility of monitoring electronic structure during actual device operation. We demonstrate here that momentum-resolved electronic spectra can indeed be obtained during reversible electrostatic gating, enabling direct visualization of chemical potential shifts and band structure changes controlled by the gate electric field.A limitation of ARPES is that it probes only occupied electron states, and so a semiconductor must first be electron-doped in order to obtain a signal from the conduction band. The usual approach is to deposit alkali metal atoms 1-7,15 which act as an n-type dopant, but this has several limitations: the density cannot be controlled accurately; it can only be reversed by high-temperature annealing; it introduces disorder through the random positions of the dopants; and it chemically perturbs the electronic structure in ways that are hard to calculate. Electrostatic doping has none of these disadvantages, and the accessible carrier densities are most relevant to practical devices.We first validate our technique using graphene, and then go on to apply it to the 2D transition metal dichalcogenide (TMD) sem...

We present an overview of the ONETEP program for linear-scaling density functional theory (DFT) calculations with large basis set (planewave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, ONETEP is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchangecorrelation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with ONETEP provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. ONETEP has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

In van der Waals heterostructures, the relative alignment of bands between layers, and the resulting band hybridisation, are key factors in determining a range of electronic properties. This work examines these effects for heterostructures of transition metal dichalcogenides (TMDs) and hexagonal boron nitride (hBN), an ubiquitous combination given the role of hBN as an encapsulating material. By comparing results of density functional calculations with experimental angle-resolved photoemission spectroscopy (ARPES) results, we explore the hybridisation between the valence states of the TMD and hBN layers, and show that it introduces avoided crossings between the TMD and hBN bands, with umklapp processes opening ‘ghost’ avoided crossings in individual bands. Comparison between DFT and ARPES spectra for the MoSe2/hBN heterostructure shows that the valence bands of MoSe2 and hBN are significantly further separated in energy in experiment as compared to DFT. We then show that a novel scissor operator can be applied to the hBN valence states in the DFT calculations, to correct the band alignment and enable quantitative comparison to ARPES, explaining avoided crossings and other features of band visibility in the ARPES spectra.