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We demonstrate through high-fidelity particle-in-cell (PIC) simulations a simple approach for efficiently generating $20+$GeV electron beams with the necessary charge, energy spread, and emittance for use as an injector in a future linear collider or a next generation XFEL. A high quality injected bunch is generated by self-focusing an unmatched electron driver in a nonlinear plasma wakefield. Over pump depletion distances, the drive beam dynamics and self-loading effects lead to high energy, low-energy spread output beams. For plasma densities of ${10}^{18}\mathrm{c}{\mathrm{m}}^{-3}$, PIC simulation results indicate that self-injected beams with $0.52\mathrm{n}\mathrm{C}$charge can be accelerated to 20 GeV with projected core energy spreads of $\lesssim 1\%$, normalized slice emittances of $110\mathrm{n}\mathrm{m}$, peak normalized brightness of $\gtrsim {10}^{19}\mathrm{A}/{\mathrm{m}}^2/{\mathrm{rad}}^2$, and transfer efficiencies of $\gtrsim 44\%$. 

Abstract Stacking two semiconducting transition metal dichalcogenide (MX₂) monolayers to form a heterobilayer creates a new variety of semiconductor junction with unique optoelectronic features, such as hosting long-lived dipolar interlayer excitons. Despite many optical, transport, and theoretical studies, there have been few direct electronic structure measurements of these junctions. Here, we apply angle-resolved photoemission spectroscopy with micron-scale spatial resolution (µARPES) to determine the band alignments in MoSe₂/WSe₂heterobilayers, usingin-situelectrostatic gating to electron-dope and thus probe the conduction band edges. By comparing spectra from heterobilayers with opposite stacking orders, that is, with either MoSe₂or WSe₂on top, we confirm that the band alignment is type II, with the valence band maximum in the WSe₂and the conduction band minimum in the MoSe₂. The overall band gap isE_G= 1.43 ± 0.03 eV, and to within experimental uncertainty it is unaffected by electron doping. However, the offset between the WSe₂and MoSe₂valence bands clearly decreases with increasing electron doping, implying band renormalisation only in the MoSe₂, the layer in which the electrons accumulate. In contrast,µARPES spectra from a WS₂/MoSe₂heterobilayer indicate type I band alignment, with both band edges in the MoSe₂. These insights into the doping-dependent band alignments and gaps of MX₂heterobilayers will be useful for properly understanding and ultimately utilizing their optoelectronic properties.