  Monolayer 1T'-WTe2 is a quantum spin Hall insulator with a gapped bulk and
gapless helical edge states persisting to temperatures around 100 K. Recent
studies have revealed a topological-to-trivial phase transition as well the
emergence of an unconventional, potentially topological superconducting state
upon tuning the carrier concentration with gating. However, despite extensive
studies, the effects of gating on the band structure and the helical edge
states have not yet been established. In this work we present a combined
low-temperature STM and first principles study of back-gated monolayer 1T'-WTe2
films grown on graphene. Consistent with a quantum spin Hall system, the films
show well-defined bulk gaps and clear edge states that span the gap. By
directly measuring the density of states with STM spectroscopy, we show that
the bulk band gap magnitude shows substantial changes with applied gate
voltage, which is contrary to the na\"ive expectation that a gate would rigidly
shift the bands relative to the Fermi level. To explain our data, we carry out
density functional theory and model Hamiltonian calculations which show that a
gate electric field causes doping and inversion symmetry breaking which
polarizes and spin-splits the bulk bands. Interestingly, the calculated spin
splitting from the effective Rashba-like spin-orbit coupling can be in the tens
of meV for the electric fields in the experiment, which may be useful for
spintronics applications. Our work reveals the strong effect of electric fields
on the bulk band structure of monolayer 1T'-WTe2, which will play a critical
role in our understanding of gate-induced phenomena in this system.
