  We report transport measurements of strained InAs/In$_{x}$Ga$_{1-x}$Sb
composite quantum wells (CQWs) in the quantum spin Hall phase, focusing on the
control of the energy gap through structural parameters and an external
electric field. For highly strained CQWs with $x = 0.4$, we obtain a gap of 35
meV, an order of magnitude larger than that reported for binary InAs/GaSb CQWs.
Using a dual-gate configuration, we demonstrate an electrical-field-driven
topological phase transition, which manifests itself as a re-entrant behavior
of the energy gap. The sizeable energy gap and high bulk resistivity obtained
in both the topological and normal phases of a single device open the
possibility of electrical switching of the edge transport.
