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

Energy gap tuning and gate-controlled topological phase transition in InAs/In$_{x}$Ga$_{1-x}$Sb composite quantum wells