  Quantum ground states on the non-trivial side of a topological quantum
critical point (TQCP) have unique properties that make them attractive
candidates for quantum information applications. A recent example is provided
by s-wave superconductivity on a semiconductor platform, which is tuned through
a TQCP to a topological superconducting (TS) state by an external Zeeman field.
Despite many attractive features of TS states, TQCPs themselves do not break
any symmetries, making it impossible to distinguish the TS state from a regular
superconductor in conventional bulk measurements. Here we show that for the
semiconductor TQCP this problem can be overcome by tracking suitable bulk
transport properties across the topological quantum critical regime itself. The
universal low-energy effective theory and the scaling form of the relevant
susceptibilities also provide a useful theoretical framework in which to
understand the topological transitions in semiconductor heterostructures. Based
on our theory, specific bulk measurements are proposed here in order to
characterize the novel TQCP in semiconductor heterostructures.
