  Three-dimensional (3D) topological insulators (TIs) are known to carry 2D
Dirac-like topological surface states in which spin-momentum locking prohibits
backscattering. When thinned down to a few nanometers, the hybridization
between the topological surface states at the top and bottom surfaces results
in a topological quantum phase transition, which can lead to the emergence of a
quantum spin Hall phase. Here, we study the thickness-dependent transport
properties across the quantum phase transition on the example of
(Bi$_{0.16}$Sb$_{0.84}$)$_2$Te$_3$ films, with a four-tip scanning tunnelling
microscope. Our findings reveal an exponential drop of the conductivity below
the critical thickness. The steepness of this drop indicates the presence of
spin-conserving backscattering between the top and bottom surface states,
effectively lifting the spin-momentum locking and resulting in the opening of a
gap at the Dirac point. Our experiments provide crucial steps towards the
detection of quantum spin Hall states in transport measurements.
