  The ability to fine-tune band gap and band inversion in topological materials
is highly desirable for the development of novel functional devices. Here we
propose that the electronic properties of a free-standing nanomembrane of
topological crystalline insulator (TCI) SnTe and Pb$_{1-x}$Sn$_x$(Se,Te) are
highly tunable by engineering elastic strain and controlling membrane
thickness, resulting in tunable band gap and giant piezoconductivity. Membrane
thickness governs the hybridization of topological electronic states on
opposite surfaces, while elastic strain can further modulate the hybridization
strength by controlling the penetration length of surface states. We propose a
frequency-resolved infrared photodetector using force-concentration induced
inhomogeneous elastic strain in TCI nanomembrane with spatially varying width.
The predicted tunable band gap accompanied by strong spin-textured electronic
states will open up new avenues for fabricating piezoresistive devices,
thermoelectrics, infrared detectors and energy-efficient electronic and
optoelectronic devices based on TCI nanomembrane.
