  We investigate the macroscopic effects of charge density waves (CDW) and
superconductivity in layered superconducting systems with broken lattice
inversion symmetry (allowing for piezoelectricity) such as two dimensional (2D)
transition metal dichalcogenides (TMD). We work with the low temperature time
dependent Ginzburg-Landau theory and study the coupling of lattice distortions
and low energy CDW collective modes to the superconducting order parameter in
the presence of electromagnetic fields. We show that superconductivity and
piezoelectricity can coexist in these singular metals. Furthermore, our study
indicates the nature of the quantum phase transition between a commensurate CDW
phase and the stripe phase that has been observed as a function of applied
pressure.
