  Transition-metal dichalcogenides (TMDs) show unique physical, optical, and
electronic properties. The known phases of TMDs are 2H and 3R in bulk form, 1T
and associated reconstructions, and 1H in monolayer form. This paper reports a
hypothetical phase, 9R, that may exist in TMDs (Mo, W)(S, Se, Te)$_2$, meeting
both dynamical stability and elastic stability criteria. 9R phase has the same
space group as 3R, $i.e.$ rhombohedral $R3m$ without inversion symmetry, and
has 9 layers in a conventional unit cell. We find that 9R has an energy within
1 meV per formula unit of 3R and can be energetically favored by a particular
strain condition. We further calculate the electronic, elastic, piezoelectric,
Raman, and second-harmonic generation signatures of 9R TMDs and compare them
with the corresponding 2H and 3R phases. 9R has similar properties to 3R but
shows distinctive Raman peaks in the low-frequency regime, improved
piezoelectric properties, and unique band splitting arising from layer coupling
at the conduction band minimum. These distinct properties make 9R an attractive
candidate for applications in piezotronics and valleytronics.
