  The B20-type cobalt germanide CoGe was investigated by measuring the specific
heat, resistivity, and $^{59}$Co nuclear magnetic resonance (NMR). We observed
a phase transition at $T_Q=13.7$ K, evidenced by a very narrow peak of the
specific heat and sharp changes of the nuclear spin-spin ($T_2^{-1}$) and
spin-lattice ($T_1^{-1}$) relaxation rates. The fact that the entropy release
is extremely small and the Knight shift is almost independent of temperature
down to low temperatures as anticipated in a paramagnetic metal indicates that
the $T_Q$ transition is of non-magnetic origin. In addition, we detected a
crossover scale $T_0\sim30$ K below which the resistivity and the NMR linewidth
increase, and $T_1^{-1}$ is progressively distributed in space, that is, a
static and dynamical spatial inhomogeneity develops. While the order parameter
for the $T_Q$ transition remains an open question, a group-theoretical analysis
suggests that the finite electric quadrupole density arising from the low local
site symmetry at cobalt sites could drive the crystal symmetry lowering from
the P2$_1$3 symmetry that is commensurate to the R3 symmetry with an
incommensurate wavevector, which fairly well accounts for the $T_Q$ transition.
The quadrupole-order-driven commensurate-incommensurate phase transition may be
another remarkable phenomenon arising from the structural chirality inherent in
the noncentrosymmetric B20 family.
