  When three particles in three dimensions interact with a short-range
potential fine-tuned to an infinite scattering length, they form an infinite
sequence of loosely bound states obeying discrete scale invariance known as
Efimov states. Here we show that analogous states are formed by three charged
particles carrying two equal charges and one opposite charge in one, two, and
three dimensions without any fine-tuning. Our finding is based on the
Born-Oppenheimer approximation, where an effective inverse-square attraction is
induced as a consequence of the dipole-charge interaction between a
hydrogenlike heavy-light atom and a far-separated heavy particle. Because the
resulting Efimovian states emerge toward the second or higher dissociation
threshold, they are to be realized as quasibound states and may be observed by
exciting hydrogen molecular ions and trions in excitonic systems. We also
consider the same system but with a logarithmic Coulomb potential relevant to
quantum vortices in two-dimensional superfluids, where the Efimovian states are
shown to emerge as genuine bound states toward the first dissociation
threshold.
