  Seven ultra low-mass and small-radius white dwarfs (LSPM J0815+1633, LP
240-30, BD+20 5125B, LP 462-12, WD J1257+5428, 2MASS J13453297+4200437, and
SDSS J085557.46+053524.5) have been recently identified with masses ranging
from $\sim$0.02 $M_\odot$ to $\sim$0.08 $M_\odot$ and radii from $\sim$ 4270 km
to 10670 km. The mass-radius measurements of these white dwarfs pose challenges
to traditional white dwarf models assuming they are mostly made of nuclei
lighter than $^{56}$Fe. In this work we consider the possibility that those
white dwarfs are made of heavier elements. Due to the small charge-to-mass
ratios in heavy elements, the electron number density in white dwarf matter is
effectively reduced, which reduces the pressure with additional contributions
of lattice energy and electron polarization corrections. This consequently
leads to white dwarfs with much smaller masses and radii, which coincide with
the seven ultra low-mass and small-radius white dwarfs. The corresponding
equation of state and matter contents of dense stellar matter with and without
reaching the cold-catalyzed ground state are presented, which are obtained
using the latest Atomic Mass Evaluation (AME 2020). Further observations are
necessary to unveil the actual matter contents in those white dwarfs via, e.g.,
spectroscopy, asteroseismology, and discoveries of other ultra low-mass and
small-radius white dwarfs.
