  The layered honeycomb magnet $\alpha$-RuCl$_3$ is the most promising
candidate for a Kitaev quantum spin liquid (KQSL) that can host charge-neutral
Majorana fermions. Recent studies have shown significant sample dependence of
thermal transport properties, which are a key probe of Majorana quasiparticles
in the KQSL state, highlighting the importance of preparing high-quality single
crystals of $\alpha$-RuCl$_3$. Here, we present a relatively simple and
reliable method to grow high-quality single crystals of $\alpha$-RuCl$_3$. We
use a two-step crystal growth method consisting of a purification process by
chemical vapor transport (CVT) and a main crystal growth process by
sublimation. The obtained crystals exhibit a distinct first-order structural
phase transition from the monoclinic ($C2/m$) to the rhombohedral ($R\bar{3}$)
structure at $\sim150$ K, which is confirmed by the nuclear quadrupole
resonance spectra with much sharper widths than previously reported. The Raman
spectra show the absence of defect-induced modes, supporting the good
crystallinity of our samples. The jumps in the thermal expansion coefficient
and specific heat at the antiferromagnetic (AFM) transition at 7.6-7.7 K are
larger and sharper than those of previous samples grown by the CVT and Bridgman
methods and do not show any additional AFM transitions at 10-14 K due to
stacking faults. The longitudinal thermal conductivity in the AFM phase is
significantly larger than previously reported, indicating a very long mean free
path of heat carriers. All the results indicate that our single crystals are of
superior quality with good crystallinity and few stacking faults, which
provides a suitable platform for studying the Kitaev physics.
