  We grew single crystals of the recently discovered heavy fermion
superconductor UTe2, and measured the resistivity, specific heat and
magnetoresistance. Superconductivity (SC) was clearly detected at Tsc=1.65K as
sharp drop of the resistivity in a high quality sample of RRR=35. The specific
heat shows a large jump at Tsc indicating strong coupling. The large Sommerfeld
coefficient, 117mJ K-2mol-1 extrapolated in the normal state and the
temperature dependence of C/T below Tsc are the signature of unconventional SC.
The discrepancy in the entropy balance at Tsc between SC and normal states
points out that hidden features must occur. Surprisingly, a large residual
value of the Sommerfeld coefficient seems quite robust (gamma_0/gamma ~ 0.5).
The large upper critical field Hc2 along the three principal axes favors
spin-triplet SC. For H // b-axis, our experiments do not reproduce the huge
upturn of Hc2 reported previously. This discrepancy may reflect that Hc2 is
very sensitive to the sample quality. A new perspective in UTe2 is the
proximity of a Kondo semiconducting phase predicted by the LDA band structure
calculations.
