  Here we establish a combined electronic phase diagram of isoelectronic
FeSe1-xSx (0.19 > x > 0.0) and FeSe1-yTey (0.04 < y < 1.0) single crystals. The
FeSe1-yTey crystals with y = 0.04 - 0.30 are grown by a hydrothermal
ion-deintercalation (HID) method. Based on combined experiments of the specific
heat, electrical transport, and angle-resolved photoemission spectroscopy, no
signature of the tetragonal-symmetry-broken transition to orthorhombic
(nematic) phase is observed in the HID FeSe1-yTey samples, as compared with the
FeSe1-xSx samples showing this transition at Ts. A ubiquitous dip-like
temperature dependence of the Hall coefficient is observed around a
characteristic temperature T* in the tetragonal regimes, which is well above
the superconducting transition. More importantly, we find that the
superconducting transition temperature Tc is positively correlated with the
Hall-dip temperature T* across the FeSe1-xSx and FeSe1-yTey systems, suggesting
that the tetragonal background is a fundamental host for the superconductivity.
