  Quantum Griffiths singularity (QGS) reveals the profound influence of
quenched disorder on the quantum phase transitions, characterized by the
divergence of the dynamical critical exponent at the boundary of the vortex
glass-like phase, named as quantum Griffiths phase. However, in the absence of
vortices, whether the QGS can exist under parallel magnetic field remains a
puzzle. Here we study the magnetic field induced superconductor-metal
transition in ultrathin crystalline PdTe2 films grown by molecular beam
epitaxy. Remarkably, the QGS emerges under both perpendicular and parallel
magnetic field in 4-monolayer PdTe2 films. The direct activated scaling
analysis with a new irrelevant correction has been proposed, providing
important evidence of QGS. With increasing film thickness to 6 monolayers, the
QGS disappears under perpendicular field but persists under parallel field, and
this discordance may originate from the differences in microscopic processes.
Our work demonstrates the universality of parallel field induced QGS and can
stimulate further investigations on novel quantum phase transitions under
parallel magnetic field.
