Unconventional superconducting phase diagram of monolayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>WTe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>

The existence of a quantum critical point (QCP) and fluctuations around it are believed to be important for understanding the phase diagram in unconventional superconductors such as cuprates, iron pnictides, and heavy fermion superconductors. However, the QCP is usually buried deep within the superconducting dome and is difficult to investigate. The connection between quantum critical fluctuations and superconductivity remains an outstanding problem in condensed matter. Here combining both electrical transport and Nernst experiments, we explicitly demonstrate the onset of superconductivity at an unconventional QCP in gate-tuned monolayer tungsten ditelluride <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mo>(</a:mo><a:msub><a:mi>WTe</a:mi><a:mn>2</a:mn></a:msub><a:mo>)</a:mo></a:mrow></a:math>, with features incompatible with the conventional Bardeen-Cooper-Schrieffer scenario. The results lead to a superconducting phase diagram that is distinguished from other known superconductors. Two distinct gate-tuned quantum phase transitions are observed at the ends of the superconducting dome. We find that quantum fluctuations around the QCP of the underdoped regime are essential for understanding how the monolayer superconductivity is established. The unconventional phase diagram we report here illustrates a previously unknown relation between superconductivity and QCP.