Bosonic Phases across the Superconductor-Insulator Transitions in Infinite-Layer Samarium Nickelate

Superconductivity arises from the global phase coherence of Cooper pairs. Modulation of phase coherence leads to quantum phase transitions, serving as an important tool for studying unconventional superconductivity. Here, we demonstrate bosonic phases across the superconductor-insulator transition in infinite-layer nickelate superconducting films by the control of spatially periodic network patterns. Magnetoresistance oscillations with a periodicity of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mi>h</a:mi> <a:mo>/</a:mo> <a:mn>2</a:mn> <a:mi>e</a:mi> </a:mrow> </a:math> provide direct evidence of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mn>2</c:mn> <c:mi>e</c:mi> </c:mrow> </c:math> Cooper pairing in nickelates. The phase transition is predominantly driven by enhanced superconducting fluctuations, and Cooper pairs are involved in charge transport across the transition. Notably, we observe two types of anomalous metallic phases, emerging, respectively, at finite magnetic fields and down to zero magnetic field. They can be characterized by bosonic excitations, suggesting the dynamic roles of vortices in the ground states. Our work establishes nickelates as a key platform for investigating the rich landscape of bosonic phases controlled via the phase coherence of Cooper pairs.