The investigations of crystalline two-dimensional (2D) superconducting systems have become a frontier of condensed matter physics and materials science due to the emergence of novel quantum phenomena. With the reduced dimensionality, the fluctuations, the disorder effect, and the intricate interactions between electrons, spins, and orbits may impose dramatic effects on the quantum behavior of 2D superconductors. This Account reviews the recent research progress in 2D crystalline superconducting films and interfacial superconducting systems, focusing on the quantum phase transitions, emergent quantum states, and unconventional superconductivity. Six topics are introduced, including quantum Griffiths singularity, anomalous metallic state, rotational-symmetry-broken superconducting state, Ising superconductivity, interfacial high-transition temperature superconductivity, and interface-induced superconductivity. As a paradigm of quantum phase transition in 2D superconductors, the superconductor-insulator/metal transition (SIT/SMT) has been intensively studied over the last three decades, which highlights the prominent effect of disorder and quantum fluctuations. The quantum Griffiths singularity (QGS) and the anomalous metallic state revealed recently go beyond the framework of the SIT/SMT at the zero-temperature limit. The QGS of SMT was first discovered in trilayer Ga films and subsequently confirmed in various 2D superconductors. The main characteristic of QGS is a divergent critical exponent, in stark contrast to a fixed critical exponent of the conventional SIT/SMT. The anomalous metallic state, characterized by a saturating resistance at ultralow temperatures, is detected as an intervening metallic ground state that disrupts the SIT/SMT. The charge-2e quantum oscillations and the absence of the Hall effect indicate that the anomalous metallic states are dominated by the bosonic Cooper pairs instead of fermionic quasiparticles. Furthermore, the 2D systems could host various kinds of interactions and ordered states, which may be intertwined with the superconductivity. Originating from the interplay between multiple orders and strong electronic correlations, the rotational symmetry breakings are observed as in the infinite-layer nickelate superconductors, revealing the unconventional superconductivity. Arisen from the strong Zeeman-type spin-orbit coupling, the Ising superconductivity is discovered in diverse 2D superconducting systems, which features a large in-plane critical magnetic field exceeding the Pauli limit. Through interface engineering or heterostructure fabrication, the superconductivity, even high transition temperature (high-T-c) superconductivity, could be achieved at the interfaces between different materials. Moreover, the interface effect and the nontrivial topology could be introduced through interface engineering or heterostructure fabrication incorporating superconductors, insulators, semiconductors, normal metals, topological materials, etc. Consequently, the unconventional high-T-c superconductivity and the potential topological superconductivity are achieved in the interfacial superconducting systems. The experimental progress discussed in this Account suggests that the crystalline 2D and interface superconductors may offer a promising platform to study quantum phase transitions and unconventional superconducting states.
