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roduction Superconductivity, the capability of quantum materials to lose all electrical resistance due to coherent pairing of electrons (formation of Cooper pairs) below a certain critical temperature Tc, ranks among the most fascinating phenomena in condensed-matter physics. The potential for applications of superconductors (i.e., magnetically levitated trains, dissipationless energy transportation, and ultraprecision scientific instruments) is large; however, applications have been severely limited by the relatively low Tc of conventional superconductors. An experimental development, which has attracted increasing attention for over a decade, is that exceptional Tc could be boosted at the interface between two dissimilar materials,1–3 where electrons are confined to a narrow potential well. This appears to be understandable intuitively since superconductivity confined in a two-dimensional (2D) interface may benefit from the two constituent building blocks of heterostructures. From the point of view of fundamental research, emergent superconductivity at the interface may exhibit extraordinary phenomena similar to the layered cuprates and iron-based superconductors,4,5 thereby providing unprecedented opportunities to unravel the microscopic mechanisms of high-Tc superconductivity therein. In addition, the modified fluctuations, electronic correlations and spin–orbit coupling in

reduced dimensionality may drive the emergence of novel quantum phenomena in a unique way that can be employed to pursue more promising technologies.6 The emergence and modification of superconductivity at the interface are the focus of this article. We review superconducting interfaces in various heterostructures that could generate unexpectedly high-Tc superconductivity. These systems include oxide heterostructures with strong interfacial bonding,1,2 as well as other quantum materials that are currently being intensively explored, such as monolayer FeSe films on oxide substrates3 and van der Waals heterostructures.7,8 Canonical high-Tc superconductors include the perovskite-type layered copper oxides5,9 and the iron pnictides,10 routinely considered to be unconventional,5,11 in which the phonons (lattice vibrations) that act as the pairing glue in classical superconductors are believed to be either irrelevant or unimportant. We attempt to compare the two categories and shed light on several implications for unconventional high-Tc superconductors.

Superconducting heterostructures A theoretical prototype of interface superconductivity can be traced back to the idea of surface superconductivity advocated by V.L. Ginzburg in early 1964.12 Experimental work has followed the advent of advanced thin-film deposition techniques, including molecular beam epitaxy (MBE) and pulsed laser

Can-Li Song, Department of Physics, Tsinghua University, China; [email protected] Xu-Cun Ma, Department of Physics, Tsinghua University, China; [email protected] Qi-Kun Xue, Department of Physics, Tsinghua University, China; [email protected].