Thickness Dependence\nof High-Temperature (Cu,C)Ba<sub>2</sub>Ca<sub>3</sub>Cu<sub>4</sub>O<sub><i>y</i></sub> Superconducting Films with Large Irreversible\nField

(Cu,C)Ba<sub>2</sub>Ca<sub>3</sub>Cu<sub>4</sub>O<sub><i>y</i></sub> ((Cu,C)-1234) is a nontoxic, non-rare-earth-element-included\nsuperconducting material characterized by high critical temperature <i>T</i><sub>C</sub>, critical current density <i>J</i><sub>C</sub>, and irreversible field μ<sub>0</sub><i>H</i><sub>irr</sub>. The growth of superconducting (Cu,C)-1234 thin films\nby using the pulsed laser deposition (PLD) method circumvents the\nchallenges associated with high-pressure bulk crystal growth. Nonetheless,\nseveral critical aspects regarding the growth mechanism, strain effects,\nand thickness-dependent behavior in PLD-grown (Cu,C)-1234 thin films\nremain poorly understood. Here, the thickness dependence of the superconducting\nproperties in (Cu,C)-1234 thin films is reported systematically. Highly\noriented, <i>a</i>-axis (Cu,C)-1234 films on LaAlO<sub>3</sub> (LAO) (1 0 0) substrates, with thickness ranging from 25 to 500\nnm, is realized. Transport measurements reveal that films with a critical\nthickness of ∼250 nm exhibit optimized superconducting performance,\nas characterized by uniform surface morphology, high critical temperature,\nstrong pining energy, and large irreversible field. Moreover, films\nnear this optimal thickness display an increase in the irreversible\nfield μ<sub>0</sub><i>H</i><sub>irr</sub>, approximately\n9 T at 49 K (0.77<i>T</i><sub>C</sub>), which could be attributed\nto an elevated effective pinning barrier. This result paves the way\nfor the application of the (Cu,C)-1234 thin film under high magnetic\nfields.