Lev Landau was the physicist whose theory of superfluidity Feynman explained using quantum mechanics.
Landau developed a phenomenological theory of liquid helium-4 in 1941. His two-fluid model describes helium II as a mixture of a frictionless superfluid component and a normal component carrying entropy. The theory also introduced excitations called phonons and rotons to explain the liquid's unusual behavior.
Feynman later pursued a more microscopic account of superfluid helium, examining how quantum statistics, particle interactions, and quantized vortices could produce the observed effects. His work complemented rather than simply replaced Landau's approach: Landau's theory was highly successful macroscopically, while Feynman sought a deeper quantum-mechanical foundation.
A common mix-up is to credit Feynman with creating the entire theory of superfluidity. Experimental discoveries involved other researchers, including Pyotr Kapitza, and earlier theoretical contributions came from Fritz London and Laszlo Tisza. Landau received the 1962 Nobel Prize in Physics for his theories of condensed matter, including superfluidity.