Superfluidity—the frictionless flow of a liquid analogous to lossless current flow in a superconductor—is well known in liquid 4He, but “supersolidity”—coexistence of crystalline order and superflow—seems counterintuitive. However, quantum mechanics allows atomic exchange even in a solid, especially if the atoms are light and the interatomic potential is weak. This makes helium the most quantum of solids and the possibility of supersolidity in helium was suggested more than 40 years ago [1]. Despite earlier searches, it was not until 2004 that Kim and Chan’s torsional oscillator experiments [2, 3] provided convincing evidence of supersolidity.

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Jack Sarfatti first predicted supersolidity in He 4 thin films in 1969
"Destruction of Superflow in Unsaturated 4He Films and the Prediction of a New Crystalline Phase of 4He with Bose-Einstein Condensation"], ''Physics Letters'', Vol 30A, No 5, Nov 1969, pp 300–301.