Halperin's research is focused on condensed matter physics, with a particular attention to ultra-low temperature investigations of quantum liquids and solids, notably liquid and solid 3He (the light isotope of helium), unconventional superconductivity, magnetic compounds, highly porous materials including aerogels, porous glasses and cements. His acoustic and nuclear magnetic resonance discoveries include transverse sound and order parameter collective modes in superfluid 3He, quantum size effects in nano-particles, and for solid 3He, the first observation of nuclear magnetic order. Halperin constructed a Pomeranchuk refrigerator, and with this device in 1974 he reached the lowest temperature achieved at that time in liquid 3He, at a temperature of 0.0007 K. He invented a
thermodynamic temperature scale leading to his discovery of
antiferromagnetism in solid 3He. This was the first observation of magnetic order in a nuclear system. and confirmed by Halperin and coworkers. within a framework of the theory of electron superconductivity by Bardeen, Cooper, and Schrieffer (1957). According to an accepted point of view at the time, the direction of polarization of sound waves in liquids must be aligned with their direction of propagation, so-called longitudinal sound. However, Halperin and coworkers, notably with his student Yoonseok Lee, discovered that sound with transverse polarization propagates robustly in superfluid 3He, rather similar to the well-known propagation of electromagnetic waves of light. This was the first demonstration of propagating transverse sound waves in any liquid. They also discovered that these transverse sound waves in 3He exhibit Faraday rotation of their polarization in the presence of a magnetic field. The analogous behavior for light waves was discovered by
Michael Faraday in 1845. These observations, replicated in superfluid helium, are in close agreement with theoretical predictions by Moores and Sauls. The phenomenon is closely related to an as yet experimentally unconfirmed prediction by Landau (1957) that transverse sound waves might propagate in normal liquid 3He in its degenerate Fermi liquid state at temperatures above those of its superfluid phases. Superconductivity in some quantum materials, such as the compound
UPt3, is thought to be closely related to
superfluidity in 3He, exhibiting chiral symmetry and breaking time reversal symmetry. A new area of research in quantum fluids opened with the discovery of impurity phases of superfluid 3He by Parpia and by Halperin described theoretically by Sauls. These are superfluid phases of liquid 3He imbibed in highly porous silica aerogel. It was found that the stability of A and B superfluids could be engineered with anisotropy introduced with strain in the aerogel, positive strain favoring stabilization of the chiral A-phase and negative strain stabilizing the isotropic B-phase. ==Awards and honors==