Superfluidity or supersolidity as a Consequence of Off-diagonal Long-range Order

TL;DR

This paper derives the phenomena of superfluidity and supersolidity from off-diagonal long-range order in Bose systems, clarifying conditions under which these effects occur, especially in solid helium.

Contribution

It provides a general derivation linking off-diagonal long-range order to superfluid phenomena and shows that supersolidity requires defects, challenging previous assumptions.

Findings

NCRI and superfluidity are consequences of ODLRO in Bose systems.

No ODLRO is found in certain variational wavefunctions for solid helium.

NCRI cannot occur without defects in solid helium.

Abstract

We present a general derivation of Hess-Fairbank effect or non-classical rotational inertial (NCRI), i.e. the refusal to rotate with its container, as well as the quantization of angular momentum, as consequences of off-diagonal long-range order (ODLRO) in an interacting Bose system. Afterwards, the path integral formulation of superfluid density is re-derived without ignoring the centrifugal potential. Finally and in particular, for a class of variational wavefunctions used for solid helium, treating the constraint of single-valuedness boundary condition carefully, we show that there is no ODLRO and, especially, demonstrate explicitly that NCRI cannot be possessed in absence of defects, even though there exist zero-point motion and exchange effect.