Researchers at Chalmers University and Montana State University have developed a theory that derives a so-called “phase crystal”, that elicits spontaneous magnetic fields and circulating currents.

The theory predicts when a phase crystal can arise, explaining previous numerical results.

Quantum mechanical states are described by a complex-valued wave function, which similar to a wave has both an amplitude and a phase. In contrast to a classical wave, the amplitude and phase of the wave function are related to purely quantum mechanical phenomena which lack an analogue in classical physics.

“A perfect example is superconductivity, which is a quantum-mechanical state that arises in certain materials due to electron pairing. The pairs have a quantum-mechanical wave function with an amplitude corresponding to the pair density, and a phase which is related to the pair momentum. The pairs move like an inviscid fluid through the material, with zero electrical resistance”, explains Chalmers’ Patric Holmvall.

“We find that the phase crystallizes and form a periodic pattern, which in turn creates a checker-board pattern of circulating currents and spontaneous magnetic fields”, says Holmvall.

Currents and magnetic fields usually only enter superconductors under external influence and perturbations, but now arise spontaneously. This is an example of spontaneous pattern-formation, where inhomogeneities which usually cost energy instead heal a destroyed system.

“We have derived the conditions for phase crystallization and use a microscopic theory to show that these conditions are satisfied in for example the material YBCO. Our theory combines and explains a number of theoretical studies reaching all the way back to the 1990s,” says Holmvall.

The researchers’ studies show that phase crystals represent a unique class of inhomogeneous ground states.

“To derive the conditions for phase crystallization, we had to generalize the commonly used Ginzburg-Landau theory, to take into account non-local interactions. Since this theory is used not just to study superconductivity, but also in, for instance, biological physics and liquid crystals, we think that new interesting phenomena might be discovered within these disciplines through a similar generalization”, says  Holmvall.