Superconducting gap

The gap feature in a superconducting single-particle excitation spectrum. In a simple BCS model, excitations have $E_{\mathbf{k}}=\sqrt{{\xi }_{\mathbf{k}}^2+|\Delta (\mathbf{k}){|}^2}$. The superconducting gap function specifies the pairing amplitude and its phase; its magnitude need not be constant, and nodes can leave gapless excitations.

A complex momentum-dependent pairing amplitude. Its crystal-symmetry transformation, nodes and relative signs distinguish candidate superconducting states. Magnitude-sensitive spectra alone generally do not establish all relative signs; phase-sensitive superconducting gap experiments test them through interference.

An experiment converting the relative phase of a superconducting pairing amplitude into a measurable interference or flux signal. Orthogonal-face Josephson junctions and tricrystal rings are examples. Junction asymmetry, trapped flux, loop inductance and comparison geometries are important controls.

Compare superconducting phase information from different crystal directions rather than only measuring the gap magnitude. Orthogonal-face junctions and a tricrystal half-flux experiment can test sign changes of a candidate d-wave gap. Junction properties, trapped flux and loop inductance must be controlled; a measured half-flux signal needs its actual device model.

A ring crossing three appropriately oriented grain-boundary junctions tests a superconducting pairing sign pattern. An odd total intrinsic $\pi$ offset frustrates integer phase matching and can favor a half-flux state. Actual enclosed flux also depends on loop inductance and junction currents; the measurement requires controls against ordinary trapped flux.^[ref]