Magnetic properties of the charged Anderson-Brinkman-Morel state: Absence of ${\mathit{H}}_{\mathit{c}1}$

Magnetic properties of the charged Anderson-Brinkman-Morel state are investigated theoretically as a special case of time-reversal-symmetry-breaking superconductivity. The magnetic field is expressed as a superposition of the one from the supercurrent ${\mathbf{j}}^{\mathit{s}}$(r) and that from the magnetic moment l(r) due to the internal motion of each Cooper pair. This procedure enables us to get rid of the paradox in zero external field that the moments are ordered (l=const) with no magnetic field nor supercurrent, leading to a natural conclusion that there is indeed a field due to l(r) which is screened almost completely by ${\mathbf{j}}^{\mathit{s}}$(r). If the system size is large enough compared with the penetration depth, the direction l(r) changes gradually toward the surface and the current ${\mathbf{j}}^{\mathit{s}}$(r) flows over the bulk. This means that the system is essentially nonuniform and forms a coreless vortex in zero external field. As for the magnetization process, the lattice of coreless vortices grows from the infinitesimal external field without ${\mathit{H}}_{\mathit{c}1}$ (i.e., no Meissner state), which is subsequently followed by the first-order transition to the lattice with cores. Finally, the transition to the normal state occurs at ${\mathit{H}}_{\mathit{c}2}$ enhanced over that of the conventional type-II superconductor due to the field l. An example of the magnetization curve is also given.