Superconductivity without diamagnetism in systems with broken time-reversal symmetry

We analyze the phase diagram of superconductors with a broken time-reversal symmetry in an external magnetic field. Ferromagnetism (broken time-reversal symmetry) originates either from the electron spin or the intrinsic angular momentum of Cooper pairs (chiral $p$-wave superconductors such as ${\text{Sr}}_2{\text{RuO}}_4$). In addition to the Meissner and the mixed states, the phase diagram includes also the cryptoferromagnetic state with intrinsic domain structure independent of sample shape and size. The cryptoferromagnetic state is not diamagnetic and can be detected by observation of magnetization curves predicted in the present analysis.

Figure 1

(Color online) Phase diagram for various values of the reduced lower critical field $h_{c1}$: (a) $h_{c1}\to \infty$; (b) $h_{c1}=2$; and (c) $h_{c1}=0.83$. The lighter shaded (yellow) area is the cryptoferromagnetic state. The darker shaded (blue) area is the mixed state. The rest is the Meissner state. The horizontal and the vertical arrows show the processes of field cooling across the SC critical temperature of spin and orbital SFs, respectively.

Figure 2

(a) Magnetic field dependencies of $\zeta =\zeta \left(h_0\right)$ (solid line) and $\delta =\delta \left(h_0\right)$ (dashed line), and (b) magnetization curves are shown at different values of parameter $w$. Vertical lines correspond to critical fields above which the intrinsic domain structure collapses.