Anomalous transition temperature oscillations in the Larkin-Ovchinnikov-Fulde-Ferrell state

We consider Aharonov-Bohm (AB) effect at normal-metal-inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell superconducting state transition. It is shown that magnetic flux can increase the transition temperature and AB oscillations can have the double-peak structure at one period. Expressions for fluctuational heat capacity and persistent current are calculated for a thin ring and a cylinder. We also discuss the effect of fluctuations interaction in the nonuniform states in the vicinity of the superconducting transition.

Figure 1

Thin superconducting cylinder and rind.

Figure 2

One period of $\left[T_c\left(\Phi \right)-T_c\right]/T_c$ oscillations in magnetic flux for a set of $\varphi =QR=\left(50,50.5,50.7\right)$, where $\left|\beta \right|/2a{Q}^2{R}^4=0.01$. See Eq. (8) in the text.

Figure 3

Magnetic-flux dependence of specific heat of the ring for $Q\zeta /\sqrt{2}=10$. Parameter $p=\sqrt{2}\pi R/\zeta =\left[1.0,1.17,2.65,3.14\right]$ measures the ratio of rings’ radius to the correlation length.

Figure 4

Magnetic-flux dependence of specific heat of the cylinder for $Q\zeta /\sqrt{2}=10$. Parameter $p=\sqrt{2}\pi R/\zeta =\left[0.42,0.75,1.12,1.9\right]$ measures the ratio of rings’ radius to the correlation length.

Figure 5

Persistent current of the ring measured in units $I_0=4\pi T_c/{\Phi }_0$ for $Q\zeta /\sqrt{2}=10$ as a function of magnetic flux. Parameter $p=\sqrt{2}\pi R/\zeta =\left[1.2,1.2,1.33,2.0\right]$.

Figure 6

Magnetic-flux dependence of persistent current of the cylinder measured in units $I_0=2T_{c}L/R{\Phi }_0$ for $Q\zeta /\sqrt{2}=10$ and large radius. Here $p=\sqrt{2}\pi R/\zeta =\left[2.54,3.0,3.16,3.4\right]$.

Figure 7

Magnetic-flux dependence of persistent current of the cylinder measured in units $I_0=2T_{c}L/R{\Phi }_0$ for $Q\zeta /\sqrt{2}=10$ and small radius. Here $p=\sqrt{2}\pi R/\zeta =\left[0.12,0.14,0.2,0.25\right]$.

Figure 8

Persistent current of the cylinder as a function of magnetic flux measured in units $I_0=2T_{c}L/R{\Phi }_0$. For the case of $Q\zeta /\sqrt{2}=0.1$ and $q=R\sqrt{\sqrt{2}Q/\zeta }=\left[0.35,0.4,0.45,0.5\right]$.

Figure 9

First-order fluctuation correction diagram.