Pseudo Jahn-Teller mechanism for symmetry-breaking phase transitions in vortex molecules

The phase transitions from a symmetric superconducting order parameter to a different or broken symmetry phase are investigated for thin mesoscopic superconductors well below the nucleation temperature. By using an effective two-state model the mechanism of these transitions has been revealed and four distinct types of transitions have been found. The symmetry-breaking phase transition has the same structure as the pseudo Jahn-Teller instability of high symmetry nuclear configurations in molecules. This analogy provides an interesting connection between real and vortex molecules. The existence of broken-symmetry phases is predicted to be strongly dependent on the size of the samples.

Figure 1

(Color online) Lower panel: LGL solutions ${ϵ}_i^{\prime }$ for a square with superconductor-vacuum boundary condition, characterized by irreps $A(m=0)$, $B(m=2)$, $E_{+}(m=1)$, and $E_{-}(m=-1)$. Upper panel: the corresponding phase diagram obtained by Monte Carlo calculations. For each phase, the vortex structure is shown schematically and the involved irreps are indicated. The number at each boundary line denotes the type of transition (Table ). In the color online version: the colors stand for the winding number of the central vortex: 0 (yellow), 1 (green), 2 (blue), and $-1$ (red).

Figure 2

Diagram of thermodynamically stable phases (solid lines) for the effective two-state model (7) as function of the parameters from Eqs. (8, 9). 1, 2 are pure phases and $1+2$ is the mixed one.

Figure 3

Upper panel: adiabatic potential for two nondegenerate electronic terms of a square molecule in the case of weak (dashed lines) and strong (solid lines) pseudo Jahn-Teller effect. Lower panel: temperature dependence of the normalized coefficient of admixure of the excited $\left(A\right)$ state close to the $B\to B+A$ transition at $\Phi =4.5{\Phi }_0$ (Fig. 1) evaluated by Monte Carlo calculations and the pseudo Jahn-Teller effect using the correspondence relations (16). The numbers in the inset denote the dimension of the basis set in the Monte Carlo calculations.