Direct Observation of the Transition from the Conventional Superconducting State to the $\pi$ State in a Controllable Josephson Junction

We measure the full supercurrent-phase relation of a controllable $\pi$ junction around the transition from the conventional 0 state to the $\pi$ state. We show that around the transition the Josephson supercurrent-phase relation changes from $I_{sc}\simeq I_c\sin (\phi )$ to $I_{sc}\simeq I_c\sin (2\phi )$. This implies that, around the transition, two minima in the junction free energy exist, one at $\phi =0$ and one at $\phi =\pi$, whereas only one minimum exists at the 0 state (at $\phi =0$) and at the $\pi$ state (at $\phi =\pi$). Theoretical calculations based on the quasiclassical theory are in good agreement with the observed behavior.

Figure 1

Controllable $\pi$ SQUID. Two controllable $\pi$ junctions form the weak links of a dc SQUID. Each junction consists of a coplanar Nb-Ag-Nb SNS junction with clean interfaces of which the normal region is coupled to the control channel. The electron distribution in the normal region is modified using $V_c$ causing the transition to a $\pi$ state at sufficiently large values of $V_c$.

Figure 2

Voltage over the SQUID (from contacts $A$ to $B$ in Fig. 1) at a bias current slightly larger than $I_{c,\mathrm{S}\mathrm{Q}\mathrm{U}\mathrm{I}\mathrm{D}}$ as a function of the ${\varphi }_{\mathrm{e}\mathrm{x}\mathrm{t}}$ for different values of $V_c$. The amplitudes of the two grey curves are multiplied by $1/10$. Around $V_{c,\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}}=602\mu \mathrm{V}$, a doubling in periodicity of the voltage oscillations is observed.

Figure 3

Experimental free energy of junction 2 as a function of ${\phi }_2$, $W({\phi }_2)$, obtained from the data presented in Fig. 2, Eq. (1), and Eq. (2).

Figure 4

Supercurrent carrying density of states $J(E,\phi )$ for three different values of the macroscopic phase difference $\phi$, using $\Delta /E_T=0.52$ with $\Delta$ the superconducting gap of the $S$ electrodes and $E$ the energy with respect to the Fermi level. The positive contributions in $J(E,\phi )$ shift to lower energies at higher values of $\phi$.

Figure 5

Theoretical critical current as a function of $\phi$ for the top junction of the device shown in Fig. 1.