Current-Voltage Characteristics of the Normal Metal-Insulator-PT-Symmetric Non-Hermitian Superconductor Junction as a Probe of Non-Hermitian Formalisms

We study theoretically a junction consisting of a normal metal, PT-symmetric non-Hermitian superconductor, and an insulating thin layer between them. We calculate current-voltage characteristics for this junction using left-right and right-right bases and compare the results. We find that in the left-right basis, the Andreev-scattered particles move in the opposite direction compared with the right-right basis and conventional Andreev scattering. This leads to profound differences in current-voltage characteristics. Based on this and other signatures, we argue that the left-right basis is not applicable in this case. Remarkably, we find that the growth and decay with time of the states with imaginary energies in the right-right basis are equilibrated.

Figure 1

Scattering of a right-moving electron (black solid circle) from the normal metal at the interface with PTS through a thin insulating barrier at $x=0$. It scatters back into the normal metal as an electron (amplitude $b_1$) and, due to Andreev scattering, as a hole ($a_1$). It transfers into PTS as an electronlike quasiparticle ($c_1$) and a hole-like quasiparticle ($d_1$). The spectrum of the normal metal is shown in green. The real part of the spectrum of PTS is shown in red, and the imaginary part is shown with the dotted blue line.

Figure 2

Averaged density of electrons with respect to momentum $k$, with red lines for momenta at real energies, and blue lines for momenta at imaginary energies (see Fig. 1). (a) $0\le ⟨{\psi }_{\uparrow }^{†}(k){\psi }_{\uparrow }(k){⟩}_{\mathrm{RR}}\le 1$; (b) $⟨{\psi }_{\uparrow }^{†}(k){\psi }_{\uparrow }(k){⟩}_{\mathrm{LR}}$ has divergences at exceptional points, $E=0$, and in the region with $E\in \Im$; see the inset.

Figure 3

Current-voltage characteristics of N-I-PTS junction in (a) the RR basis and (b) the LR basis. The green dots correspond to no barrier ($I=0$) and almost no superconducting pairing. The blue and red dots correspond to $I=0$ and $I=10$, respectively, and a noticeable effect of superconducting pairing. Remarkably, Andreev scattering has opposite effects in different bases: (a) enhancing current and (b) suppressing current. The sign of the effect in (a) is the same as in conventional N-I-S junctions.