Non-hermitian topology in multiterminal superconducting junctions

Abstract

Recent experimental advancements in dissipation control have yielded significant insights into non-hermitian Hamiltonians for open quantum systems. Of particular interest are the topological characteristics exhibited by these non-hermitian systems, that arise from exceptional points - distinct degeneracies unique to such systems. In this study, we focus on Andreev bound states in multiterminal Josephson junctions with non-hermiticity induced by normal metal or ferromagnetic leads. By investigating several systems of different synthetic dimensions and symmetries, we predict fragile and stable non-hermitian topological phases in these engineered superconducting systems.

Figures (3)

• Figure 1: (a) Schematic of a double quantum dot two-terminal junction where a normal lead adds a non-hermiticity in one of the dots. (b) Real- and imaginary part of the eigenvalues of the effective non-hermitian Hamiltonian, $\epsilon_{\pm,1/2}$ as functions of phase difference $\phi$. Solid lines are for the symmetric case where EPs emerge (Parameters: $\Gamma_{\rm L/R} = r = 1$, $\Gamma_{\rm N} = 1$, $\epsilon_{\rm L/R} = 0$). Dotted lines are for the non-symmetric case where there are no EPs (Parameters: $\Gamma_{\rm R} = 1$, $\Gamma_{\rm L} = 1.2$, $\Gamma_{\rm N}= 1$, $r = 1$, $\epsilon_{\rm L/R} = 0$). (c) Energy spectrum $\epsilon_{\pm,1/2}(\phi)$ in the complex plane for both parameter configurations with EP and no EP shown in panel (b).
• Figure 2: (a) Schematic of a double quantum dot three-terminal junction where a normal metal lead adds a non-hermiticity to one of the dots. (b) Complex ABS energies $\epsilon_{\pm,1/2}$ of the effective non-hermitian Hamiltonian depending on the phase $\phi_{1}$ for two parameters configurations. Solid lines correspond to parameters $\Gamma_{\rm L/R/M1/M2} = \Gamma_{\rm N} = 1$, $\epsilon_{1/2} = 0$, $r = 2$ and $\phi_2 = 2.1$ whereas dotted lines correspond to $\Gamma_{\rm L} = 1.4$, $\Gamma_{\rm R}= 1.1$, $\Gamma_{\rm M1} = 1.0$, $\Gamma_{\rm M2} = 0.5$, $\Gamma_{\rm N} = 1$, $\epsilon_1 = 0.1$, $\epsilon_2 = 0.3$, $r = 2$ and $\phi_2 = 1.75$. The positions of the EPs are indicated by the solid and dashed vertical line. (c) The energy spectrum $\epsilon_{-,1/2}(\phi_1)$ for fixed values of $\phi_2$ indicated in the legend. The system goes from two gapped bands, to exhibiting an EP where both eigenvalues coalesce, to a winding where the two bands form a combined loop. (d) The same as in (c) except for the other parameter configuration.
• Figure 3: (a) Schematic of a double quantum dot four-terminal junction where one dot is coupled to a ferromagnet inducing spin-rotation symmetry breaking and non-hermiticity. (b) An exceptional ring where the real-part of the eigenenergies $\epsilon_{\pm}^{\Uparrow,\Downarrow}$ is degenerate inside the ring (marked by blue) whereas the eigenvalues coalesce on the ring (marked by red). (Parameters chosen: $\Gamma_{0,1,2,3} = 1$, $\Gamma_{+} = 0.15$, $\Gamma_- = 0.05$, $\epsilon_{1/2} = 1$, $r = 1.5$). The line puncturing the exceptional ring along the $\phi_3$-direction shows the parameters used for the sweep in panel (c). (c) Energy spectrum $\epsilon_{\pm}^\Uparrow(\phi_3)$ and $\epsilon_{\pm}^\Downarrow(\phi_3)$ for the eigenenergies closest to zero (real) energy of the effective non-hermitian Hamiltonian for the line trace in (b) with phases $\phi_1 =1.96$ and $\phi_2 =5.1$.