Fig. 1 | Communications Physics

Fig. 1

From: Non-hermitian topology as a unifying framework for the Andreev versus Majorana states controversy

Fig. 1

Exceptional points. a Sketch of a generic normal-superconductor (NS) junction formed when a proximitized nanowire with inhomogeneous chemical potential and pairing, \(\mu (x)\) and \(\Delta (x)\), is coupled to a reservoir at \(x=0\). Such junction is a natural host for Majorana zero modes. These can emerge even below the critical Zeeman field \(B\ < \ {B}_{{\rm{c}}}\) as a result of an exceptional point (EP) bifurcation in the complex non-Hermitian spectrum, that in turn develops when the two Majorana components of a Bogoliubov mode (i.e. an Andreev level originally located at \(\pm E\) for \(B\) = 0) couple to the reservoir asymmetrically (\({\Gamma }_{0}^{{\rm{L}}}\ > \ {\Gamma }_{0}^{{\rm{R}}}\)) due to their spatial non-locality. Purple/light blue wave functions correspond to the spatially-separated, left (L) and right(R) Majorana components of the Bogoliubov mode, respectively. b Representation of the eigenvalues of the non-Hermitian Hamiltonian of the open system in the complex plane. The eigenvalues evolve as a function of some external parameter \(B\) until they coalesce at a so-called EP and then bifurcate into two purely imaginary eigenvalues with different decay rates to the reservoir, \({\Gamma }_{\pm }\) (quasi-bound Majorana zero modes). Inset shows the evolution of real and imaginary eigenenergies across the EP

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