Title: Non-Hermitian zero-energy pinning of Andreev and Majorana bound states in superconductor-semiconductor systems

Abstract: The emergence of Majorana bound states in finite length superconductor-semiconductor hybrid systems has been predicted to occur in the form of oscillatory energy levels with parity crossings around zero energy. Each zero-energy crossing is expected to produce a quantized zero-bias conductance peak but several studies have reported conductance peaks pinned at zero energy over a range of Zeeman fields, whose origin, however, is not clear. In this work we consider superconducting systems with spin-orbit coupling under a Zeeman field and demonstrate that non-Hermitian effects, due to coupling to ferromagnet leads, induce zero-energy pinning of Majorana and trivial Andreev bound states. We find that this zero-energy pinning effect occurs due to the formation of non-Hermitian spectral degeneracies known as exceptional points, whose emergence can be controlled by the interplay of non-Hermiticity, the applied Zeeman field, and chemical potentials. Moreover, depending on the non-Hermitian spatial profile, we find that non-Hermiticity changes the single point Hermitian topological phase transition into a flattened zero energy line bounded by exceptional points from multiple low energy levels. This seemingly innocent change notably enables a gap closing well below the Hermitian topological phase transition, which can be in principle simpler to achieve. Furthermore, we reveal that the energy gap separating Majorana and trivial Andreev bound states from the quasicontinuum remains robust for the values that give rise to the zero-energy pinning effect. While reasonable values of non-Hermiticity can be indeed beneficial, very strong non-Hermitian effects can be detrimental as it might destroy superconductivity. Our findings can be therefore useful for understanding the zero-energy pinning of trivial and topological states in Majorana devices.