Real non-Hermitian energy spectra without any symmetry

Non-Hermitian models with real eigenenergies are highly desirable for their stability.Yet,most of the currently known ones are constrained by symmetries such as PT-symmetry,which is incompatible with realizing some of the most exotic non-Hermitian phenomena.In this work,we investigate how the non-Hermitian skin effect provides an alternative route towards enforcing real spectra and system stability.We showcase,for different classes of energy dispersions,various ansatz models that possess large parameter space regions with real spectra,despite not having any obvious symmetry.These minimal local models can be quickly implemented in non-reciprocal experimental setups such as electrical circuits with operational amplifiers.