Non-Bloch $\mathrm{PT}$ symmetry and topological phase transition in one-dimensional nonreciprocal topolectrical circuits

We propose a feasible scheme to implement a one-dimensional non-Hermitian Su-Schrieffer-Heeger model with long-range hopping using the electrical circuit system. We investigate the admittance spectrum and node voltage density distribution of the current system. The non-Bloch $\mathrm{PT}$ symmetry and its breaking can be effectively demonstrated using the saddle point theory and the ratio of complex eigenenergy. It is important to note that the phase boundary of non-Bloch $\mathrm{PT}$ symmetry is solely determined by the long-range hopping strengths. Moreover, we observe that the system exhibits zero-admittance topological end and gap modes with varying strength relations between intercell and long-range hopping. We further represent the winding number phase diagram, which reveals the distinct topological phase transition from $w=\pm 1$ to $w=0$. Our work provides a method to simulate nonreciprocal topolectrical circuits and contributes to understanding the interplay between topology and non-Hermiticity.