Dual-frequency wave funnel induced by continuous Landau modes in topolectrical circuits

In recent years, non-Hermitian systems and artificial gauge fields have made possible realization of continuous Landau modes (CLMs), which exhibit Gaussian spatial envelopes and continuous spectra in the complex plane. However, existing studies on CLMs have mostly focused on the analysis of band structures in two-dimensional (2D) systems; it is a challenge to achieve spatial energy localization, especially multipoint energy concentration in the form of a wave funnel effect. In this work, we propose and experimentally demonstrate a circuit-based design framework that successfully realizes CLMs in one-dimensional and 2D topolectrical circuits. By introducing a spatial gradient of resistors, we implement non-Hermiticity and pseudomagnetic field, thereby establishing the necessary conditions for CLMs. More importantly, through carefully engineered inductor-capacitor coupling, we observe a dual-frequency wave funnel phenomenon, where wave energy becomes strongly concentrated at two distinct locations along the boundary with the lowest loss. Our results reveal an extension of Landau physics in discrete artificial systems and offer an effective approach for achieving multipoint spatial energy localization in circuit platforms.