Recently, the research groups of Prof. Zhang Xiangdong and Prof. Sun Houjun of BIT have made significant progress in non-Hermitian topological circuits and higher-order skin effect, and the relevant research results were published in the Nature Communications. The research work was supported by the National Natural Science Foundation of China and other national key research and development programs.

Compared with Hermitian systems, non-Hermitian systems can show some unique behaviors, such as the aggregation of state distribution in one direction, that is, skin effect. In addition, topological states can also be constructed by designing parameters in non-Hermitian systems. Recent theoretical studies show that when skin effect and topological state exist at the same time, there will be hybrid effect, that is, hybrid higher-order skin topological effect. This hybrid effect is particularly interesting, which shows a new high-dimensional state that does not exist in Hermitian or non-topological systems. Its characteristic is that topological localization allows non-Hermitian skin effect to only act on special topological modes, which greatly enhances the richness of high-dimensional robustness, goes beyond the usual higher-order topological phenomenon, and leads to the re-expression of the edge theorem of higher-order topological body, and it is suitable for new higher-order skin and topological interactions.

Due to the complexity of the system, it is necessary to construct patterns that can show topological localization in one spatial direction, and make these topological patterns show skin effect in the other direction. This makes experimental observation very difficult, so this phenomenon has never been observed experimentally.

Recently, the research team of BIT designed a non-Hermitian classical circuit and observed the hybrid higher-order skin-topological effect for the first time. The researchers realize 2D and 3D hybrid higher-order skin topological states through the topological circuit platform, and make the skin effect selectively act only on the topological boundary mode, not on the phantom. The experiment is carried out on specially designed non-reciprocal 2D and 3D topological circuit networks. It shows how irreversible pumping and topological localization interact dynamically to form various novel states, such as 2D skin topology, 3D skin topology, topological hybrid states, and 2D and 3D higher-order non-Hermitian skin states. The circuit design method is highly versatile and scalable.

Fig.1

(a) 2D skin topological effect experimental sample diagram

(b) 2D second-order skin effect experimental sample diagram

(c) 2D skin topological effect energy distribution

(d) 2D second-order skin effect energy distribution

Fig. 1 shows the design circuit and measurement results of 2D skin topological effect. It can be clearly seen from Fig. 1 (c) that a large voltage amplitude appears in the upper left corner and the lower right corner, and the amplitude of the protocell neutron lattice is not equal. For example, in the upper left corner of the circuit, only the protocell sublattice d has a large amplitude, while the adjacent sublattices a and b have a very small amplitude. These non-uniform distributions on different sublattices show that the angular modes are caused by the non-reciprocal skin effect of one-dimensional topological modes along the X and Y directions. Due to the lack of complete destructive interference, they are locally non-reciprocal. The spontaneous breaking of the symmetry of the seed lattice and the resulting non-reciprocity are common in the topological mode, which leads to the mixed skin topological mode. In Fig. 2 (d), the angular mode is represented by the large amplitude voltage in the lower right corner of the circuit. The voltages at different sublattices in the lower right corner are almost the same, which is a typical second-order skin effect.

Fig. 2

(a) and (b) 3D skin topological effect experimental sample diagram

(c) 3D higher-order skin effect experimental sample diagram

(d) 3D skin topological effect energy distribution

(e) 3D higher-order skin effect energy distribution

Fig. 2 shows the design circuit and measurement results of 3D skin topological effect, and its voltage distribution characteristics are similar to the 2D results. In other words, the 3D skin topological hybrid effect is also confirmed by the designed circuit experiments. Relevant work was published in the Nature Communications [NAT commun 12, 7201 (2021)]. The co-first authors are Zou Deyuan (post-doctor) and associate professor Chen Tian of BIT, the co-authors include He Wenjing (master) and Bao Jiacheng (doctor) of BIT and Ching Hua Lee of National University of Singapore, and associate professor Chen Tian, Prof. Zhang Xiangdong and Prof. Sun Houjun are the co-corresponding authors

Paper link: https://www.nature.com/articles/s41467-021-26414-5