Physics Paradigm Challenge

A new material has been found that allows two 'mutually exclusive' states of matter to exist in the same place at once.

March 31, 2026

Original Paper

Tomonaga-Luttinger liquid and charge-density wave in a quasi-one-dimensional material

Jing Li, Guo-Wei Yang, Bai-Zhuo Li, Yi Liu, Si-Qi Wu, Ji-Yong Liu, Jin-Ke Bao, Xiaoxian Yan, Hua-Xun Li, Jia-Xin Li, Jia-Lu Wang, Yun-Lei Sun, Yi-Ming Lu, Jia-Yi Lu, Yi-Qiang Lin, Hui Xing, Chao Cao, Hao Jiang, Yang Liu, Guang-Han Cao, Hai-Qing Lin

arXiv · 2603.28186

The Takeaway

In certain one-dimensional systems, electrons are supposed to choose between two specific patterns (a liquid-like state or a crystal-like wave), but never both. Scientists discovered a crystal where these two opposite behaviors coexist and intertwine, defying a fundamental rule of how matter behaves in small spaces.

From the abstract

In one-dimensional (1D) electron systems, the Fermi liquid state breaks down due either to electron interactions, which results in a Tomonaga-Luttinger liquid (TLL) state, or to Peierls instability, which leads to an insulating charge-density-wave (CDW) phase. In general, these two phenomena are mutually exclusive, and their coexistence remains elusive in real materials. Here, we report the discovery of a new quasi-1D material, Cs$_{1-\delta}$Cr$_3$S$_3$, which unexpectedly exhibits coexistence