Intersecting topological nodal ring and nodal wall states in superhard superconductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>FeB</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math>
Feng Zhou, Ying Liu, Jianhua Wang, Minquan Kuang, Tie Yang, Hong Chen, Xiaotian Wang, Zhenxiang Cheng
Abstract
Novel materials with both topological nontrivial states and superconductivity have attracted considerable attention in recent years. Single-crystal ${\mathrm{FeB}}_{4}$ was recently synthesized and demonstrated to exhibit superconductivity at temperatures lower than 2.9 K, and its nanoindentation hardness was measured to be 65 GPa. In this study, based on first-principles calculations and the low-energy $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ effective Hamiltonian, we found that this $Pnnm$-type superhard ${\mathrm{FeB}}_{4}$ superconductor hosts topological behaviors with intersecting nodal rings (INRs) in the ${k}_{x}=0$ and ${k}_{z}=0$ planes and nodal wall states in the ${k}_{y}=\ensuremath{\pi}$ and ${k}_{z}=\ensuremath{\pi}$ planes. The observed surface drum-head-like (D-H-L) states on the [100] and [001] surfaces confirmed the presence of INR states in this system. According to our investigation results, ${\mathrm{FeB}}_{4}$, with its superconductivity, superior mechanical behaviors, one-dimensional and two-dimensional topological elements, and D-H-L surface states, is an existing single-phase target material that can be used to realize the topological superconducting state in the near future.