The superconducting critical temperature of H₃S ranks among the highest measured, at 203 K. This impressive value stems from a singularity in the electronic density-of-states, induced by a flat-band region that consists of saddle points. The peak sits right at the Fermi level, so that it gives rise to a giant electron–phonon coupling constant. In this work, we show how atomic orbital interactions and space group symmetry work in concert to shape the singularity. The body-centered cubic Brillouin Zone offers a unique 2D hypersurface in reciprocal space: fully connecting squares with two different high-symmetry points at the corners, Γ and H, and a third one in the center, N. Orbital mixing leads to the collapse of fully connected 1D saddle point lines around the square centers, due to a symmetry-enforced s-p energy inversion between Γ and H. The saddle-point states are invariably nonbonding, which explains the unconventionally weak response of the superconductor’s critical temperature to pressure. Although H₃S appears to be a unique case, the theory shows how it is possible to engineer flat bands and singularities in 3D lattices through symmetry considerations.

中文翻译：

---

高温超导体 H3S 中的对称形状奇点


H ₃ S 的超导临界温度是测量到的最高温度之一，为 203 K。这个令人印象深刻的值源于电子态密度的奇点，这是由平带区域引起的，该区域由鞍点。该峰正好位于费米能级，因此它产生了巨大的电子声子耦合常数。在这项工作中，我们展示了原子轨道相互作用和空间群对称性如何协同作用来塑造奇点。体心立方布里渊区在倒易空间中提供了一个独特的二维超曲面：完全连接正方形，其角点有两个不同的高对称点 Г 和 H，中心有第三个点 N。轨道混合导致坍缩围绕正方形中心的完全连接的一维鞍点线，由于 Γ 和 H 之间对称强制的 s-p 能量反转。鞍点状态总是非键合的，这解释了超导体的临界温度对压力的非常规弱响应。尽管 H ₃ S 似乎是一个独特的情况，但该理论表明如何通过对称性考虑来设计 3D 晶格中的平带和奇点。