The topological states of matter and topological materials have been attracting extensive interests as one of the frontier topics in condensed matter physics and materials science since the discovery of quantum Hall effect in 1980s. So far all the topological phases such as integer quantum Hall effect and topological insulators are characterized by integer topological invariants. None is a half integer or fractional. Here we propose a type of semimetals which hosts a single cone of Wilson fermions. The Wilson fermions possess linear dispersion near the Dirac point, but break the chiral or parity symmetry such that an unpaired Dirac cone can be realized on a lattice. In order to avoid the fermion doubling problem, the chiral symmetry or parity symmetry must be broken explicitly if the hermiticity, locality and translational invariance all hold. We find that the system can be classified by the relative homotopy group, and a half-integer topological invariant. We term the nontrivial quantum phase as quantum anomalous semimetal. The work opens the door towards exploring novel states of matter with fractional topological charge.

自 1980 年代发现量子霍尔效应以来，物质的拓扑态和拓扑材料作为凝聚态物理和材料科学的前沿课题之一，一直受到广泛关注。到目前为止，整数量子霍尔效应和拓扑绝缘体等所有拓扑相都具有整数拓扑不变量的特征。None 是半整数或小数。在这里，我们提出了一种半金属，其中包含单个威尔逊费米子锥。威尔逊费米子在狄拉克点附近具有线性色散，但破坏了手性或奇偶对称性，因此可以在晶格上实现不成对的狄拉克锥。为了避免费米子倍增问题，如果隐秘性、局部性和平移不变性都成立，则必须明确打破手性对称性或奇偶性对称性。我们发现系统可以通过相对同伦群和半整数拓扑不变量进行分类。我们将非平凡的量子相称为量子反常半金属。这项工作为探索具有分数拓扑电荷的新物质状态打开了大门。