The Berry curvature (BC)—a quantity encoding the geometric properties of the electronic wavefunctions in a solid—is at the heart of different Hall-like transport phenomena, including the anomalous Hall and the non-linear Hall and Nernst effects. In non-magnetic quantum materials with acentric crystalline arrangements, local concentrations of BC are generally linked to single-particle wavefunctions that are a quantum superposition of electron and hole excitations. BC-mediated effects are consequently observed in two-dimensional systems with pairs of massive Dirac cones and three-dimensional bulk crystals with quartets of Weyl cones. Here, we demonstrate that in materials equipped with orbital degrees of freedom local BC concentrations can arise even in the complete absence of hole excitations. In these solids, the crystals fields appearing in very low-symmetric structures trigger BCs characterized by hot-spots and singular pinch points. These characteristics naturally yield giant BC dipoles and large non-linear transport responses in time-reversal symmetric conditions.

Berry 曲率 (BC)——一个编码固体中电子波函数几何特性的量——是不同类霍尔传输现象的核心，包括反常霍尔和非线性霍尔和能斯特效应。在具有非中心晶体排列的非磁性量子材料中，BC 的局部浓度通常与单粒子波函数有关，单粒子波函数是电子和空穴激发的量子叠加。因此，在具有成对的大质量狄拉克锥体和具有四重外尔锥体的三维块状晶体的二维系统中观察到了 BC 介导的效应。在这里，我们证明了在配备轨道自由度的材料中，即使在完全没有空穴激发的情况下，局部 BC 浓度也会出现。在这些固体中，出现在极低对称结构中的晶体场触发以热点和奇异夹点为特征的 BC。这些特性自然会在时间反演对称条件下产生巨大的 BC 偶极子和大的非线性传输响应。