Abstract Based on the axiom system of kinetic topology, this paper comprehensively reinterprets the transdimensional anomalous Hall effect (TDAHE) first experimentally discovered by the joint team from Nanjing University and ShanghaiTech University in rhombohedrally stacked few-layer graphene (3–15 layers, thickness 2–5 nm). This paper clearly points out that the transdimensional state is not a simple transitional dimension between two-dimensional (2D) and three-dimensional (3D) systems as recognized in traditional physics, but a dynamic steady state induced by topological winding number vacancy in the old-K recursive nesting structure. The intrinsic origin of this effect lies in the three-dimensional spiral topological circulation formed by the spin of the old-K skeleton of electrons, which are double-old-K orthogonal coupling units. This circulation spontaneously breaks time-reversal symmetry, mirror symmetry, and rotational symmetry, ultimately leading to the unique transport phenomenon of coexisting in-plane and out-of-plane orbital magnetizations. This paper strictly proves that the TDAHE is a direct experimental verification of the kinetic topology axiom system, and also the first clear experimental evidence of the dynamic steady state dominated by topological vacancies in condensed matter systems. The transdimensional behavior strictly follows the odd-even layer iron law and the old-K topological resonance condition, and all experimental characteristics such as thickness window, stacking dependence, and symmetry breaking can be derived unambiguously from the kinetic topology axioms through a complete logical chain. This study not only fills a new transdimensional branch in the family of anomalous Hall effects, but also provides a new underlying paradigm and theoretical basis for the precise design, artificial regulation, and physical property programming of topological quantum materials. Keywords kinetic topology; old-K orthogonal nesting; topological winding number conservation; kinetic entanglement degree; dimensional emergence; transdimensional effect; anomalous Hall effect; graphene; odd-even layer law
Jian Wen (Wed,) studied this question.