The quantum Hall effect(QHE),which is usually observed in two-dimensional systems,was predicted theoretically and observed experimentally in three-dimensional(3 D)topological semimetal.However,there are some inconsist...The quantum Hall effect(QHE),which is usually observed in two-dimensional systems,was predicted theoretically and observed experimentally in three-dimensional(3 D)topological semimetal.However,there are some inconsistencies between the theory and the experiments showing the theory is imperfect.Here,we generalize the theory of the 3 D QHE of Fermi arcs in Weyl semimetal.Through calculating the sheet Hall conductivity of a Weyl semimetal slab,we show that the 3 D QHE of Fermi arcs can occur in a large energy range and the thickness dependences of the QHE in different Fermi energies are distinct.When the Fermi energy is near the Weyl nodes,the Fermi arcs give rise to the QHE which is independent of the thickness of the slab.When the Fermi energy is not near the Weyl nodes,the two Fermi arcs form a complete Fermi loop with the assistance of bulk states giving rise to the QHE which is dependent on the sample thickness.We also demonstrate how the band anisotropic terms influence the QHE of Fermi arcs.Our theory complements the imperfections of the present theory of 3 D QHE of Fermi arcs.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11974168)(L.S.)。
文摘The quantum Hall effect(QHE),which is usually observed in two-dimensional systems,was predicted theoretically and observed experimentally in three-dimensional(3 D)topological semimetal.However,there are some inconsistencies between the theory and the experiments showing the theory is imperfect.Here,we generalize the theory of the 3 D QHE of Fermi arcs in Weyl semimetal.Through calculating the sheet Hall conductivity of a Weyl semimetal slab,we show that the 3 D QHE of Fermi arcs can occur in a large energy range and the thickness dependences of the QHE in different Fermi energies are distinct.When the Fermi energy is near the Weyl nodes,the Fermi arcs give rise to the QHE which is independent of the thickness of the slab.When the Fermi energy is not near the Weyl nodes,the two Fermi arcs form a complete Fermi loop with the assistance of bulk states giving rise to the QHE which is dependent on the sample thickness.We also demonstrate how the band anisotropic terms influence the QHE of Fermi arcs.Our theory complements the imperfections of the present theory of 3 D QHE of Fermi arcs.
