Higher-order quantum magnetic inductions in chiral topological materials

The classic magnetic induction effect is usually considered in electric circuits or conductor coils. In this paper, we propose quantum induction effects induced by the Berry curvature in homogenous solids. Two different types of quantum inductions are identified in the higher order of a magnetic field. They are closely related to the magnetic-field-induced anomalous velocity proportional to the Berry curvature so that both quantum inductions become significantly enhanced near the Weyl points. Further, we propose an ac-magnetic-field measurement to detect quantum induction effects and distinguish them from classical induction.

Figure 1

CI and QI in CoSi. (a) Chiral crystal structure of CoSi with cubic point group symmetry $T$. (b) Brillouin zone (BZ) and high-symmetry lines. (c) Bulk band structure and CI of CoSi. (d) $C_{\alpha \alpha }$ as a function of Fermi energy ${\varepsilon }_F$. (e) Bulk band structure and second QI of CoSi. (f) $Q_{\alpha \alpha }^{\left(2\right)}$ as a function of ${\varepsilon }_F$. The first QI $Q_{\alpha }^{\left(1\right)}=0$ due to TRS.

Figure 2

CI and QIs in MnSi. (a) Crystal and ferromagnetic structure of MnSi under an external magnetic field $\mathit{B}$. (b) Bulk band structure and CI of ferromagnetic MnSi. (c) $C_{\alpha \alpha }$ as a function of ${\varepsilon }_F$. (d), (f) Bulk band structure and the first (d) and second (f) QI of MnSi. (e), (g) $Q_{\alpha }^{\left(1\right)}$ and $Q_{\alpha \alpha }^{\left(2\right)}$ as functions of ${\varepsilon }_F$. $Q_{x,y}^{\left(1\right)}=0$ due to the twofold (skew) rotation symmetry along the $z$ axis.

Figure 3

Different signatures of CI and QIs in an external ac magnetic field. (a), (b) Schematic setup of a sample (red) under an external ac magnetic field $B\left({\omega }_{1}t\right)=B_0+B_{1}sin\left({\omega }_{1}t\right)$ having a frequency-dependent output electrical current $I\left(\omega \right)$. (c)–(e) Schematic of the output signals of classical and quantum induction currents $I^c\left(\omega \right), I_1^q\left(\omega \right)$, and $I_2^q\left(\omega \right)$ as a function of frequency, respectively. The estimated typical orders of each peak are given in Table 1.