Floquet composite Dirac semimetals

Abstract

Dirac semimetals can be classified into types I, II, and III based on the topological charge of their Dirac points. If a three-dimensional (3D) system can be sliced into a family of kz-dependent normal and topological insulators, type I Dirac points separate a 2D normal insulator from a 2D first-order topological insulator, while type II (III) Dirac points separate a 2D normal (first-order) insulator from a 2D second-order topological insulator. To investigate the effects arising from the interplay of distinct Dirac points, one may wonder whether these Dirac points can coexist in a single system. Here, we propose a scheme to induce composite Dirac semimetals by a special Floquet driving that preserves time-reversal and space-inversion symmetries. A general description is established to characterize Dirac semimetals in Floquet systems. The results show that Dirac semimetals hosting coexisting type I, II, and III Dirac points can be induced by delta-function or harmonic driving. Our results provide a promising new avenue for exploring novel Dirac semimetals.

Figures (5)

• Figure 1: The Schematic of of (a) type I Dirac, (b) type II Dirac, and (c) type III Dirac semimetals. DP denotes Dirac point. Green, yellow, and blue surfaces denote trivial (NI), first-order topological (FOTI), and second-order topological (SOTI) insulators in 2D $k_z$-dependent subsystems, respectively.
• Figure 2: The probability distributions of (a) zero- and (b) $\pi/T$-mode topological states in different $k_z$-dependent 2D subsystem. We use $\lambda=0.3$, $t_1=1.5$, $t_2=1.6$, and $T=1$.
• Figure 3: (a) $\mathcal{W}_{\alpha/T}$ and (b) $\mathcal{V}_{\alpha/T}$ with the change of $k_z$. We use $\lambda=0.3$, $t_1=1.5$, $t_2=1.6$, and $T=1$.
• Figure 4: Phase diagram. We use $t_1=0.75$, $t_2=2.25$, and $T=1$.
• Figure 5: The probability distributions of (a) zero- and (b) $\pi/T$-mode topological states in different $k_z$-dependent 2D subsystem. We use $\lambda=0.3$, $t_1=3$, and $w=2\pi$.