Anomalous Floquet Chiral Topological Superconductivity in a Topological Insulator Sandwich Structure

We show that Floquet chiral topological superconductivity arises naturally in Josephson junctions made of magnetic topological insulator-superconductor sandwich structures. The Josephson phase modulation associated with an applied bias voltage across the junction drives the system into the anomalous Floquet chiral topological superconductor hosting chiral Majorana edge modes in the quasienergy spectrum, with the bulk Floquet bands carrying zero Chern numbers. The bias voltage acts as a tuning parameter enabling novel Floquet topological quantum phase transitions driving the system into a myriad of exotic Majorana-carrying Floquet topological superconducting phases. Our theory establishes a new paradigm for realizing Floquet chiral topological superconductivity in solid-state systems, which should be experimentally directly accessible.

Figure 1

(a) A chiral topological Josephson junction. The low-energy physics is governed by the gapped Dirac surface states of the magnetic topological insulator thin film, along with the intersurface tunneling $t(\mathbf{k})$ and the proximitized superconducting orders ${\mathrm{\Delta }}_{t,b}$. Applying a bias voltage $V_0$ achieves a modulation of the Josephson phase $\phi (t)$ and drives the system into a Floquet superconductor. (b) Tuning $V_0$ induces the Floquet topological phase transition, which further leads to the anomalous Floquet chiral TSC phase. The anomalous chiral Majorana edge modes denote those that cannot be explained by the BdG Chern number of the Floquet bulk bands.

Figure 2

(a) and (b) show the topological phase diagram of $h_{\omega }^{(0)}$ for $\alpha =1$ and $\alpha =\frac{1}{2}$, respectively. The orange, blue, and red phase boundaries denote band gap closing at zero energy at $\mathrm{\Gamma }$, $X$ and $Y$, and $M$, respectively. (c) Bulk band spectrum of $h_{\omega }^{(0)}$ for our choice of parameters with the BdG Chern number $C=1$. (d) Edge spectrum of the $C=1$ phase, which clearly shows a single chiral Majorana edge mode. $\tilde{\mathrm{\Gamma }}$ and $\tilde{Y}$ are the high-symmetry momenta in the edge BZ.

Figure 3

(a) The Floquet topological phase transition happens whenever the reference line of $ϵ=\omega /2$ intersects with the static bands of $h_{\omega }^{(0)}$ at high-symmetry momenta. Here we only plot the upper half spectrum of $h_{\omega }^{(0)}$ [i.e., the $E>0$ part of Fig. 2] for simplicity. (b) Driving-induced topological phase diagram as a function of the driving period $T$. Each phase is labeled by two integer-valued topological invariants: the BdG Chern number $C$ and the winding number $\mathcal{W}$. (c) Edge spectrum of the AFCTSC phase at $T=1.5$ with $(C,\mathcal{W})=(0,1)$. This phase features a single right-moving chiral Majorana edge mode penetrating the quasienergy gaps at both $ϵ=0$ and $ϵ=\omega /2$. (d) Another Floquet TSC phase with $(C,\mathcal{W})=(2,-1)$ occurs at $T=2.5$. This phase features a right-moving (left-moving) chiral Majorana edge mode within the $ϵ=0$ ($ϵ=\omega /2$) gap. The zoomed plots in (c) and (d) range from $0.45\omega$ to $0.55\omega$.