High-Temperature Majorana Corner States

Majorana bound states often occur at the end of a 1D topological superconductor. Validated by a new bulk invariant and an intuitive edge argument, we show the emergence of one Majorana Kramers pair at each corner of a square-shaped 2D topological insulator proximitized by an $s_{\pm }$-wave (e.g., Fe-based) superconductor. We obtain a phase diagram that addresses the relaxation of crystal symmetry and edge orientation. We propose two experimental realizations in candidate materials. Our scheme offers a higher-order and higher-temperature route for exploring non-Abelian quasiparticles.

Figure 1

Schematics of (a) a 2D TI proximitized by a nodeless high-$T_c$ (e.g., Fe-based $s_{\pm }$-wave) superconductor yielding Majorana corner states and (b) a square-lattice model to realize (a). Details in (b) are described below Eq. (1).

Figure 2

(a) Band structure of a 2D TI ribbon exhibiting a $(0\overline{1})$ helical edge state at $k_x=\pi$. (b) BdG spectrum of (a) with an $s_{\pm }$-wave pairing. (c)–(d) Similar to (a)–(b), but exhibiting a $(\overline{1}0)$ helical edge state at $k_y=0$. (e) Schematic of the $s_{\pm }$-wave pairing in the bulk BZ and the $s$-wave pairing of opposite signs acquired by the two edge states. (f) Exact diagonalization revealing the four pairs of Majorana corner states for the $15\times 15$ square size TI. The density plot displays their corner localized probability distribution, and the inset features their symmetry enforced zero energy. We have chosen $t_1=1$, $t=2$, $\lambda =1.5$, ${\mathrm{\Delta }}_0=0$, ${\mathrm{\Delta }}_1=0.5$, and $\mu =0.5$ in all panels.

Figure 3

(a) Phase diagram of the second-order TSC versus ${\mathrm{\Delta }}_0$ and $\mu$, distinguishing the topological (1), trivial (0), and nodal ($N$) phases. (b) Effective pairing ${\mathrm{\Delta }}_{\mathrm{eff}}$ acquired by the edge state versus the tilted edge orientation $\theta$. (c) Schematic of ${\mathrm{\Delta }}_{\mathrm{eff}}=0$ for the $(\overline{1}1)$ edge state. (d) Spatial probability distribution revealing the four pairs of Majorana corner states for the $11\times 21$ parallelogram size TI. We have chosen $t_1=1$, $t=2$, $\lambda =1.5$, ${\mathrm{\Delta }}_1=1$ in (a)–(d), $\mu =0$ in (b)–(d), and ${\mathrm{\Delta }}_0=0$ in (c) and (d).