Majorana Crystal in Rhombohedral Graphene

Abstract

Recent experiments in rhombohedral graphene report an unusual superconducting phase emerging from a spin- and valley-polarized quarter-metal state. The prevailing interpretation invokes chiral topological superconductivity, but the role of the `Fulde-Ferrell' phase factor due to intra-valley pairing has remained largely unexplored. Here we show, via a gauge transformation, that this phase is equivalent to an ordinary chiral topological superconductor on the triangular lattice, while simultaneously forming an extraordinary Majorana crystal on the dual honeycomb lattice reminiscent of the Haldane model.

Figures (3)

• Figure 1: (a) Embedded vortices (black dots) and antivortices (open dots) at the centers of the up and down triangles of a triangular lattice (blue dots). $\bm{a}_{1}$ and $\bm{a}_{2}$ are the primitive lattice vectors. $+\bm{b}_i$ and $-\bm{b}_i$ ($i=1,2,3$) are the positions of vortices and antivortices relative to a lattice point, respectively. The blue dashed lines outline a $\sqrt{3}\times\sqrt{3}$ supercell. (b) Color plot of the superconducting phase field $\theta(\bm{r})$.
• Figure 2: (a) Schematics of the spatial phase-structures of the six types of MBSs, localized at vortex (solid circle) and antivortex (open circle) cores. Red, green, and blue colors indicate their phases of $2\pi/3$, $4\pi/3$, and 0 along the $+\hat{x}$ direction, respectively. Arrows indicate the corresponding phases. (b-d) Schematics of the the Majorana crystal relative to the graphene honeycomb lattice of the layer to which the electrons are polarized, as well as the (b) vortex-vortex, (c) antivortex-antivortex, and (d) vortex-antivortex couplings. The dashed lines outline the same $\sqrt{3}\times\sqrt{3}$ supercell shown in Fig \ref{['fig1']}(a).
• Figure 3: (a) The phase diagram of the Majorana crystal model Eq. (\ref{['eq:MC_2band']}). The Chern number is $1$ ($-1$) for the light red (blue) region. There is no indirect gap in the shaded region. (b) The Majorana-band Dirac cones at the $K$ and $K$' points for the case with $t_{vv} = t_{aa} = 0$ and $t_{va} = 1$ meV. (c) The bulk and (d) the armchair-edge Majorana band structures for the case with $t_{vv} = 1/5, t_{aa} = -1/15$, and $t_{va} = 1$ meV.