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Topological defects of tetratic liquid-crystal order on a soft spherical surface

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We model the orientational and positional order of tetratically shaped molecules each having four-fold structural symmetryconfined on a spherical surface. Our Monte Carlo simulation shows that at a high molecular density a tetratic orientational orderdevelops in the system accompanied by eight disclinations arranged in an anticube form on the hard spherical surface. We alsoconsider an elastic-energy model which consists of both Helfrich and Frank energies for a soft surface; the solution confirms theMonte Carlo study and further predicts the tetratic morphology that can be realized on the surface of a soft vesicle. Assumingthat the induced interaction between these disclinations are repulsive we demonstrate that the anticube structure has a lower freeenergy than for example the cubic structure.