We report on a study of intrinsic superconductivity in a Weyl metal, i.e. a doped Weyl semimetal. Two distinct superconducting states are possible in this system in principle: a zero-momentum pairing BCS state, with point nodes in the gap function; and a finite-momentum FFLO-like state, with a full nodeless gap. We find that, in an inversion-symmetric Weyl metal the odd-parity BCS state has a lower energy than the FFLO state, despite the nodes in the gap. The FFLO state, on the other hand, may have a lower energy in a noncentrosymmetric Weyl metal, in which Weyl nodes of opposite chirality have different energy. However, realizing the FFLO state is in general very difficult since the paired states are not related by any exact symmetry, which precludes a weak-coupling superconducting instability. We also discuss some of the physical properties of the nodal BCS state, in particular Majorana and Fermi arc surface states.Comment: 10 pages, 3 figures, published versio

We explore the phenomenon of emergent Lorentz invariance in strongly coupled theories. The strong dynamics is handled using the gauge/gravity correspondence. We analyze how the renormalization group flow towards Lorentz invariance is reflected in the two-point functions of local operators and in the dispersion relations of the bound states. The deviations of these observables from the relativistic form at low energies are found to be power-law suppressed by the ratio of the infrared and ultraviolet scales. We show that in a certain subclass of models the velocities of the light bound states stay close to the emergent 'speed of light' even at high energies. We comment on the implications of our results for particle physics and condensed matter.

Twist engineering of van der Waals magnets has emerged as an outstanding platform for manipulating exotic magnetic states. However, the complicated form of spin interactions in the large moirésuperlattice obstructs a concrete understanding of such spin systems. To tackle this problem, for the first time, we developed a generic ab initio spin Hamiltonian for twisted bilayer magnets. Our atomistic model reveals that strong AB sublattice symmetry breaking due to the twist introduces a promising route to realize the novel noncentrosymmetric magnetism. Several unprecedented features and phases are uncovered including the peculiar domain structure and skyrmion phase induced by noncentrosymmetricity. The diagram of those distinctive magnetic phases has been constructed, and the detailed nature of their transitions analyzed. Further, we established the topological band theory of moirémagnons relevant to each of these phases. By respecting the full lattice structure, our theory provides the characteristic features that can be detected in experiments.

In this paper, we study topological properties of 3D lattice dimer model. We demonstrate, that the dimer model on a bipartite lattice possesses topological defects, which are exactly characterized by Hopf invariant. We derive its explicit algebraic expression in terms of effective magnetic field of a dimer configuration. Thus, we solve the problem of topological classification of possible states in 3D lattice dimer model. Furthermore, since the lattice dimer model is known to be dual to spin ice, our work can be viewed as a proposal to search for hopfions in classical, as well as, artificial spin ice and related materials. arXiv:1901.04527v2 [cond-mat.stat-mech]

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