We study superconductivity in a Weyl semimetal with a tilted dispersion around two Weyl points of opposite chirality. In the absence of any tilt, the state with zero momentum pairing between two Fermi sheets enclosing each Weyl point has four point nodes in the superconducting gap function. Moreover, the surface of the superconductor hosts Fermi arc states and Majorana flat bands. We show that a quantum phase transition occurs at a critical value of the tilt, at which two gap nodes disappear by merging at the center of the first Brillouin zone, or by escaping at its edges, depending on the direction of the tilt. The region in the momentum space that the Majorana flat band occupies is found to increase as the tilt parameter is made larger. Additionally, the superconducting critical temperature and electronic specific heat can be enhanced in the vicinity of the quantum phase transition due to the singularity in the electronic density of states.

After more than a decade, direct observation of the odd frequency triplet pairing state in superconducting hybrid structures remains elusive. We propose an experimentally feasible setup that can unambiguously reveal the zero energy peak due to proximity-induced equal spin superconducting triplet correlations. We theoretically investigate a two-dimensional Josephson junction in the diffusive regime. The nanostructure consists of a normal metal sandwiched between two ferromagnetic layers with spiral magnetization patterns. By applying an external magnetic field perpendicular to the junction plane, vortices nucleate in the normal metal. The calculated energy and spatially resolved density of states, along with the pair potential, reveal that remarkably, only triplet Cooper pairs survive in the vortex cores. These isolated odd frequency triplet correlations result in well defined zero energy peaks in the local density of states that can be identified through tunneling spectroscopy experiments. Moreover, the diffusive regime considered here rules out the possibility of Andreev bound states in the vortex core as contributors to the zero energy peaks.

We study the anomalous Nernst and thermal Hall effects in a linearized low-energy model of a tilted Weyl semimetal, with two Weyl nodes separated in momentum space. For inversion symmetric tilt, we give analytic expressions in two opposite limits: For a small tilt, corresponding to a type-I Weyl semimetal, the Nernst conductivity is finite and independent of the Fermi level; for a large tilt, corresponding to a type-II Weyl semimetal, it acquires a contribution depending logarithmically on the Fermi energy. This result is in a sharp contrast to the nontilted case, where the Nernst response is known to be zero in the linear model. The thermal Hall conductivity similarly acquires Fermi surface contributions, which add to the Fermi level-independent, zero-tilt result, and is suppressed as one over the tilt parameter at half filling in the type-II phase. In the case of inversion-breaking tilt, with the tilting vector of equal modulus in the two Weyl cones, all Fermi surface contributions to both anomalous responses cancel out, resulting in zero Nernst conductivity. We discuss two possible experimental setups, representing open and closed thermoelectric circuits.

We study the interplay of disorder and band-structure topology in a Weyl semimetal with a tilted conical spectrum around the Weyl points. The spectrum of particles is given by the eigenvalues of a non-Hermitian matrix, which contains contributions from a Weyl Hamiltonian and complex self-energy due to electron elastic scattering on disorder. We find that the tilt-induced matrix structure of the self-energy gives rise to either a flat band or a nodal line segment at the interface of the electron and hole pockets in the bulk band structure of type-II Weyl semimetals depending on the Weyl cone inclination. For the tilt in a single direction in momentum space, each Weyl point expands into a flat band lying on the plane, which is transverse to the direction of the tilt. The spectrum of the flat band is fully imaginary and is separated from the in-plane dispersive part of the spectrum by the "exceptional nodal ring" where the matrix of the Green's function in momentum-frequency space is defective. The tilt in two directions might shrink a flat band into a nodal line segment with "exceptional edge points." We discuss the connection to the non-Hermitian topological theory.

We study topological excitations in two-component nematic superconductors, with a particular focus on CuxBi2Se3 as a candidate material. We find that the lowest-energy topological excitations are coreless vortices: a bound state of two spatially separated half-quantum vortices. These objects are nematic Skyrmions, since they are characterized by an additional topological charge. The inter-Skyrmion forces are dipolar in this model, i.e., attractive for certain relative orientations of the Skyrmions, hence forming multi-Skyrmion bound states.

We study second-harmonic generation in centrosymmetric Weyl semimetal with broken time reversal symmetry. We calculate electric current density at the double frequency of the propagating electromagnetic field in the presence of an applied constant magnetic field, using the method of kinetic equation for electron distribution function. It is shown that the chiral anomaly contribution to second-harmonic generation in the lowest order is linearly proportional to the applied magnetic field. The limit when the chiral anomaly dominates over the Lorentz-type contribution to second-harmonic generation is discussed.