Majorana quasi-particles can be realised using magnetic field in the form of diamagnetic (orbital) or paramagnetic effects. In both cases, the magnetic field induces a topologically non-trivial phase of matter. In this paper, the influence of orbital effects on Majorana bound states induced by paramagnetic effects in 1D nanowire is elaborated. The role of orbital effects in density of states and eigenstates of the system is also discussed. Additionally, we show the phase diagram-the magnetic field versus the magnetic flux, which displays a relation between topologically trivial and non-trivial phases. The Majorana bound states existence in the presence of relatively small orbital effects is indicated.

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We study the properties of ultra-compact spherically symmetric dark matter sector star objects, being the solution of Einstein equations with two U(1)-gauge fields. One of them is the ordinary Maxwell field, while the auxiliary gauge field pertains to the hidden sector, and mimics the properties of dark matter. The visible and hidden sectors are coupled by a kinetic mixing term with a coupling constant α. We also investigate the possibility of condensation of charged scalar field around the reflecting dark matter star object. It happens that dark matter sector, both dark matter charge and coupling constant, cause shrinking of the star radius for which the condensation may occur.

The gauge-gravity duality has been applied to examine the properties of holographic superconducting quantum device (SQUID), composed of two S-N-S Josephson junctions, influenced by dark sector modelled by the additional U(1)-gauge field coupled to the ordinary Maxwell one. The dark matter sector is known to affect the properties of superconductors and is expected to enter the current-phase relation. The kinetic mixing between two gauge fields provides a mechanism allowing for the conceivable observation of the effect. We find small but visible effect of the dark matter particle traversing the device, which shows up as a change of its maximal current.