Impurity-Induced Magnetization of Graphene

We present a model of impurity-induced magnetization of graphene assuming that the main source of graphene magnetization is related to impurity states with a localized spin. The analysis of solutions of the Schrödinger equation for electrons near the Dirac point has been performed using the model of massless fermions. For a single impurity, the solution of Schrödinger’s equation is a linear combination of Bessel functions. We found resonance energy levels of the non-magnetic impurity. The magnetic moment of impurity with a localized spin was accounted for the calculation of graphene magnetization using the Green’s function formalism. The spatial distribution of induced magnetization for a single impurity is obtained. The energy of resonance states was also calculated as a function of interaction. This energy is depending on the impurity potential and the coupling constant of interaction.

Instability of Majorana states in Shiba chains due to leakage into a topological substrate

We revisit the problem of Majorana states in chains of scalar impurities deposited on a superconductor with a mixed s-wave and p-wave pairing. We also study the formation of Majorana states for magnetic impurity chains. We find that the magnetic impurity chains exhibit well-localized Majorana states when the substrate is trivial, but these states hybridize and get dissolved in the bulk when the substrate is topological. Most surprisingly, and contrary to previous predictions, the scalar impurity chain does not support fully localized Majorana states except for very small and finely tuned parameter regimes, mostly for a non-topological substrate close to the topological transition. Our results indicate that a purely p-wave or a dominant p-wave substrate are not good candidates to support either magnetic or scalar impurity topological Shiba chains.

Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal

We theoretically demonstrate non-Hermitian indirect interaction between two magnetic impurities placed at the interface between a 3D topological insulator and a ferromagnetic metal. The coupling of topological insulator and the ferromagnet introduces not only Zeeman exchange field on the surface states but also broadening to transfer the charge and spin between the surface states of the topological insulator and the metallic states of the ferromagnet. While the former provides bandgap at the charge neutrality point, the latter causes non-Hermiticity. Using the Green’s function method, we calculate the range functions of magnetic impurity interactions. We show that the charge decay rate provides a coupling between evanescent modes near the bandgap and traveling modes near the band edge. However, the spin decay rate induces a stronger coupling than the charge decay rate so that higher energy traveling modes can be coupled to lower energy evanescent ones. This results in a non-monotonic behavior of the range functions in terms of distance and decay rates in the subgap regime. In the over gap regime, depending on the type of decay rate and on the distance, the amplitude of spatial oscillations would be damped or promoted.

Nonlinear theory of macroscopic flow induced in a drop of ferrofluid

We present results of theoretical modelling of macroscopic circulating flow induced in a cloud of ferrofluid by an oscillating magnetic field. The cloud is placed in a cylindrical channel filled by a nonmagnetic liquid. The aim of this work is the development of a scientific basis for a progressive method of addressing drug delivery to thrombus clots in blood vessels with the help of the magnetically induced circulation flow. Our results show that the oscillating field can induce, inside and near the cloud, specific circulating flows with the velocity amplitude about several millimetres per second. These flows can significantly increase the rate of transport of the molecular non-magnetic impurity in the channel. This article is part of the theme issue ‘Transport phenomena in complex systems (part 1)’.

The exact solution of magnetic susceptibility for finite Ising ring with a magnetic impurity

We connected the two ends of a finite spin-1/2 antiferromagnetic Ising chain with a magnetic impurity at one end to form a closed ring, and studied the magnetic susceptibility of it exactly by using the transfer matrix method. We calculated the magnetic susceptibility in the whole temperature range and gave the phase diagram at ground state of the system about the anisotropy of the impurity and strength of the connection exchange interaction for spin-1 and 3/2 impurities. We also gave the ground state entropy of system and derived the asymptotic expression of the magnetic susceptibility multiplied by temperature at zero temperature limit and high temperature limit. It is found that degenerate phase may exist in some parameter region at zero temperature for the spin number of system being odd, and the ground state entropy is ln⁡(2) in the nondegenerate phase and is dependent on the number of spin in the degenerate phase. The magnetic susceptibility of the system at low temperature exhibits ferromagnetic behavior, and the Curie constant is related to the spin configuration at ground state. When the ground state is nondegenerate, the Curie constant is equal to the square of the net spin, regardless of the parity of the number of the spin. When the number of spin is odd and the ground state is degenerate, the Curie constant may be related to the total number of spin. In high temperature limit, the magnetic susceptibility multiplied by temperature is related to the spin quantum number of impurity and the number of spin in the ring.