Abstract
We present an exhaustive study of Andreev crystals (ACs) -- quasi-one-dimensional superconducting wires with a periodic distribution of magnetic regions. The exchange field in these regions is assumed to be much smaller than the Fermi energy. Hence, the transport through the magnetic region can be described within the quasiclassical approximation. In the first part of the paper, by assuming that the separation between the magnetic regions is larger than the coherence length, we derive the effective nearest-neighbour tight-binding equations for ACs with a helical magnetic configuration. The spectrum within the gap of the host superconductor shows a pair of energy-symmetric bands. By increasing the strength of the magnetic impurities in ferromagnetic ACs, these bands cross without interacting. However, in any other helical configuration, there is a value of the magnetic strength at which the bands touch each other, forming a Dirac point. Further increase of the magnetic strength leads to a system with an inverted gap. We study junctions between ACs with inverted spectrum and show that junctions between (anti)ferromagnetic ACs (always) never exhibit bound states at the interface. In the second part, we extend our analysis beyond the nearest-neighbour approximation by solving the Eilenberger equation for infinite and junctions between semi-infinite ACs with collinear magnetization. From the obtained quasiclassical Green functions, we compute the local density of states and the local spin polarization in anti- and ferromagnetic ACs. We show that these junctions may exhibit bound states at the interface and fractionalization of the surface spin polarization.
Highlights
Magnetic defects and regions in a superconductor may lead to bound states that strongly change the local spectrum [1,2,3,4,5,6,7,8,9,10,11,12]
Our results demonstrate the validity of the first neighbor tight-binding approximation regarding the gap closing in infinite antiferromagnetic Andreev crystals (ACs) at half-integer values of /π, the appearance of a pair of states bounded to the interface between two antiferromagnetic ACs with inverted gaps, and the fractionalization of the surface spin polarization in such junctions [23]
IV C, we present the method to solve the Eilenberger equation in junctions between semi-infinite collinear ACs and we apply it to obtain the quasiclassical Green’s functions (GFs) in junctions between antiferromagnetic ACs
Summary
Magnetic defects and regions in a superconductor may lead to bound states that strongly change the local spectrum [1,2,3,4,5,6,7,8,9,10,11,12]. If the exchange coupling is small compared to the Fermi energy, μ, a pair of degenerate bound states appear [4,12,13] The origin of such degeneracy can be understood from a semiclassical perspective: electrons at the Fermi level traveling through the magnetic region are not back-scattered, but they accumulate a phase,. Our results demonstrate the validity of the first neighbor tight-binding approximation regarding the gap closing in infinite antiferromagnetic ACs at half-integer values of /π , the appearance of a pair of states bounded to the interface between two antiferromagnetic ACs with inverted gaps, and the fractionalization of the surface spin polarization in such junctions [23].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
