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Register a new userZero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions
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We study Majorana zero energy modes (MZEM) that occur in a s-wave superconducting surface, at the ends of a ferromagnetic (FM) chain of adatoms, in the presence of Rashba spin-orbit interaction (SOI) considering both non self-consistent and self-consistent superconducting order. We find that in the self-consistent solution the average superconducting gap function over the adatom sites has a discontinuous drop with increasing exchange interaction at the same critical value where the topological phase transition occurs. We also study the MZEM for both treatments of superconducting order and find that the decay length is a linear function of the exchange coupling strength, chemical potential and superconducting order. For wider FM chains the MZEM occur at smaller exchange couplings and the slope of the decay length as a function of exchange coupling grows with chain width. Thus we suggest experimental detection of different delocalization of MZEM in chains of varying widths. We discuss similarities and differences between the MZEM for the two treatments of the superconducting order.
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We theoretically study the superconducting proximity effect in a quantum dot coupled to two superconducting leads when the intradot interaction between electrons is made attractive. Because of the superconducting proximity effect, the electronic states for the embedded quantum dot are either spin-polarized states with an odd occupation number or BCS-like states with an even occupation number. We show that in the presence of an external magnetic field, the system can exhibit quantum phase transitions of fermion parity associated with the occupation number. In this work, we adopt a self-consistent theoretical method to extend our considerations beyond the so-called superconducting atomic limit in which the superconducting gap for the leads is assumed to be the largest energy scale. The method enables us to numerically investigate the electronic structure of the dot as results of the attractive interaction. For energy phase diagrams in the regime away from the atomic limit, we find a reentrant behavior where a BCS-like phase of the dot exists in an intermediate range of the hybridization strength between the quantum dot and the leads. We also consider Josephson current phase relations and identify a number of examples showing $0-pi$ phase transitions that may offer important switching effects.
Realizing topological superconductivity and Majorana zero modes in the laboratory is one of the major goals in condensed matter physics. We review the current status of this rapidly-developing field, focusing on semiconductor-superconductor proposals for topological superconductivity. Material science progress and robust signatures of Majorana zero modes in recent experiments are discussed. After a brief introduction to the subject, we outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana-based topological quantum computation in these systems.
We study theoretically the spectral and transport properties of a superconducting wire with a magnetic defect. We start by modelling the system as a one dimensional magnetic Josephson junction and derive the equation determining the full subgap spectrum in terms of the normal-state transfer matrix for arbitrary length and exchange field of the magnetic region. We demonstrate that the quantum phase transition predicted for a short-range magnetic impurity, and associated with a change of the total spin of the system, also occurs in junctions of finite length. Specifically, we find that the total spin changes discontinuously by integer jumps when bounds states cross the Fermi level. The spin can be calculated by using a generalization of Friedel sum rule for the superconducting state, which we also derive. With these tools, we analyze the subgap spectrum of a junction with the length of the magnetic region smaller than the superconducting coherence length and demonstrate how phase transitions also manifest as change of the sign of the supercurrent.
The nature of the magnetic-field driven superconductor-to-insulator quantum-phase transition in two-dimensional systems at zero temperature has been under debate since the 1980s, and became even more controversial after the observation of a quantum-Griffiths singularity. Whether it is induced by quantum fluctuations of the superconducting phase and the localization of Cooper pairs, or is directly driven by depairing of these pairs, remains an open question. We herein experimentally demonstrate that in weakly-pinning systems and in the limit of infinitely wide films, a sequential superconductor-to-Bose insulator-to-Fermi insulator quantum-phase transition takes place. By limiting their size smaller than the effective penetration depth, however, the vortex interaction alters, and the superconducting state re-enters the Bose-insulating state. As a consequence, one observes a direct superconductor-to-Fermi insulator in the zero-temperature limit. In narrow films, the associated critical-exponent products diverge along the corresponding phase boundaries with increasing magnetic field, which is a hallmark of the quantum-Griffiths singularity.
The recent realization of pristine Majorana zero modes (MZMs) in vortices of iron-based superconductors (FeSCs) provides a promising platform for long-sought-after fault-tolerant quantum computation. A large topological gap between the MZMs and the lowest excitations enabled detailed characterization of vortex MZMs in those materials. Despite those achievements, a practical implementation of topological quantum computation based on MZM braiding remains elusive in this new Majorana platform. Among the most pressing issues are the lack of controllable tuning methods for vortex MZMs and inhomogeneity of the FeSC Majorana compounds that destroys MZMs during the braiding process. Thus, the realization of tunable vortex MZMs in a truly homogeneous compound of stoichiometric composition and with a charge neutral cleavage surface is highly desirable. Here we demonstrate experimentally that the stoichiometric superconductor LiFeAs is a good candidate to overcome these two obstacles. Using scanning tunneling microscopy, we discover that the MZMs, which are absent on the natural surface, can appear in vortices influenced by native impurities. Our detailed analysis and model calculations clarify the mechanism of emergence of MZMs in this material, paving a way towards MZMs tunable by controllable methods such as electrostatic gating. The tunability of MZMs in this homogeneous material offers an unprecedented platform to manipulate and braid MZMs, the essential ingredients for topological quantum computation.
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