# Study of the influence of an inmpurity on a system with spin-orbit coupling in the real space

Grant ID: 2016/20/S/ST3/00274

## Yu-Shiba-Rushinov bound states

Magnetism (driven either by external fields or internal magnetic impurities) is usually known to have a detrimental influence on the superconducting state of bulk materials. Recent progress of STM and AFM experimental techniques has enabled us to manipulate and probe individual atoms/molecules embedded in superconducting samples of various crystallographic symmetries. In particular, there has been observed that local magnetic fields (e.g., magnetic impurities) induce the subgap bound states, dubbed Yu-Shiba-Rusinov (YSR) quasiparticles. Upon arranging such impurities into chains or lattices in the presence of the strong spin-orbit interactions, one can engineer a novel, topologically non-trivial, states of matter.

In this paper, we explore the influence of the spin-orbit interaction on the YSR states, both for single and dimer magnetic impurities embedded in a 2-dimensional triangular lattice of the superconducting substrate. This situation can be encountered in the recently discovered superconducting compound of NbSe2. Our study shows, that a long spatial extent (reaching a few nanometers) of the YSR states [reported experimentally by G.C. M'enard et al., Nat.Phys. 11, 1013 (2015)], can be partly amplified by the in-plane spin-orbit coupling. We have also investigated topography and polarization of the YSR states for several representative configurations of dimer impurities. Information about these subgap bound states could be useful for designing novel topological phases, suitable for the realization of quantum bits and/or quantum computing

**Yu-Shiba-Rusinov states of impurities in a triangular lattice of NbSe2 with spin-orbit coupling**,__A. Ptok__, S. Glodzik and T. Domanski, Physical Review B**96**, 184425 (2017), PDF, arXiv:1707.03257**Quantum phase transition induced by magnetic impurity - triangular lattice with on-site pairing study**, S. Glodzik and__A. Ptok__, Journal of Superconductivity and Novel Magnetism DOI:10.1007/s10948-017-4360-6, PDF

## Majorana quasiparticles

This type of work is important in the application of Majorana quasiparticles in quantum computing and therefore, can widen the knowledge about this topic. Majorana quasiparticle is a special type of particle which is its antiparticle. Quantum computers can significantly improve computational power concerning conventional supercomputers or typical PC. However, to use quantum computers in the future, we must first learn how to control the sum of its parts. The discovery of Majorana quasiparticles in condensed matter systems inspired hope in many researchers for a bright future in quantum computing. Recent experiments using the quantum dot coupled to the topological superconducting nanowire revealed that Majorana bound states could coalesce from the Andreev bound states. Such quasiparticle states, present in the quantum dot, can be controlled by the magnetic and electrostatic means. We use a microscopic model of the quantum-dot-nanowire structure to reproduce the experimental results and propose further improvements to the topic. We also show the manipulation of various types of bound states and mutual influence between them. We apply that to control the zero-energy bound states that can emerge from the Andreev bound states in the studied system. Moreover, in a non-trivial topological phase, we show the possible interplay between zero-energy bound states of the quantum dot with Majorana bound states. We discuss and explain these phenomena as a result of the dominant spin character of discussed bound states. Presented results can be applied in experimental studies by using the nanodevice proposed in the paper, which can help to establish such control upon Majorana nanodevices applicable to quantum computing.

**Controlling the bound states in a quantum-dot hybrid nanowire**,__A. Ptok__, A. Kobialka and T. Domanski, Physical Review B**96**, 195430 (2017), PDF, arXiv:1710.06387**Influence of the orbital effects on the Majorana quasi-particles in a nanowire**, B. Kiczek and__A. Ptok__, Journal of Physics: Condensed Matter**29**, 495301 (2017), PDF**Quantum engineering of Majorana quasiparticles in one-dimensional optical lattices**,__A. Ptok__, A. Cichy and T. Domanski, Journal of Physics: Condensed Matter**30**, 355602 (2018), PDF, arXiv:1706.04155

## Other publications

**Counting defects in quantum computers with Graphics Processing Units**, B. Gardas and__A. Ptok__, Journal Of Computational Physics**366**, 320 (2018), PDF,**Superconducting monolayer deposited on substrate: Effects of the spin-orbit coupling induced by proximity effects**,__A. Ptok__, K. Rodriguez and Konrad J. Kapcia, Physical Review Materials**2**, 024801 (2018), PDF, arXiv:1801.08055**Reentrant Fulde-Ferrell-Larkin-Ovchinnikov superfluidity in the honeycomb lattice**, A. Cichy and__A. Ptok__, Physical Review A**97**, 053619 (2018), PDF, arXiv:1710.06395, Fig. 2 in Phys. Rev. A Kaleidoscope.**The influence of the dimensionality of the system on the realization of unconventional Fulde-Ferrell-Larkin-Ovchinnikov pairing in ultra-cold Fermi gases**, A. Ptok, Journal of Physics: Condensed Matter**29**, 475901 (2017), PDF**Diversity of charge orderings in correlated systems**, K. J. Kapcia, J. Baranski and__A. Ptok__, Physical Review E**96**, 042104 (2017), PDF, arXiv:1710.01757**Phase transitions in**,*quasi*-one dimensional system with unconventional superconductivity__A. Ptok__, A. Cichy, K. Rodriguez and K. J. Kapcia, Journal of Superconductivity and Novel Magnetism DOI:10.1007/s10948-017-4366-0, PDF, arXiv:1710.01617**The**,*ab initio*study of unconventional superconductivity in CeCoIn5 and FeSe__A. Ptok__, K. J. Kapcia, P. Piekarz and A. M. Oles, New Journal of Physics**19**, 063039 (2017), PDF, arXiv:1710.01988**Critical behavior in one dimension: Unconventional pairing, phase separation, BEC-BCS crossover, and magnetic Lifshitz transition**,__A. Ptok__, A. Cichy, K. Rodriguez and K. J. Kapcia, Physical Review A**95**, 033613 (2017), PDF, arXiv:1702.02193**Magnetic Lifshitz transition and its consequences in multi-band iron-based superconductors**,__A. Ptok__, K. J. Kapcia, A. Cichy, A. M. Oles and P. Piekarz, Scientific Reports**7**, 41979 (2017), PDF, arXiv:1702.02612**Various charge-ordered states in the extended Hubbard model with on-site attraction in the zero-bandwidth limit**, K. J. Kapcia, J. Baranski, S. Robaszkiewicz and__A. Ptok__, Journal of Superconductivity and Novel Magnetism**30**, 109 (2017), PDF**Influence of finite size effects on the Fulde-Ferrell-Larkin-Ovchinnikov state**,__A. Ptok__and D. Crivelli, Communications in Computational Physics**21**, 748 (2017), PDF