Theoretical Studies Towards Materials Realization Of Topological Superconductors

The introduction of topological concept into condensed matter physics wins a great success not only because the awarded 2016 Nobel prize but also for the reason that it enriches our understandings of quantum phases in a manner beyond Landau's paradigm of spontaneous symmetry breaking.Along the road towards the colorful topological world,the innovative topological concept has been utilized to classify numerous quan-tum matters,including insulators,metals,superconductors,and bosonic systems.For example,topological insulators,which are electronic materials that have a bulk insu-lating gap associated with topologically protected gapless surface or edge states.In analogy with topological insulators,topological superconductors possess a full bulk superconducting gap and gapless Majorana boundary states protected by particle-hole symmetry.Beyond the fundamental interests,the primary motivation for studying topo-logical superconductors is that they are ideal platforms for detecting and manipulating Majorana fermions,which are their own anti-particles obeying non-Abelian statistics and were proposed as building blocks for realizing fault-tolerant topological quantum computation.There are substantial theoretical and experimental works devoted to pro-vide smoking-gun evidences for proving the existence of Majorana fennions in realis-tic materials.Although step-forward progresses had been successively made in recent years,the current situation is yet too early to say definitive.In this thesis,we develop a specific research line to carry out theoretical studies towards the realistic materials realization of topological superconductors.The thesis is organized as follows:In chapter 1,we give a brief introduction to the developments of topological con-cept in condensed matter physics along a historical line,focusing on topological insula-tors and topological superconductors.At the end of this chapter,we also provide a table that lists various topological classifications of insulators and fully gaped superconduc-tors according to the time reversal,particle-hole,and chiral symmetries.Chapter 2 is devoted to discuss our work on investigating the behaviors and effects of magnetic impurities at the interface of a topological insulator and a superconductor.It was proposed that such an interface resembles spinless px±ipy superconductor,sup-porting Majorana zero modes and edge states around magnetic vortices and geometrical edges,respectively.In this work,we first show that randomly distributed magnetic im-purities at the interface will induce Yu-Shiba states that broaden into impurity bands inside the superconducting gap,which remains open unless the impurity concentration is too high.Next,we find that an increase in the superconducting gap suppresses both the oscillation magnitude and period of the RKKY interaction between two magnetic impurities.Within a mean-field approximation,the ferromagnetic Curie temperature is revealed to be essentially independent of the superconducting gap as a result of the delicate compensation effect between the short-range ferromagnetic and long-range an-tiferromagnetic interactions.The simultaneous existence of robust superconductivity and persistent ferromagnetism at the interface allows the realization of a novel topolog-ical phase transition from a non-chiral to a chiral superconducting state at sufficiently low temperatures.Given the inherent experimental inconvenience arising at the interface investigated in chapter 2,we design chapter 3 to study the feasibilities of disorder-induced topologi-cal phase transitions,especially the potential disorder-assisted realization of topological superconductors,in two-dimensional Rashba spin-orbit coupled superconductors.In this chapter,we first show that a topologically trivial superconductor can be driven into a chiral topological superconductor upon diluted doping of isolated magnetic disorder,which close and reopen the superconducting quasiparticle gap in a nontrivial manner.Secondly,we find that the superconducting nature of a topological superconductor is robust against Anderson disorder,while the topological nature is fragile,and the sys-tem will be converted into a topologically trivial state.Quantitatively,these topological phase transitions are distinctly characterized by variations in the topological invariant.We also discuss the central findings in connection with existing experiments.Since most of the theoretical proposals for realizing topological superconductors rely the proximity effect.Realistic and reliable recipes of incorporating both the super-conductivity and topological character into a single material are certainly of interest and desirable for the community.In chapter 4,we devote ourself to study the feasibilities of realizing topological superconductivity in monolayer Pb3Bi alloy.We first calculate the band structures of Pb3Bi/Ge(111),and find a huge Rashba split throughout the whole Brillouin zone(BZ).More importantly,we identify six saddle points located below the Fermi surface of about 100 meV in the BZ,leading to a type-? van Hove singularity of the density of states,which is experimentally achievable via hole doping or external electrical gating.Based on renormalization group analysis,we show that the present system undergoes a superconducting phase transition at sufficient low temperatures,and prefers either a f-wave or degenerated p-wave pairing symmetry depending on a specific parameter.At the end of this chapter,we discuss the central findings in con-nection with the potential realization of topologically nontrivial superconducting state in this 2D material.Finally,in chapter 5,we present a short conclusion and outlook of this thesis.