Majorana bound states in a superconducting Rashba nanowire in the presence of antiferromagnetic order

Kobiałka, Aksel; Sedlmayr, Nicholas; Ptok, Andrzej

doi:10.1103/physrevb.103.125110

Cited by 16 publications

(13 citation statements)

References 133 publications

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“…where the change of basis has permitted us to have a zero component of τ z because τ z anticommutes with the Hamiltonian and defines the chiral symmetry of the system [62]. In the fermionic basis set of the original Hamiltonian [33,39], the symmetry representation is the above C = τ x σ 0 .…”

Section: A Topological Invariantsmentioning

confidence: 99%

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Calculations of in-gap states of ferromagnetic spin chains on s -wave wide-band superconductors

2021

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Magnetic impurities create in-gap states on superconductors. Recent experiments explore the topological properties of one-dimensional arrays of magnetic impurities on superconductors, because in certain regimes p-wave pairing can be locally induced leading to new topological phases. A byproduct of the new accessible phases is the appearance of zero-energy edge states that have non-Abelian exchange properties and can be used for topological quantum computation. Despite the large amount of theory devoted to these systems, most treatments use approximations that render their applicability limited when comparing with usual experiments of 1D impurity arrays on wide-band superconductors. These approximations either involve tight-binding-like approximations where the impurity energy scales match the minute energy scale of the superconducting gap and are many times unrealistic, or they assume strongly-bound in-gap states. Here, we use a theory for s-wave superconductors based on a wide-band normal metal, with any possible energy scale for the magnetic impurities and develop an efficient way of computing the well-known topological invariants of infinite chains. We perform concrete calculations on ferromagnetic spin chains using BCS Green's function for the superconductor and including Rashba coupling to compare with recent experimental results. The infinite-chain properties can be analytically obtained, giving us a way to compare with finite-chain calculations. We show that it is possible to converge to the infinite limit by doing finite-size numerical calculation, paving the way for numerical calculations not based on analytical Green's functions. As an application, we show that energy oscillations around zero with increasing number of atoms in the spin chain does not reflect the topological origin of the low-energy state.

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Section: A Topological Invariantsmentioning

confidence: 99%

“…A helical spin structure [2,[5][6][7]34,35] has been shown to be equivalent to the effect of a Rashba interaction caused by the superconductors spin-orbit coupling [35][36][37]. The possibility of emergence of MBS in antiferromagnetically ordered chains has been also discussed [38,39].…”

Section: Introductionmentioning

confidence: 99%

Calculations of in-gap states of ferromagnetic spin chains on s -wave wide-band superconductors

2021

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“…The quantity W in Eq. ( 3) provides the same information as the Pfaffian but is simpler to calculate, see [66,67] for related Pfaffian studies. In Fig.…”

Section: Phase Diagrammentioning

confidence: 99%

Robust topological superconductivity in weakly coupled nanowire-superconductor hybrid structures

Awoga,

Cayao,

Black-Schaffer

2021

Preprint

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We investigate the role of the coupling between a spin-orbit coupled semiconductor nanowire and a conventional s-wave superconductor on the emergence of the topological superconducting phase with Majorana bound states in an applied magnetic field. We show that when the coupling is strong, the topological phase transition point is very sensitive to the size of the superconductor and in order to reach the topological phase a strong magnetic field is required, which can easily be detrimental for superconductivity. Moreover, the induced energy gap separating the Majorana bound states and other quasi-particles in the topological phase is substantially suppressed compared to the gap at zero field. In contrast, in the weak coupling regime, we find that the situation is essentially the opposite, with the topological phase emerging at much lower magnetic fields and a sizable induced energy gap in the topological phase, that can also be controlled by the chemical potential of the superconductor. Furthermore, we show that the weak coupling regime does not generally allow for the formation of topologically trivial zero-energy states at the wire end points, in stark contrast to the strong coupling regime where such states are found for a wide range of parameters. Our results thus put forward the weak coupling regime as a promising route to mitigate the most unwanted problems present in nanowires for realizing topological superconductivity and Majorana bound states.

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“…where the change of basis has permitted us to have a zero component of τ z because τ z anticommutes with the Hamiltonian and defines the chiral symmetry of the system 47 . In the fermionic basis set of the original Hamiltonian 29,35 , the symmetry representation is the above C = τ x σ 0 .…”

Section: A Topological Invariantsmentioning

confidence: 99%

“…A helical spin structure 2,[5][6][7]30,31 has been shown to be equivalent to the effect of a Rashba interaction caused by the superconductors spin-orbit coupling [31][32][33] . The possibility of emergence of MBS in antiferromagnetically ordered chains has been also discussed 34,35 .…”

Section: Introductionmentioning

confidence: 99%

Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors

Mier,

Choi,

Lorente

2021

Preprint

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Magnetic impurities create in-gap states on superconductors. Recent experiments explore the topological properties of one-dimensional arrays of magnetic impurities on superconductors, because in certain regimes p-wave pairing can be locally induced leading to new topological phases. A by-product of the new accessible phases is the appearance of zero-energy edge states that have non-Abelian exchange properties and can be used for topological quantum computation. Despite the large amount of theory devoted to these systems, most treatments use approximations that render their applicability limited when comparing with usual experiments of 1-D impurity arrays on wide-band superconductors. These approximations either involve tight-binding-like approximations where the impurity energy scales match the minute energy scale of the superconducting gap and are many times unrealistic, or they assume strongly-bound in-gap states. Here, we present a theory for s-wave superconductors based on a wide-band normal metal, with any possible energy scale for the magnetic impurities. The theory is based on free-electron Green's functions. We include Rashba coupling and compare with recent experimental results, permitting us to analyze the topological phases and the experimental edge states. The infinite-chain properties can be analytically obtained, giving us a way to compare with finite-chain calculations. We show that it is possible to converge to the infinite limit by doing finite numerical calculation, paving the way for numerical calculations not based on analytical Green's functions.

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Majorana bound states in a superconducting Rashba nanowire in the presence of antiferromagnetic order

Cited by 16 publications

References 133 publications

Calculations of in-gap states of ferromagnetic spin chains on s -wave wide-band superconductors

Calculations of in-gap states of ferromagnetic spin chains on s -wave wide-band superconductors

Robust topological superconductivity in weakly coupled nanowire-superconductor hybrid structures

Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors

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