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Black-Schaffer, Annica M.
Publications (10 of 56) Show all publications
Teixeira, R. L. R., Kuzmanovski, D., Black-Schaffer, A. M. & da Silva, L. G. G. (2019). Gap oscillations and Majorana bound states in magnetic chains on superconducting honeycomb lattices. Physical Review B, 99(3), Article ID 035127.
Open this publication in new window or tab >>Gap oscillations and Majorana bound states in magnetic chains on superconducting honeycomb lattices
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 3, article id 035127Article in journal (Refereed) Published
Abstract [en]

Magnetic chains on superconducting systems have emerged as a platform for realization of Majorana bound states (MBSs) in condensed-matter systems with possible applications to topological quantum computation. In this work, we study the MBSs formed in magnetic chains on two-dimensional honeycomb materials with induced superconductivity. We establish chemical potential vs Zeeman splitting phase diagrams showing that the topological regions (where MBSs appear) are strongly dependent on the spiral angle along the magnetic chain. In some of those regions, the topological phase is robust even for large values of the local Zeeman field, thus producing topological regions which are, in a sense, "unbounded" in the large-field limit. Moreover, we show that the energy oscillations with magnetic field strength due to MBS splitting can show very different behaviors depending on the parameters. In some regimes, we find oscillations with increasing amplitudes and decreasing periods, while in the other regimes the complete opposite behavior is found. We also find that the topological phase can become dependent on the chain length, particularly in topological regions with a very high or no upper bound. In these systems, we see a very smooth evolution from MBSs localized at chain end points to in-gap Andreev bound states spread over the full chain.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-375872 (URN)10.1103/PhysRevB.99.035127 (DOI)000455823600004 ()
Funder
Swedish Research Council, 621-2014-3721Swedish Foundation for Strategic Research Knut and Alice Wallenberg FoundationCarl Tryggers foundation Göran Gustafsson Foundation for Research in Natural Sciences and Medicine
Available from: 2019-02-04 Created: 2019-02-04 Last updated: 2019-02-04Bibliographically approved
Mashkoori, M., Moghaddam, A. G., Hajibabaee, M. H., Black-Schaffer, A. M. & Parhizgar, F. (2019). Impact of topology on the impurity effects in extended s-wave superconductors with spin-orbit coupling. Physical Review B, 99(1), Article ID 014508.
Open this publication in new window or tab >>Impact of topology on the impurity effects in extended s-wave superconductors with spin-orbit coupling
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2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 1, article id 014508Article in journal (Refereed) Published
Abstract [en]

We investigate the impact of topology on the existence of impurity subgap states in a time-reversal-invariant superconductor with an extended s-wave pairing and strong spin-orbit coupling. By simply tuning the chemical potential, we access three distinct phases: topologically trivial s-wave, topologically nontrivial s(+/-)-wave, and nodal superconducting phase. For a single potential impurity, we find subgap impurity bound states in the topological phase, but notably no subgap states in the trivial phase. This is in sharp contrast with the expectation that there would be no subgap state in the presence of potential impurities in s-wave superconductors. These subgap impurity states have always finite energies for any strength of the potential scattering and, subsequently, the superconducting gap in the topological s(+/-)-wave phase survives but is attenuated in the presence of finite disorder. By creating islands of potential impurities, we smoothly connect the single impurity results to topological edge states of impurity islands. On the other hand, magnetic impurities lead to the formation of Yu-Shiba-Rusinov states in both the trivial and topological phases, which even reach zero energy at certain scattering strengths. We thus propose that potential impurities can be a very valuable tool to detect time-reversal-invariant topological superconductivity.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-375878 (URN)10.1103/PhysRevB.99.014508 (DOI)000455815800005 ()
Funder
Swedish Research Council, 621-2014-3721Swedish Foundation for Strategic Research Knut and Alice Wallenberg FoundationGöran Gustafsson Foundation for Research in Natural Sciences and Medicine
Available from: 2019-02-04 Created: 2019-02-04 Last updated: 2019-02-04Bibliographically approved
Mashkoori, M. & Black-Schaffer, A. M. (2019). Majorana bound states in magnetic impurity chains: Effects of d-wave pairing. Physical Review B, 99(2), Article ID 024505.
Open this publication in new window or tab >>Majorana bound states in magnetic impurity chains: Effects of d-wave pairing
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 99, no 2, article id 024505Article in journal (Refereed) Published
Abstract [en]

We consider an atomic chain of magnetic impurities on the surface of a spin-orbit coupled superconductor with a dominating d-wave and subdominating s-wave order parameters. In particular, we investigate the properties of the Majorana bound states (MBSs) emerging at the chain end points in the topological phase and how MBSs are affected by the d-wave order parameter. We provide a comprehensive picture by both studying time-reversal invariant and breaking superconducting substrates as well as chains oriented in different directions relative to the d-wave rotation. We show that increasing the d-wave order parameter significantly enhances the localization of MBSs and their protective minigap, as long as the direction along which the impurity chain is oriented does not cross any nodal lines of the gap function. Moreover, we find an extra gap-closing for a specific condensate and chain orientation within the topological phase, which we are able to attribute to simple geometrical effects in the corresponding two-dimensional limit. These results show how high-temperature d-wave superconductors can be used to significantly enhance the properties and stability of MBSs.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-375879 (URN)10.1103/PhysRevB.99.024505 (DOI)000455820200006 ()
Funder
Swedish Research Council, 621-2014-3721Swedish Foundation for Strategic Research Knut and Alice Wallenberg FoundationGöran Gustafsson Foundation for Research in Natural Sciences and Medicine
Available from: 2019-02-04 Created: 2019-02-04 Last updated: 2019-02-04Bibliographically approved
Triola, C. & Black-Schaffer, A. M. (2019). Odd-frequency pairing in a superconductor coupled to two parallel nanowires. Physical Review B, 100(2), Article ID 024512.
Open this publication in new window or tab >>Odd-frequency pairing in a superconductor coupled to two parallel nanowires
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 100, no 2, article id 024512Article in journal (Refereed) Published
Abstract [en]

We study the behavior of Cooper pair amplitudes that emerge when a two-dimensional superconductor is coupled to two parallel nanowires, focusing on the conditions for realizing odd-frequency pair amplitudes in the absence of spin-orbit coupling or magnetism. In general, any finite tunneling between the superconductor and the two nanowires induces odd-frequency spin-singlet pair amplitudes in the substrate as well as a substantial odd-frequency interwire pairing, both of which vanish locally. Interestingly, in the regime of strong superconductor-nanowire tunneling, we find that the presence of two nanowires allows for the conversion of nonlocal odd-frequency pairing to local even-frequency pairing. By studying this higher-order symmetry conversion process, we are able to identify a notable effect of the odd-frequency pairing in the superconductor on local quantities accessible by experiments. Specifically, we find that the odd-frequency pairing plays a direct role in the emergence of certain subgap features in the local density of states and, importantly, it is responsible for a reduction of the maximum Josephson current between the two nanowires, measurable using Josephson scanning tunneling microscopy. We discuss ways to control the sizes of these effects induced by odd-frequency superconductivity by tuning the parameters describing the nanowires.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-391938 (URN)10.1103/PhysRevB.100.024512 (DOI)000476686100005 ()
Funder
Swedish Research Council, 621-2014-3721Knut and Alice Wallenberg FoundationEU, Horizon 2020, ERC-2017-StG-757553
Available from: 2019-08-29 Created: 2019-08-29 Last updated: 2019-08-29Bibliographically approved
Tsintzis, A., Black-Schaffer, A. M. & Cayao, J. (2019). Odd-frequency superconducting pairing in Kitaev-based junctions. Physical Review B, 100(11), Article ID 115433.
Open this publication in new window or tab >>Odd-frequency superconducting pairing in Kitaev-based junctions
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 100, no 11, article id 115433Article in journal (Refereed) Published
Abstract [en]

We investigate odd-frequency superconducting correlations in normal-superconductor (NS) and short superconductor-normal-superconductor (SNS) junctions with the S region described by the Kitaev model of spinless fermions in one dimension. We demonstrate that, in both the trivial and topological phases, Andreev reflection is responsible for the coexistence of even- and odd-frequency pair amplitudes in N and S close to the interfaces, while normal reflections additionally only contributes to odd-frequency pairing in S. In the S region close to the NS interface we find that the odd-frequency pair amplitude exhibits large, but finite, values in the topological phase at low frequencies due to the emergence of a Majorana zero mode at the interface which also spreads into the N region. We also show that in S both the local density of states and local odd-frequency pairing can be characterized solely by Andreev reflections deep in the topological phase. Moreover, in the topological phase of short SNS junctions, we find that both even- and odd-frequency amplitudes capture the emergence of topological Andreev bound states. For a superconducting phase difference 0 < phi < pi the odd-frequency magnitude exhibits a linear frequency (similar to vertical bar omega vertical bar) dependence at low frequencies, while at phi = pi it develops a resonance peak (similar to 1/vertical bar omega vertical bar) due to the protected Majorana zero modes.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-395838 (URN)10.1103/PhysRevB.100.115433 (DOI)000488255500006 ()
Funder
Swedish Research Council, 621-2014-3721Knut and Alice Wallenberg FoundationEU, European Research Council, ERC-2017-StG-757553Göran Gustafsson Foundation for Research in Natural Sciences and Medicine
Available from: 2019-10-25 Created: 2019-10-25 Last updated: 2019-10-25Bibliographically approved
Triola, C. & Black-Schaffer, A. M. (2019). Odd-frequency superconductivity induced by nonmagnetic impurities. Physical Review B, 100(14), Article ID 144511.
Open this publication in new window or tab >>Odd-frequency superconductivity induced by nonmagnetic impurities
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 100, no 14, article id 144511Article in journal (Refereed) Published
Abstract [en]

A growing body of literature suggests that odd-frequency superconducting pair amplitudes can be generated in normal-metal-superconductor junctions. The emergence of odd-frequency pairing in these systems is often attributed to the breaking of translation invariance. In this work, we study the pair symmetry of a one-dimensional s-wave superconductor in the presence of a single nonmagnetic impurity and demonstrate that translation-symmetry breaking is not sufficient for inducing odd-frequency pairing. We consider three kinds of impurities: a local perturbation of the chemical potential, an impurity possessing a quantum energy level, and a local perturbation of the superconducting gap. Surprisingly, we find local perturbations of the chemical potential do not induce any odd-frequency pairing, despite the fact that they break translation invariance. Moreover, although odd frequency can be induced by both the quantum impurity and the perturbation of the gap, we find these odd-frequency amplitudes emerge from entirely different kinds of scattering processes. The quantum impurity generates odd-frequency pairs by allowing one of the quasiparticles belonging to an equal-time Cooper pair to tunnel onto the impurity state and then back to the superconductor, giving rise to odd-frequency amplitudes with a temporal broadening inversely proportional to the energy level of the impurity. In contrast to this, the perturbation of the gap leads to odd-frequency pairing by "gluing together" normal-state quasiparticles from different points in space and time, leading to odd-frequency amplitudes which are very localized in the time domain.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-396706 (URN)10.1103/PhysRevB.100.144511 (DOI)000491167700005 ()
Funder
Swedish Research Council, 621-2014-3721Swedish Research Council, 2018-03488Knut and Alice Wallenberg FoundationEU, European Research Council, ERC-2017-StG-757553
Available from: 2019-11-08 Created: 2019-11-08 Last updated: 2019-11-08Bibliographically approved
Dutta, P. & Black-Schaffer, A. M. (2019). Signature of odd-frequency equal-spin triplet pairing in the Josephson current on the surface of Weyl nodal loop semimetals. Physical Review B, 100(10), Article ID 104511.
Open this publication in new window or tab >>Signature of odd-frequency equal-spin triplet pairing in the Josephson current on the surface of Weyl nodal loop semimetals
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 100, no 10, article id 104511Article in journal (Refereed) Published
Abstract [en]

We theoretically predict proximity-induced odd-frequency (odd-omega) pairing on the surface of a Weyl nodal loop semimetal, characterized by a nodal loop Fermi surface and drumheadlike surface states (DSSs), attached to conventional spin-singlet s-wave superconducting leads. Due to the complete spin polarization of the DSS, only odd-omega equal-spin triplet pairing is present, and we show that it gives rise to a finite Josephson current. Placing an additional ferromagnet in the junction can also generate odd-omega) mixed-spin triplet pairing, but the pairing and current are not affected if the magnetization is orthogonal to the DSS spin polarization, which further confirms the equal-spin structure of the pairing.

National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-394954 (URN)10.1103/PhysRevB.100.104511 (DOI)000485311800006 ()
Funder
Swedish Research Council, 621-2014-3721Knut and Alice Wallenberg FoundationEU, European Research Council, ERC-2017-StG757553
Available from: 2019-10-21 Created: 2019-10-21 Last updated: 2019-10-21Bibliographically approved
Awoga, O., Cayao, J. & Black-Schaffer, A. M. (2019). Supercurrent Detection of Topologically Trivial Zero-Energy States in Nanowire Junctions. Physical Review Letters, 123(11), Article ID 117001.
Open this publication in new window or tab >>Supercurrent Detection of Topologically Trivial Zero-Energy States in Nanowire Junctions
2019 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 123, no 11, article id 117001Article in journal (Refereed) Published
Abstract [en]

We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with a strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in the junction when the superconductors induce a large energy shift in the nanowire, such that the junction naturally forms a quantum dot, a process that is highly tunable by the superconductor width. Most importantly, we demonstrate that the zero-energy states produce a re shift in the phase-biased supercurrent, which can be used as a simple tool for their unambiguous detection, ruling out any Majorana-like interpretation.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-395315 (URN)10.1103/PhysRevLett.123.117001 (DOI)000485315000011 ()31573272 (PubMedID)
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research Knut and Alice Wallenberg Foundation
Available from: 2019-10-18 Created: 2019-10-18 Last updated: 2019-10-18Bibliographically approved
Bouhon, A., Black-Schaffer, A. M. & Slager, R.-J. (2019). Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry. Physical Review B, 100(19), Article ID 195135.
Open this publication in new window or tab >>Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry
2019 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 100, no 19, article id 195135Article in journal (Refereed) Published
Abstract [en]

We present a general methodology toward the systematic characterization of crystalline topological insulating phases with time-reversal symmetry. In particular, taking the two-dimensional spinful hexagonal lattice as a proof of principle, we study windings of Wilson loop spectra over cuts in the Brillouin zone that are dictated by the underlying lattice symmetries. Our approach finds a prominent use in elucidating and quantifying the recently proposed "topological quantum chemistry" concept. Namely, we prove that the split of an elementary band representation (EBR) by a band gap must lead to a topological phase. For this we first show that in addition to the Fu-Kane-Mele Z(2) classification, there is C2T-symmetry-protected Z classification of two-band subspaces that is obstructed by the other crystalline symmetries, i.e., forbidding the trivial phase. This accounts for all nontrivial Wilson loop windings of split EBRs that are independent of the parametrization of the flow of Wilson loops. Then, by systematically embedding all combinatorial four-band phases into six-band phases, we find a refined topological feature of split EBRs. Namely, we show that while Wilson loop winding of split EBRs can unwind when embedded in higher-dimensional band space, two-band subspaces that remain separated by a band gap from the other bands conserve their Wilson loop winding, hence revealing that split EBRs are at least "stably trivial," i.e., necessarily nontrivial in the nonstable (few-band) limit but possibly trivial in the stable (many-band) limit. This clarifies the nature of fragile topology that has appeared very recently. We then argue that in the many-band limit, the stable Wilson loop winding is only determined by the Fu-Kane-Mele Z(2) invariant implying that further stable topological phases must belong to the class of higher-order topological insulators.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-398430 (URN)10.1103/PhysRevB.100.195135 (DOI)000498057300001 ()
Funder
Swedish Research Council, 621-2014-3721Knut and Alice Wallenberg Foundation
Available from: 2019-12-06 Created: 2019-12-06 Last updated: 2019-12-06Bibliographically approved
Cayao, J., Black-Schaffer, A. M., Prada, E. & Aguado, R. (2018). Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states. Beilstein Journal of Nanotechnology, 9, 1339-1357
Open this publication in new window or tab >>Andreev spectrum and supercurrents in nanowire-based SNS junctions containing Majorana bound states
2018 (English)In: Beilstein Journal of Nanotechnology, ISSN 2190-4286, Vol. 9, p. 1339-1357Article in journal (Refereed) Published
Abstract [en]

Hybrid superconductor-semiconductor nanowires with Rashba spin-orbit coupling are arguably becoming the leading platform for the search of Majorana bound states (MBSs) in engineered topological superconductors. We perform a systematic numerical study of the low-energy Andreev spectrum and supercurrents in short and long superconductor-normal-superconductor junctions made of nanowires with strong Rashba spin-orbit coupling, where an external Zeeman field is applied perpendicular to the spin-orbit axis. In particular, we investigate the detailed evolution of the Andreev bound states from the trivial into the topological phase and their relation with the emergence of MBSs. Due to the finite length, the system hosts four MBSs, two at the inner part of the junction and two at the outer one. They hybridize and give rise to a finite energy splitting at a superconducting phase difference of p, a wellvisible effect that can be traced back to the evolution of the energy spectrum with the Zeeman field: from the trivial phase with Andreev bound states into the topological phase with MBSs. Similarly, we carry out a detailed study of supercurrents for short and long junctions from the trivial to the topological phases. The supercurrent, calculated from the Andreev spectrum, is 2 pi-periodic in the trivial and topological phases. In the latter it exhibits a clear sawtooth profile at a phase difference of pi when the energy splitting is negligible, signalling a strong dependence of current-phase curves on the length of the superconducting regions. Effects of temperature, scalar disorder and reduction of normal transmission on supercurrents are also discussed. Further, we identify the individual contribution of MBSs. In short junctions the MBSs determine the current-phase curves, while in long junctions the spectrum above the gap (quasi-continuum) introduces an important contribution.

Place, publisher, year, edition, pages
BEILSTEIN-INSTITUT, 2018
Keywords
hybrid superconductor-semiconductor nanowire-superconductor junctions, Josephson effect, Majorana bound states, nanowires, spin-orbit coupling, Zeeman interaction
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:uu:diva-356396 (URN)10.3762/bjnano.9.127 (DOI)000431383200001 ()
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research Knut and Alice Wallenberg Foundation
Available from: 2018-07-25 Created: 2018-07-25 Last updated: 2018-07-25Bibliographically approved
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