Odd-frequency superconducting pairing due to multiple Majorana edge modes in driven topological superconductors

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   Odd-frequency superconductivity in a nanowire coupled to Majorana zero modes

   Shu-Ping Lee, R. Lutchyn, J. Maciejko · 2016 · Physical Review B · cité 32 fois · Pas encore résumé

   Résumé scientifique

   Here, the authors argue that the recent experimental discovery of Majorana zero modes in topological superconductors may be the key to realizing an elusive state of matter, the odd-frequency superconductor, in which Cooper pairing is entirely dynamical in nature. Via an exactly soluble model, it is shown that when Majorana zero modes couple to a spin-polarized metallic system, equal-spin $s$-wave odd-frequency pairing is generically induced in the spin-polarized metal. The key properties of odd-frequency superconductivity, such as a vanishing static superconducting order parameter and a paramagnetic Meissner effect, are demonstrated in this system by explicit calculations.

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   Odd-frequency superconducting pairing in one-dimensional systems

   Jorge Cayao, Christopher Triola, A. Black-Schaffer · 2019 · The European Physical Journal Special Topics · cité 88 fois · Pas encore résumé

   Résumé scientifique

   Odd-frequency superconductivity represents a truly unconventional ordered state which, in contrast to conventional superconductivity, exhibits pair correlations which are odd in relative time and, hence, inherently dynamical. In this review article we provide an overview of recent advances in the study of odd-frequency superconducting correlations in one-dimensional systems. In particular, we focus on recent developments in the study of nanowires with Rashba spin-orbit coupling and metallic edges of two-dimensional topological insulators in proximity to conventional superconductors. These systems have recently elicited a great deal of interest due to their potential for realizing one-dimensi…

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   Odd-frequency superconducting pairing in topological insulators

   A. Black-Schaffer, A. Balatsky · 2012 · Physical Review B · cité 61 fois · Pas encore résumé

   Résumé scientifique

   We discuss the appearance of odd-frequency spin-triplet s-wave superconductivity, first proposed by Berezinskii [J. Exp. Theor. Phys. 20, 287 (1974)], on the surface of a topological insulator proximity coupled to a conventional spin- singlet s-wave superconductor. Using both analytical and numerical methods, we show that this disorder robust odd-frequency state is present whenever there is an in-surface gradient in the proximity induced gap, including superconductor-normal state junctions. The time-independent order parameter for the odd-frequency superconductor is proportional to the in-surface gap gradient. The induced odd-frequency component does not produce any low-energy states.

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   Odd-frequency superconducting pairing and subgap density of states at the edge of a two-dimensional topological insulator without magnetism

   Jorge Cayao, A. Black-Schaffer · 2017 · Physical Review B · cité 69 fois · Pas encore résumé

   Résumé scientifique

   We investigate the emergence and consequences of odd-frequency spin-triplet s-wave pairing in superconducting hybrid junctions at the edge of a two-dimensional topological insulator without any mag ...

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   Suppression of odd-frequency pairing by phase disorder in a nanowire coupled to Majorana zero modes

   D. Kuzmanovski, A. Black-Schaffer, Jorge Cayao · 2019 · Physical review B · cité 20 fois · Pas encore résumé

   Résumé scientifique

   Odd-frequency superconductivity is an exotic phase of matter in which Cooper pairing between electrons is entirely dynamical in nature. Majorana zero modes exhibit pure odd-frequency superconductin ...

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   Odd frequency pairing of interacting Majorana fermions

   Zhoushen Huang, P. Wölfle, A. V. Balatsky · 2015 · Physical Review B · cité 25 fois · Pas encore résumé

   Résumé scientifique

   In this study, Majorana fermions are rising as a promising key component in quantum computation. Although the prevalent approach is to use a quadratic (i.e., noninteracting) Majorana Hamiltonian, when expressed in terms of Dirac fermions, generically the Hamiltonian involves interaction terms. Here we focus on the possible pair correlations in a simple model system. We study a model of Majorana fermions coupled to a boson mode and show that the anomalous correlator between different Majorana fermions, located at opposite ends of a topological wire, exhibits odd-frequency behavior. It is stabilized when the coupling strength g is above a critical value gc. We use both, conventional diagrammat…

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   Odd-frequency pairing in normal-metal/superconductor junctions

   Yukio Tanaka, Y. Tanuma, A. Golubov · 2007 · Physical Review B · cité 123 fois · Pas encore résumé

   Résumé scientifique

   We theoretically study the induced odd-frequency pairing states in ballistic normal-metal/superconductor (N/S) junctions where a superconductor has even-frequency symmetry in the bulk and a normal-metal layer has an arbitrary length. Using the quasiclassical Green's function formalism, we demonstrate that, quite generally, the pair amplitude in the junction has an admixture of an odd-frequency component due to the breakdown of translational invariance near the N/S interface where the pair potential acquires spatial dependence. If a superconductor has an even-parity pair potential (spin-singlet s-wave or spin-singlet dxy-wave state), the odd-frequency pairing component with odd parity is indu…

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   Generalized conditions for odd-frequency pairing in superconducting systems

   Florian Kayatz, A. Black-Schaffer, Jorge Cayao · 2026 · Pas encore résumé

   Résumé scientifique

   Odd-frequency superconducting pairing has been predicted to arise in many systems and is known to lead to phenomena such as paramagnetic Meissner response and long-range superconducting proximity effect. Here, we provide generalized necessary and sufficient conditions for odd-frequency pairing appearing in any superconducting system, from bulk superconductors to superconducting hybrid structures. This generalizes an earlier first-order expression in multiband bulk superconductors to all superconducting systems and to all orders, in both order parameter and frequency. We then apply the derived conditions to several systems, including superconducting-ferromagnet and superconducting Josephson j…

Les travaux antérieurs sur lesquels il s’appuie

1. Très proche Utilisé en profondeur par cet article Pas pertinent

   Generating many Majorana modes via periodic driving: A superconductor model

   Qing-Jun Tong, Jun-Hong An, J. Gong et al. · 2012 · Physical Review B · cité 154 fois · Pas encore résumé

   Résumé scientifique

   Realizing Majorana modes (MMs) in condensed-matter systems is of vast experimental and theoretical interests, and some signatures of MMs have been measured already. To facilitate future experimental observations and to explore further applications of MMs, generating many MMs at ease in an experimentally accessible manner has become one important issue. This task is achieved here in a one-dimensional $p$-wave superconductor system with the nearest- and next-nearest-neighbor interactions. In particular, a periodic modulation of some system parameters can induce an effective long-range interaction (as suggested by the Baker-Campbell-Hausdorff formula) and may recover time-reversal symmetry alre…

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   Odd-frequency pairs in chiral symmetric systems: Spectral bulk-boundary correspondence and topological criticality

   S. Tamura, S. Hoshino, Yukio Tanaka · 2018 · Physical review B · cité 30 fois · Pas encore résumé

   Résumé scientifique

   Odd-frequency Cooper pairs with chiral symmetry emerging at the edges of topological superconductors are a useful physical quantity for characterizing the topological properties of these materials. In this work, we show that the odd-frequency Cooper pair amplitudes can be expressed by a winding number extended to a nonzero frequency, which is called a ``spectral bulk-boundary correspondence,'' and can be evaluated from the spectral features of the bulk. The odd-frequency Cooper pair amplitudes are classified into two categories: the amplitudes in the first category have the singular functional form $\ensuremath{\sim}1/z$ (where $z$ is a complex frequency) that reflects the presence of a topo…

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   Theory of Surface Andreev Bound States and Odd-Frequency Pairing in Superconductor Junctions

   Yukio Tanaka, S. Tamura · 2020 · Journal of Superconductivity and Novel Magnetism · cité 15 fois · Pas encore résumé
4. Très proche Pas pertinent

   Odd-frequency superconducting pairing in Kitaev-based junctions

   Athanasios Tsintzis, A. Black-Schaffer, Jorge Cayao · 2019 · Physical review B · cité 23 fois · Pas encore résumé

   Résumé scientifique

   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 at interfaces, while normal reflections solely contribute to odd-frequency pairing. At NS interfaces we find that the odd-frequency pair amplitude exhibits large, but finite, values in the topological phase at low frequencies. This enhancement is due to the emergence of a Majorana zero mode at the i…

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   Odd-frequency superconducting pairing in junctions with Rashba spin-orbit coupling

   Jorge Cayao, A. Black-Schaffer · 2018 · Physical review B · cité 43 fois · Pas encore résumé

   Résumé scientifique

   We consider NS and SNS junctions based on one-dimensional nanowires with Rashba spin-orbit coupling and proximity-induced $s$-wave spin singlet superconductivity and analytically demonstrate how both even- and odd-frequency and spin-singlet and triplet superconducting pair correlations are always present. In particular, by using a fully quantum mechanical scattering approach, we show that Andreev reflection induces mixing of spatial parities at interfaces, thus being the unique process which generates odd-frequency pairing; on the other hand, both Andreev and normal reflections contribute to even-frequency pairing. We further find that locally neither odd-frequency nor spin-triplet correlati…

Les articles qui le citent

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   Odd‐Frequency Pairing in Josephson Junctions Coupled by Magnetic Textures

   Ignacio Sardinero, Jorge Cayao, Rubén Seoane Souto et al. · 2025 · Physica Status Solidi (a) · cité 1 fois · Pas encore résumé

   Résumé scientifique

   Josephson junctions (JJs) coupled through magnetic textures provide a controllable platform for odd‐frequency superconductivity and Majorana physics. Within a tight‐binding Green function framework, induced pair correlations and spectral properties are analyzed under various magnetic and geometric conditions. When the junction is in the topologically trivial regime, even‐frequency singlet pairing is dominant, whereas the topological phase is characterized by the coexistence of Majorana bound states and robust odd‐frequency equal‐spin triplet pairing at the interface edges. The odd‐frequency polarized triplets reveal a divergent 1/ω$1 / \omega$ behavior when the Majorana states are decoupled,…

2. Proche Pas pertinent

   Single and multifrequency driving protocols in a Rashba nanowire proximitized to an s -wave superconductor

   Koustav Roy, S. Basu · 2024 · Physical review B · cité 9 fois · Pas encore résumé

   Résumé scientifique

   We perform systematic analyses of single and multi-frequency driving protocols on a Rashba nanowire with superconducting correlations induced by proximity effects. The results for the single-mode drive reveal interesting frequency dependencies of the Majorana modes, in the sense that the parameters corresponding to the trivial and topological limits of the undriven (static) case host Majorana zero modes, respectively at low and high frequencies. Further, emergence of long-range interactions are noted that give rise to multiple gap-closing scenarios, which imply occurrence of multiple Majorana modes. On the other hand, the multi-frequency driving protocol, sub-grouped into commensurate and in…

3. Proche Pas pertinent

   Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets

   Pei-Hao Fu, Sayan Mondal, Jun-Feng Liu et al. · 2025 · SciPost Physics · cité 33 fois · Pas encore résumé

   Résumé scientifique

   The recently predicted unconventional magnets offer a new ground for exploring the formation of nontrivial spin states due to their inherent nonrelativistic momentum-dependent spin splitting. In this work, we consider unconventional magnets with d d - and p p -wave parities, and investigate the effect of time-periodic light drives for inducing the formation of spin-triplet phases in the normal and superconducting states. In particular, we consider unconventional magnets without and with conventional superconductivity under linearly and circularly polarized light drives and treat the time-dependent problem within Floquet formalism, which naturally unveils photon processes and Floquet bands de…

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   Dissipation-induced Majarona <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mn>0</mml:mn> </mml:math> - and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"

   Koustabh Gogoi, T. Nag, A. Ghosh · 2025 · Physical review B · cité 1 fois · Pas encore résumé

   Résumé scientifique

   Periodic drive is an intriguing way of creating topological phases in a non-topological setup. However, most systems are often studied as a closed system, despite being always in contact with the environment, which induces dissipation. Here, we investigate a periodically driven Rashba nanowire in proximity to an $s$-wave superconductor in a dissipative background. The system's dynamics is governed by a periodic Liouvillian operator, from which we construct the Liouvillian time-evolution operator and use the third-quantization method to obtain the `Floquet damping matrix', which captures the spectral and topological properties of the system. We show that the system exhibits edge-localized top…

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   Transport signatures of single and multiple Floquet Majorana modes in one-dimensional Rashba nanowire and Shiba chain

   Debashish Mondal, Rekha Kumari, T. Nag et al. · 2024 · cité 4 fois · Pas encore résumé

   Résumé scientifique

   We theoretically investigate the transport signature of single and multiple Floquet Majorana end modes~(FMEMs), appearing in an experimentally feasible setup with Rashba nanowire~(NW) placed in closed proximity to a conventional $s$-wave superconductor, in the presence of an external Zeeman field. Periodic drive causes the anomalous $\pi$-modes to emerge in addition to the regular $0$-modes in the driven system where the former does not exhibit any static analog. For single $0$- and/or $\pi$-FMEM, differential conductance exhibits a quantized value of $2e^{2}/h$ while we consider the sum over all the photon sectors, supporting Floquet sum rule. We examine the stability of this summed conduct…