arXiv subjects

Annica M. Black-Schaffer

Publications and source records attributed to Annica M. Black-Schaffer.

At least 91 records · Page 5Linked to original sources

arXiv2020

Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model

The Su-Schrieffer-Heeger model describes fermions that hop on a one-dimensional chain with staggered hopping amplitude, where the unit cell contains two sites, or two sublattices. In this work we consider the Su-Schrieffer-Heeger model with superconducting pairing and show that the sublattice index acts as an additional quantum number in the classification of Cooper pairs, giving rise to inter- and intra-sublattice odd-frequency pair correlations in the bulk. Interestingly, this system behaves as a two band superconductor where the bulk odd-frequency correlations depend solely on the intrinsic staggering properties of the model. In general, odd-frequency correlations coexist with even-frequency correlations in both the trivial and topological phases, with comparable and even larger odd-frequency amplitudes at the topological phase transition points at low frequencies, due to the closing of the energy gap at these points. Furthermore, we also discuss how bulk odd-frequency amplitudes are correlated with pseudo-gaps in the density of states and also with a charge density wave that appears due to the chemical potential imbalance between sublattices.

cond-mat.mes-hall↗

arXiv2020

Odd-frequency superconductivity and Meissner effect in the doped topological insulator Bi$_2$Se$_3$

Doped Bi$_2$Se$_3$ is proposed to be a nematic superconductor originating from unusual inter-orbital pairing. We classify all induced superconducting pair correlations in Bi$_2$Se$_3$ and discover that intra-orbital odd-frequency pairing dominates over a significant range of frequencies. Moreover, we explore the contributions of even- and odd-frequency pairing to the Meissner effect, including separating intra- and inter-band processes in the response function. Contrary to expectations, and due to inter-band contributions, we find a diamagnetic odd-frequency Meissner effect.

cond-mat.supr-con↗

arXiv2020

Highly tunable magnetic coupling in ultrathin topological insulator films due to impurity resonances

We theoretically investigate the exchange interaction between magnetic impurities in ultrathin Bi$_2$Se$_3$ topological insulator films by taking into account the low-energy states produced by the impurities. We find that the locally induced impurity resonances strongly influence the exchange interaction between magnetic moments. In particular, we find a non-collinear alignment being more favorable than the collinear ferromagnetic alignment preferred when impurity states are ignored and only the pristine topological insulator band structure is considered. Moreover, we show that by applying of an electric field perpendicular to the ultrathin film, the exchange interaction can be drastically enhanced. This opens for the possibility of highly tunable magnetism by electric field.

cond-mat.mtrl-sci↗

arXiv2020

Finite bulk Josephson currents and chirality blockade removal from inter-orbital pairing in magnetic Weyl semimetals

Magnetic Weyl semimetals (WSMs) have been presumed to be immune to proximity-induced spin-singlet superconducting pairing due to a chirality blockade of the regular Andreev reflection. In this work we study all possible superconducting pairing induced in a WSM sandwiched between two conventional superconductors in a Josephson junction setup. We confirm that, while conventional intra-orbital $s$-wave pairing is present on the surface of the WSM, it cannot propagate into the bulk due to the chirality blockade. However, inter-orbital $s$-wave pairing, with both even-frequency spin-singlet and odd-frequency mixed-spin triplet symmetry, propagates into the bulk of the WSM, as do several $p$-wave symmetries. To demonstrate the importance of these finite inter-orbital and $p$-wave pair amplitudes in an experimental setup, we calculate the Josephson current and find a finite and even increasing current when the chirality blockade effect for the conventional intra-orbital pairing is enhanced.

cond-mat.supr-con↗

arXiv2020

Odd-frequency superconducting pairing in one-dimensional systems

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-dimensional topological superconductivity whose edges can host Majorana zero modes. We also provide a detailed discussion of the intimate relationship between Majorana zero modes and odd-frequency pairing. Throughout this review, we highlight the ways in which odd-frequency pairing provides a deeper understanding of the unconventional superconducting correlations present in each of these intriguing systems and how the study and control of these states holds the potential for future applications.

cond-mat.mes-hall↗

arXiv2019

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

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 superconducting correlations due to their specific properties. Thus, by tunnel-coupling an array of Majorana zero modes to a spin-polarized wire, it is in principle possible to engineer a bulk one-dimensional odd-frequency spinless $s$-wave superconductor. We here point out that each tunnel coupling element, being dependent on a large number of material-specific parameters, is generically complex with sample variability in both its magnitude and phase. Using this, we demonstrate that, upon averaging over phase-disorder, the induced superconducting, including odd-frequency, correlations in the spin-polarized wire are significantly suppressed. We perform both a rigorous analytical evaluation of the disorder-averaged $T$-matrix in the wire, as well as numerical calculations based on a tight-binding model, and find that the anomalous, i.e. superconducting, part of the $T$-matrix is highly suppressed with phase disorder. We also demonstrate that this suppression is concurrent with the filling of the single-particle excitation gap by smearing the near-zero frequency peaks, due to formation of bound states that satisfy phase-matching conditions between spatially separated Majorana zero modes. Our results convey important constraints on the parameter control needed in practical realizations of Majorana zero mode structures and suggest that the achievement of a bulk 1D odd-$ω$ superconductivity from MZMs demand full control of the system parameters.

cond-mat.supr-con↗

arXiv2019

Odd-frequency superconductivity induced by non-magnetic impurities

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 non-magnetic 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.

cond-mat.supr-con↗

arXiv2019

Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry

We present a general methodology towards the systematic characterization of crystalline topological insulating phases with time reversal symmetry (TRS).~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" (TQC) 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 $\mathbb{Z}_2$ classification, there is $C_2\mathcal{T}$-symmetry protected $\mathbb{Z}$ 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 \textit{that are independent of the parameterization of the flow of Wilson loops}.~Then, 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 non-trivial in the non-stable (few-band) limit but possibly trivial in the stable (many-band) limit.~This clarifies the nature of \textit{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 $\mathbb{Z}_2$ invariant implying that further stable topological phases must belong to the class of higher-order topological insulators.

cond-mat.mes-hall↗

arXiv2019

Odd-frequency superconducting pairing in Kitaev-based junctions

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 interface, but notably there is no divergence and a finite odd-frequency pair amplitude also exists outside the topological phase. We also show that 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 $0<ϕ<π$ the odd-frequency magnitude exhibits a linear frequency ($\sim |ω|$) dependence at low-frequencies, while at $ϕ=π$ it develops a resonance peak ($\sim 1/|ω|$) due to the protected Majorana zero modes.

cond-mat.mes-hall↗

arXiv2019

Supercurrent detection of topologically trivial zero-energy states in nanowire junctions

We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with 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 $π$-shift in the phase-biased supercurrent, which can be used as a simple tool for their unambiguous detection, ruling out any Majorana-like interpretation.

cond-mat.mes-hall↗

arXiv2019

Signature of odd-frequency equal-spin triplet pairing in the Josephson current on the surface of Weyl nodal loop semimetals

We theoretically predict proximity-induced odd-frequency (odd-$ω$) pairing on the surface of a Weyl nodal loop semimetal, characterized by a nodal loop Fermi surface and drumhead-like surface states (DSSs), attached to conventional spin-singlet $s$-wave superconducting leads. Due to the complete spin polarization of the DSS, odd-$ω$ 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-$ω$ mixed-spin triplet pairing, but the pairing and current is not affected if the magnetization is orthogonal to the DSS spin-polarization, which further confirms the equal-spin structure of the pairing.

cond-mat.supr-con↗

arXiv2019

The Role of Odd-Frequency Pairing in Multiband Superconductors

In this article we review recent progress in the understanding of multiband superconductivity and its relationship to odd-frequency pairing. We begin our discussion by reviewing the emergence of odd-frequency pairing in a simple two-band model, providing a brief pedagogical overview of the formalism. We then examine several examples of multiband superconducting systems in each case describing, both, the origin of the band degree of freedom and the nature of the odd-frequency pairing. Throughout, we attempt to convey a unified picture of how odd-frequency pairing emerges in these materials and propose that similar mechanisms are responsible for odd-frequency pairing in several analogous systems: layered two-dimensional heterostructures, double quantum dots, double nanowires, Josephson junctions, and systems described by isolated valleys in momentum space. We also review experimental probes of odd-frequency pairing in multiband systems, focusing on hybridization gaps in the electronic density of states, paramagnetic Meissner effect, and Kerr effect.

cond-mat.supr-con↗

arXiv2019

Odd-frequency pairing in a superconductor coupled to two parallel nanowires

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 non-local 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.

cond-mat.supr-con↗

arXiv2019

Majorana bound state localization and energy oscillations for magnetic impurity chains on conventional superconductors

We study a chain of magnetic impurities on a conventional superconductor with spin-orbit coupling, treating the superconducting order fully self-consistently. We find and quantify strong hybridization between the topological edge Majorana bound states (MBSs) and in-gap Yu-Shiba-Rusinov (YSR) states, which causes increasing energy oscillations as a function of magnetic impurity strength, even when the direct MBS overlap is negligible. By treating the MBS as a topological boundary state, dependent only on the effective mass gap, we arrive at a fully parameter-free functional form of the its localization which decreases with magnetic impurity strength, opposite to the behavior of the superconducting coherence length.

cond-mat.supr-con↗

arXiv2019

Gap oscillations and Majorana bound states in magnetic chains on superconducting honeycomb lattices

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 phase diagrams showing the topological regions (where MBSs appear), which are strongly dependent on the spiral angle along the chain of the magnetic moments. In particular, find large regions where the topological phase is robust even at large values of the local Zeeman field, thus producing topological regions without an upper bound. Moreover, we show that the energy oscillations of the MBSs can show very different behavior with magnetic field strength. In some parameter regimes we find increasing oscillations amplitudes and decreasing periods, while in the other regimes the complete opposite behavior is found with increasing magnetic field strength. 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.

cond-mat.mes-hall↗

arXiv2019

Finite length effect on supercurrents between trivial and topological superconductors

We numerically analyze the effect of finite length of the superconducting regions on the low-energy spectrum, current-phase curves, and critical currents in junctions between trivial and topological superconductors. Such junctions are assumed to arise in nanowires with strong spin-orbit coupling under external magnetic fields and proximity-induced superconductivity. We show that all these quantities exhibit a strong dependence on the length of the topological sector in the topological phase and serve as indicators of the topological phase and thus the emergence of Majorana bound states at the end of the topological superconductor.

cond-mat.mes-hall↗

arXiv2018

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

We consider normal-superconductor (NS) and superconductor-normal-superconductor (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 correlations are induced, but only even-frequency spin-singlet pairing. In the superconducting regions of NS junctions, the interface-induced amplitudes decay into the bulk, with the odd-frequency components being generally much larger than the even-frequency components at low frequencies. The odd-frequency pairing also develops short and long-period oscillations due to the chemical potential and spin-orbit coupling, respectively, leading to a visible beating feature in their magnitudes. Moreover, we find that in short SNS junctions at $π$-phase difference and strong spin-orbit coupling, the odd-frequency spin-singlet and -triplet correlations strongly dominate with an alternating spatial pattern for a large range of sub-gap frequencies.

cond-mat.mes-hall↗

arXiv2018

Probing unconventional superconductivity in proximitized graphene by impurity scattering

We demonstrate how potential impurities are a very powerful tool for determining the pairing symmetry in graphene proximity-coupled to a spin-singlet superconductor. All d-wave states are characterized by subgap resonances, with spatial patterns clearly distinguishing between nodal and chiral d-wave symmetry, while s-wave states have no subgap resonances. We also find strong supergap impurity resonances associated with the normal state Dirac point. Sub- and supergap resonances only interact at very low doping levels, then causing suppression of the supergap resonances.

cond-mat.supr-con↗