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Annica M. Black-Schaffer

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

At least 55 records · Page 3Linked to original sources
arXiv2024

Nonlocality of Majorana bound states revealed by electron waiting times in a topological Andreev interferometer

The analysis of waiting times of electron transfers has recently become experimentally accessible owing to advances in noninvasive probes working in the short-time regime. We study electron waiting times in a topological Andreev interferometer: a superconducting loop with controllable phase difference connected to a quantum spin Hall edge, where the edge state helicity enables the transfer of electrons and holes into separate leads, with transmission controlled by the loop's phase difference $ϕ$. This setup features gapless Majorana bound states at $ϕ=π$. The waiting times for electron transfers across the junction are sensitive to the presence of the gapless states, but are uncorrelated for all $ϕ$. By contrast, at $ϕ=π$ the waiting times of Andreev-scattered holes show a strong correlation and the crossed (hole-electron) distributions feature a unique behavior. Both effects exclusively result from the nonlocal properties of Majorana bound states. Consequently, electron waiting times and their correlations could circumvent some of the challenges for detecting topological superconductivity and Majorana states beyond conductance signatures.

cond-mat.supr-con↗
arXiv2023

Superconductivity and magnetism in the surface states of ABC-stacked multilayer graphene

ABC-stacked multilayer graphene (ABC-MLG) exhibits topological surface flat bands with a divergent density of states, leading to many-body instabilities at charge neutrality. Here, we explore electronic ordering within a mean-field approach with full generic treatment of all spin-isotropic, two-site charge density and spin interactions up to next-nearest neighbor (NNN) sites. We find that surface superconductivity and magnetism are significantly enhanced over bulk values. We find spin-singlet $s$ wave and unconventional NNN bond spin-triplet $f$ wave to be the dominant superconducting pairing symmetries, both with a full energy gap. By establishing the existence of ferromagnetic intra-sublattice interaction, $(J_2<0)$ we conclude that the $f$-wave state is favored in ABC-MLG, in sharp contrast to bulk ABC-graphite where chiral $d$- or $p$-wave states, together with s-wave states, display stronger ordering tendencies albeit not achievable at charge neutrality. We trace this distinctive surface behavior to the strong sublattice polarization of the surface flat bands. We also find competing ferrimagnetic order, fully consistent with density functional theory (DFT) calculations. The magnetic order interpolates between sublattice ferromagnetism and antiferromagnetism, but only with the ratio of the sublattice magnetic moments ($R$) being insensitive to the DFT exchange correlation functional. We finally establish the full phase diagram by constraining the interactions to the $R$-value identified by DFT. We find $f$-wave superconductivity being favored for all weak to moderately strong couplings $J_2$ and as long as $J_2$ is a sufficiently large part of the full interaction mix. Gating ABC-MLG away from charge neutrality further enhances the $f$-wave state over the ferrimagnetic state, establishing ABC-MLG as a strong candidate for $f$-wave superconductivity.

cond-mat.supr-con↗
arXiv2023

Enhanced chiral edge currents and orbital magnetic moment in chiral $d$-wave superconductors from mesoscopic finite-size effects

Chiral superconductors spontaneously break time-reversal symmetry and host topologically protected edge modes, supposedly generating chiral edge currents which are typically taken as a characteristic fingerprint of chiral superconductivity. However, recent studies have shown that the total edge current in two dimensions (2D) often vanishes for all chiral superconductors except for chiral $p$-wave, especially at low temperatures, thus severely impeding potential experimental verification and characterization of these superconductors. In this work, we use quasiclassical theory of superconductivity to study mesoscopic disc-schaped chiral $d$-wave superconductors. We find that mesoscopic finite-size effects cause a dramatic enhancement of the total charge current and orbital magnetic moment (OMM), even at low temperatures. We study how these quantities scale with temperature, spontaneous Meissner screening, and system radius $\mathcal{R} \in [5,200]ξ_0$ with superconducting coherence length $ξ_0$. We find a general $1/\mathcal{R}$ scaling in the total charge current and OMM for sufficiently large systems, but this breaks down in small systems, instead producing a local maximum at $\mathcal{R} \approx 10{\text{--}}20ξ_0$ due to mesoscopic finite-size effects. These effects also cause a spontaneous charge-current reversal opposite to the chirality below $\mathcal{R} < 10ξ_0$. Our work highlights mesoscopic systems as a route to experimentally verify chiral $d$-wave superconductivity, measurable with magnetometry.

cond-mat.supr-con↗
arXiv2023

Topological superconductivity enhanced by exceptional points

Majorana zero modes (MZMs) emerge as edge states in topological superconductors and are promising for topological quantum computation, but their detection has so far been elusive. Here we show that non-Hermiticity can be used to obtain dramatically more robust MZMs. The enhanced properties appear as a result of an extreme instability of exceptional points to superconductivity, such that even a vanishingly small superconducting order parameter already opens a large energy gap, produces well-localized MZMs, and leads to strong superconducting pair correlations. Our work thus illustrates the large potential of enhancing topological superconductivity using non-Hermitian exceptional points.

cond-mat.supr-con↗
arXiv2023

Robust and tunable coreless vortices and fractional vortices in chiral $d$-wave superconductors

Chiral $d$-wave superconductivity has recently been proposed in a wide range of materials based on both experiment and theoretical works. Chiral superconductors host a finite Chern number set by the winding of the superconducting order parameter and associated topologically protected chiral edge modes. However, the chiral edge currents and orbital angular momentum (OAM) generated by the edge modes are not topologically protected and another, more robust, experimental probe is therefore needed to facilitate experimental verification of chiral $d$-wave superconductors. We have recently shown the appearance of quadruply quantized coreless vortices (CVs) in chiral $d$-wave superconductors, consisting of a closed domain wall decorated with eight fractional vortices, and generating a smoking-gun signature of the Chern number, chirality, and the superconducting pairing symmetry [P. Holmvall and A. M. Black-Schaffer, arXiv:2212.08156 (2023)]. Specifically, the CV spontaneously breaks axial symmetry for parallel chirality and vorticity, with a signature appearing directly in the local density of states (LDOS) measurable with scanning-tunneling spectroscopy (STS). In this work, we first demonstrate a strong tunability of the CV size and shape directly reflected in the LDOS and then show that the LDOS signature is robust in the presence of regular Abrikosov vortices, strong confinement, system and normal-state anisotropy, different Fermi surfaces (FSs), non-degenerate order parameters, and even non-magnetic impurities. In conclusion, our work establishes CVs as a tunable and robust signature of chiral $d$-wave superconductivity.

cond-mat.supr-con↗
arXiv2023

Defect-induced band restructuring and length scales in twisted bilayer graphene

We investigate the effects of single, multiple, and extended defects in the form of non-magnetic impurities and vacancies in twisted bilayer graphene (TBG) at and away from the magic angle, using a fully atomistic model and focusing on the behavior of the flat low-energy moiré bands. For strong impurities and vacancies in the $AA$ region we find a complete removal of one of the four moiré bands, resulting in a significant depletion of the charge density in the $AA$ regions even at extremely low defect concentrations. We find similar results for other defect locations, with the exception of the least coordinated sites in the $AB$ region, where defects instead result in a peculiar band replacement process within the moiré bands. In the vacancy limit, this process yields a band structure misleadingly similar to the pristine case. Moreover, we show that triple point fermions (TPFs), which are the crossing of the Dirac point by a flat band, appearing for single, periodic, defects, are generally not preserved when adding extended or multiple defects, and thus likely not experimentally relevant. We further identify two universal length scales for defects, consisting of charge modulations on the atomic scale and on the moiré scale, illustrating the importance of both the atomic and moiré structures for understanding TBG. We show that our conclusions hold beyond the magic angle and for fully isolated defects. In summary, our results demonstrate that the normal state of TBG and its moiré flat bands are extremely sensitive to both the location and strength of non-magnetic impurities and vacancies, which should have significant implications for any emergent ordered state.

cond-mat.mes-hall↗
arXiv2023

Mitigating disorder-induced zero-energy states in weakly-coupled semiconductor-superconductor hybrid systems

Disorder has appeared as one of the main mechanisms to induce topologically trivial zero-energy states in superconductor-semiconductor systems, thereby challenging the detection of topological superconductivity and Majorana bound states. Here we demonstrate that, for disorder in any part of the system, the formation of disorder-induced trivial zero-energy states can to a large extent be mitigated by keeping the coupling between the semiconductor and superconductor weak. The only exception is strong disorder in the semiconductor, where instead the strong coupling regime is somewhat more robust against disorder. Furthermore, we find that the topological phase in this weak coupling regime is robust against disorder, with a large and well-defined topological gap which is highly beneficial for topological protection. Our work shows the advantages and disadvantages of weak and strong couplings under disorder, important for designing superconductor-semiconductor hybrid structures.

cond-mat.supr-con↗
arXiv2023

Coreless vortices as direct signature of chiral $d$-wave superconductivity

Chiral $d$-wave superconductivity has been proposed in a number of different materials, but characteristic experimental fingerprints have been largely lacking. We show that quadruply quantized coreless vortices are prone to form and offer distinctive signatures of the chiral $d$-wave state in both the local density of states and the total magnetic moment. Their dissimilarity in positive versus negative magnetic fields further leads to additional spontaneous symmetry breaking, producing clear evidence of time-reversal symmetry breaking, chiral superconductivity, and the Chern number.

cond-mat.supr-con↗
arXiv2023

Bulk Bogoliubov Fermi arcs in non-Hermitian superconducting systems

We consider a non-Hermitian superconducting system by coupling a conventional superconductor to a ferromagnet lead and demonstrate the emergence of exceptional points when an external Zeeman field is applied. We discover that, depending on the non-Hermiticity and the Zeeman field, the exceptional points mark the ends of lines with zero real energy, thus giving rise to topologically protected and highly tunable bulk Fermi arcs, which we coin bulk Bogoliubov Fermi arcs due to their superconducting nature. We show that these bulk Bogoliubov Fermi arcs are the non-Hermitian counterparts of the Hermitian topological phase transition but are much more prevalent and also experimentally detectable through large spectral signatures.

cond-mat.supr-con↗
arXiv2023

Detrimental effects of disorder in two-dimensional time-reversal invariant topological superconductors

The robustness against local perturbations, as long as the symmetry of the system is preserved, is a distinctive feature of topological quantum states. Magnetic impurities and defects break time-reversal invariance and, consequently, time-reversal invariant (TRI) topological superconductors are fragile against this type of disorder. Non-magnetic impurities, however, preserve time-reversal symmetry and one naively expects a TRI topological superconductor to persist in the presence of non-magnetic impurities. In this work, we study the effect of non-magnetic disorder on a TRI topological superconductor with extended $s$-wave pairing, which can be engineered at the interface of an Fe-based superconductor and a strongly spin-orbit coupled Rashba layer. We model two different types of non-magnetic random disorder and analyze both the bulk density of states and edge state spectrum. Contrary to naive expectations, we find that the disorder strongly affects the topological phase by closing the energy gap, while trivial superconducting phases remain stable and fully gapped. The disorder phase diagram reveals a strong expansion of a nodal phase with increasing disorder. We further show the decay of the helical Majorana edge states in the topological phase and how they eventually disappear with increasing disorder. These results alter our understanding of effects of impurities and disorder on TRI topological phases and may help explain the difficulty of experimental observation of TRI topological superconductors.

cond-mat.supr-con↗
arXiv2023

Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions

We propose a method to distinguish between trivial and topological, Majorana, zero-energy states in both short and long superconductor-normal-superconductor junctions based on Rashba nanowires using phase-biased equilibrium transport measurements. In particular, we show how the sawtooth profile of the supercurrent, due to the Majorana oscillation suppression in the topological phase for sufficiently long superconductor regions, leads to a strong signal in its zero-frequency susceptibility for a phase difference of $ϕ=π$. This signal is notably insensitive to the chemical potential in the normal region, while trivial zero-energy states only causes signals in the susceptibility that is highly varying with the chemical potential, thus turning gating of the normal region into a simple experimental control knob. Furthermore, we obtain that, by tuning the junction transparency, critical currents in both short and long junctions undergo a reduction in the number of oscillations as a function of magnetic field only in the topological phase, an effect that find to be intimately linked to Majorana non-locality. Finally, we show that our results also hold at finite temperatures, thus highlighting their potential measurability under realistic experimental conditions.

cond-mat.mes-hall↗
arXiv2023

Disorder-robust phase crystal in high-temperature superconductors stabilized by strong correlations

The simultaneous interplay of strong electron-electron correlations, topological zero-energy states, and disorder is yet an unexplored territory but of immense interest due to their inevitable presence in many materials. Copper oxide high-temperature superconductors (cuprates) with pair breaking edges host a flat band of topological zero-energy states, making them an ideal playground where strong correlations, topology, and disorder are strongly intertwined. Here we show that this interplay in cuprates generates a new phase of matter: a fully gapped ``phase crystal" state that breaks both translational and time-reversal invariance, characterized by a modulation of the $d$-wave superconducting phase co-existing with a modulating extended $s$-wave superconducting order. In contrast to conventional wisdom, we find that this phase crystal state is remarkably robust to omnipresent disorder, but only in the presence of strong correlations, thus giving a clear route to its experimental realization.

cond-mat.supr-con↗
arXiv2023

Interplay of finite-energy and finite-momentum superconducting pairing

Understanding the nature of Cooper pairs is essential to describe the properties of superconductors. The original proposal of Bardeen, Cooper, and Schrieffer (BCS) was based on electrons pairing with same energy and zero center-of-mass momentum. With the advent of new superconductors, different forms of pairing have been discussed. In particular, Cooper pairs with finite center-of-mass momentum have received large interest. Along with such finite-momentum pairs, pairing of electrons at different energies is also central to understanding some superconductors. Here, we investigate the interplay of finite-momentum and finite-energy Cooper pairs considering two different systems: a conventional $s$-wave superconductor under applied magnetic field and a $d$-wave finite-momentum pairing state in the absence of magnetic field relevant to correlated superconductors. Investigating both these systems, we find finite-energy pairs persisting independently of finite-momentum pairing, and that they lead to odd-frequency superconducting correlations. We contrast this finding by showing that the even-frequency correlations are predominantly driven by zero-energy pairs for most frequencies. We further calculate the Meissner effect and find that odd-frequency correlations are essential for correctly describing the Meissner effect.

cond-mat.supr-con↗
arXiv2023

Quasiparticle interference as a direct experimental probe of bulk odd-frequency superconducting pairing

We show that quasiparticle interference (QPI) due to omnipresent weak impurities and probed by Fourier transform scanning tunneling microscopy and spectroscopy acts as a direct experimental probe of bulk odd-frequency superconducting pairing. Taking the example of a conventional $s$-wave superconductor under applied magnetic field, we show that the nature of the QPI peaks can only be characterized by including the odd-frequency pairing correlations generated in this system. In particular, we identify that the defining feature of odd-frequency pairing gives rise to a bias asymmetry in the QPI, present generically in materials with odd-frequency pairing irrespective of its origin.

cond-mat.supr-con↗
arXiv2022

Superconductivity in monolayer and few-layer graphene: I. Review of possible pairing symmetries and basic electronic properties

We review all symmetry-allowed spin-singlet and spin-triplet superconducting (SC) order parameters in graphene ($s$-wave, $d$-wave, $p$-wave, and $f$-wave) generated by generic onsite, nearest-neighbor (NN), and next-to-nearest-neighbor (NNN) pairing interactions in a tight-binding model. For each pairing channel, we calculate both the band structure and the dependence of the density of states on energy, chemical potential, and on the pairing strength. In particular, we distinguish between nodal superconducting states and fully gapped states and study the dependence of gap closing points on the chemical potential and the superconducting pairing strength. We further investigate the difference between mono-, bi-, and tri-layer ABC and ABA graphene, including accounting for the effects of trigonal warping.

cond-mat.supr-con↗
arXiv2022

Superconductivity in monolayer and few-layer graphene: III Impurity-induced subgap states and quasi-particle interference patterns

We consider the most energetically favorable symmetry-allowed spin-singlet and spin-triplet superconducting pairing symmetries in monolayer and few-layer graphene, and for each calculate the energy spectrum in the presence of a scalar or magnetic impurity. We find that two doubly degenerate subgap states exist for scalar impurities for all types of pairing, except for the spin-singlet $s$-wave state. For magnetic impurities, two or four subgap states may form depending on the order parameter symmetry. We find that the spin polarization of these states allows one to distinguish between spin-singlet and triplet pairing, for example, only the spin-triplet states show opposite-energy subgap states with the same spin. We also calculate the quasi-particle interference patterns associated with the subgap states and find that they exhibit features that could distinguish between different types of pairing symmetries, especially a breaking of rotational symmetry for nodal states, stronger for the spin-singlet $d_{xy}$ and $d_{x^2-y^2}$ than for the spin-triplet $p_x$ and $p_y$ states.

cond-mat.supr-con↗
arXiv2022

Superconductivity in monolayer and few-layer graphene: II. Topological edge states and Chern numbers

We study the emergence of electronic edge states in superconducting (SC) monolayer, bilayer, and trilayer graphene for both spin-singlet and spin-triplet SC order parameters. We focus mostly on the gapped chiral $p+ip'$- and $d+id'$-wave SC states that show a non-zero Chern number and a corresponding number of edge states. For the $p+ip'$-wave state, we observe a rich Chern phase diagram when tuning the chemical potential and the SC order parameter amplitudes, which depends strongly on the number of layers and their stacking, and is also modified by trigonal warping. At small parameter values we observe a region whose Chern number is unique to rhombohedrally stacked graphene, and is independent of the number of layers. Our results can be understood in relation not only to the SC order parameter winding as expected, but also to the normal state band structure. This observation establishes the importance of the normal state characteristics for understanding the topology in SC graphene systems.

cond-mat.supr-con↗
arXiv2022

Phase-tunable electron transport assisted by odd-frequency Cooper pairs in topological Josephson junctions

We consider a finite-size topological Josephson junction formed at the edge of a two-dimensional topological insulator in proximity to conventional superconductors and study the impact of Cooper pair symmetries on the electron transport. We find that, due to the finite junction size, electron transport is highly tunable by the superconducting phase difference $ϕ$ across the junction. At zero frequency and $ϕ=π$, the setup exhibits vanishing local Andreev reflection and perfect normal transmission due to the interplay of finite junction size and formation of topological Andreev bound states in the middle of the junction. We reveal that this striking behavior enables odd-frequency Cooper pairs to become the only type of pairing inside the topological junction that contribute to transport. Our paper thus offers a highly tunable detection scheme for odd-frequency Cooper pairs.

cond-mat.supr-con↗