Gapless Superconductivity and Topological Phases in Ammann-Beenker Quasicrystals

核心概念

Ammann-Beenker quasicrystals can host gapless superconductivity under magnetic field, originating from the interplay of broken translational symmetry and highly degenerate confined states. The gapless superconducting phase can also be topologically nontrivial when Rashba spin-orbit coupling is present.

摘要

The authors investigate superconductivity in Ammann-Beenker quasicrystals (QCs) under magnetic field. They find that these systems can host a stable gapless superconducting phase at and near half filling, where the bulk energy spectrum is gapless despite the finite superconducting order parameter at all sites.

The mechanism of this quasicrystalline gapless superconductivity originates from the interplay of broken translational symmetry and the highly degenerate flat band of confined states unique to QCs. At or close to half filling, the large number of confined states results in a sharp peak in the normal-state density of states (DOS) at zero energy, which enhances the superconducting order parameter. Simultaneously, the underlying inhomogeneity of the quasicrystalline lattice broadens the coherence peaks, leading to a situation where the bulk gap is smaller than the mean superconducting order parameter.

When Rashba spin-orbit coupling is present, the gapless superconducting phase can be topologically nontrivial, characterized by a nonzero pseudospectrum invariant given by a spectral localizer. This topological gapless superconductor exhibits topologically protected edge states with near-zero energy.

The authors conclude that quasicrystals can be a unique platform for realizing gapless superconductivity with nontrivial topology, presenting Majorana-like edge modes buried in the bulk spectrum.

统计

"Superconductivity is destroyed at hz ≃-0.195t (-0.366t) when λR = 0 (0.5t)."
"The bulk gap closes at hz ≃-0.17t (-0.265t) for λR = 0 (0.5t), while the superconducting order parameter remains finite at all sites."

引用

"Gapless superconductivity was originally studied in conventional s-wave superconductors with magnetic impurities [36–38]. In such systems, a band is formed inside the superconducting energy gap, which is broadened as the impurity concentration is increased, leading up to gapless superconductivity [39–41]. In the presence of magnetic field, disordered superconductors can also exhibit gapless superconductivity [42–44]. In contrast to these previous studies, we find that quasicrystalline gapless superconductivity occurs without additional disorder or magnetic impurities, and only at and very close to half filling in Ammann-Beenker QCs."
"Therefore, the highly degenerate flat band of confined states at zero kinetic energy is key to the formation of gapless spectrum, and in this sense, this phenomenon is unique to QCs."

从中提取的关键见解

Gapless superconductivity and its real-space topology in quasicrystals

by Kazuma Saito... 在 arxiv.org 10-03-2024

https://arxiv.org/pdf/2410.01236.pdf

更深入的查询

How do the properties of gapless superconductivity in Ammann-Beenker quasicrystals differ from those in periodic systems with magnetic impurities or disorder?

The properties of gapless superconductivity in Ammann-Beenker quasicrystals are fundamentally distinct from those observed in periodic systems with magnetic impurities or disorder due to the unique structural characteristics of quasicrystals. In periodic systems, gapless superconductivity typically arises from the introduction of magnetic impurities, which create localized states within the superconducting energy gap. This phenomenon is often associated with a gradual broadening of the energy gap as the concentration of impurities increases, leading to a situation where the superconducting order parameter may vanish at certain lattice sites.
In contrast, the gapless superconductivity observed in Ammann-Beenker quasicrystals occurs intrinsically at and near half filling without the need for additional disorder or magnetic impurities. This unique behavior is attributed to the presence of highly degenerate confined states and the broken translational symmetry inherent in the quasicrystalline structure. The flat band of confined states at zero kinetic energy allows for a stable gapless superconducting phase, where the bulk energy spectrum remains gapless while the superconducting order parameter is finite across all sites. This phenomenon is qualitatively different from disordered systems, where the order parameter can vanish at some sites due to strong impurities. Thus, the gapless superconductivity in Ammann-Beenker quasicrystals represents a unique state of matter that does not have a direct counterpart in periodic systems.

Can gapless topological superconductivity be realized in other types of quasicrystals beyond the Ammann-Beenker structure?

Yes, gapless topological superconductivity can potentially be realized in other types of quasicrystals beyond the Ammann-Beenker structure. The key factors that enable the emergence of gapless superconductivity with nontrivial topology in quasicrystals include the presence of confined states, broken translational symmetry, and the ability to manipulate spin-orbit coupling. These characteristics are not exclusive to the Ammann-Beenker quasicrystal; other quasicrystalline structures, such as Penrose and Socolar dodecagonal quasicrystals, also exhibit similar features.
The theoretical framework established in the study of Ammann-Beenker quasicrystals can be extended to investigate the superconducting properties of these other quasicrystals. If they possess a flat band of confined states and can support Rashba spin-orbit coupling, it is plausible that they could also host gapless topological superconducting phases characterized by nonzero pseudospectrum invariants and topologically protected edge states. Therefore, the exploration of gapless topological superconductivity in various quasicrystalline materials could lead to the discovery of new quantum phases and enhance our understanding of topological phenomena in aperiodic systems.

What are the potential applications or implications of gapless superconductivity with nontrivial topology in quasicrystals for quantum technologies or materials science?

The discovery of gapless superconductivity with nontrivial topology in quasicrystals has significant implications for quantum technologies and materials science. One of the most promising applications lies in the development of topological quantum computing. The presence of topologically protected edge states, such as Majorana modes, in gapless topological superconductors could provide a robust platform for fault-tolerant quantum computation. These edge states are less susceptible to local perturbations, making them ideal candidates for qubits that can maintain coherence over longer timescales.
Additionally, the unique properties of quasicrystals, including their aperiodic structure and the resulting confinement of electronic states, could lead to novel superconducting devices with enhanced performance characteristics. For instance, quasicrystalline superconductors may exhibit improved critical temperatures or magnetic field resilience compared to their periodic counterparts, making them suitable for applications in superconducting electronics, such as quantum sensors and superconducting qubits.
Moreover, the study of gapless superconductivity in quasicrystals can deepen our understanding of quantum materials and their emergent phenomena. This knowledge could pave the way for the design of new materials with tailored electronic properties, potentially leading to advancements in energy storage, conversion technologies, and other applications in materials science. Overall, the exploration of gapless superconductivity in quasicrystals represents a frontier in condensed matter physics with far-reaching implications for future technological innovations.