Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2404.07423

Fermi sea and sky in the Bogoliubov-de Gennes equation

Xian-Peng Zhang·Yugui Yao
View original source ↗Read source document ↗Export metadata ↓

Abstract

We develop a comprehensive logical framework for effectively handling the overcomplete basis set in the Bogoliubov-de Gennes equation that contains two orthonormal basis sets conjugate with each other, such as particle and hole orthonormal basis sets. We highlight the significant implications of our logical framework from theoretical concepts and experimental predictions. Firstly, we rigorously derive all many-body eigenfunctions of arbitrary nonuniform superconductors and uncover that the many-body eigenstates are full of superconducting spin clouds-the electron configuration within the Cooper-like pair of an arbitrary nonuniform superconductor. Secondly, we demonstrate a conjugate loop formed by the effective vacuum states of two orthonormal basis sets conjugate with each other, such as the Fermi sea and sky-the effective vacuum states of positive and negative orthonormal basis sets, respectively. Thirdly, we present a gate-, field-, and phase-tunable tunnel spectroscopy asymmetry arising from the imbalanced particle-hole distribution of the subgap quasiparticles in a quantum-dot Josephson junction. These findings underscore the power of our logical framework and its implications for advancing our understanding and utilization of solid-state devices based on superconductivity.

Explore related subjects

cond-mat.supr-con

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xian-Peng Zhang, Yugui Yao. 2024-04-11. Fermi sea and sky in the Bogoliubov-de Gennes equation. https://arxiv.org/abs/2404.07423

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Collective excitation-mediated transport in nanoscale Josephson junctions that exhibit quantum confinement

Quantum confinement can strongly modify transport through Josephson junctions. Here, we study local tunneling transport through nanoscale Josephson junction stacks in the Coulomb blockade regime, where the metallic layers exhibit strong vertical quantum confinement. We find that quasiparticle transport is strongly enhanced by a collective excitation mode intrinsic to the junction and localized in the isolated metallic overlayer. We quantify both the collective-mode energy and the Coulomb gap and show that both exhibit strong layer-dependent modulation, consistent with the modulation of the underlying quantum well states. We further investigate how the collective excitation responds to various perturbations, including mechanical motion and an applied magnetic field. Our results suggest that this collective mode is sensitive to quasiparticles near the Fermi level and may therefore provide an indirect probe of the superconducting state.

cond-mat.supr-con↗
arXiv2026

Universal Dzyaloshinski-Moriya interaction dictates pairing in unconventional superconductor families

The collinear-antiferromagnetic spin-fluctuation paradigm has long guided unconventional superconductivity research, yet fails to reconcile the noncollinear spin phenomena observed across cuprates, iron-based superconductors, and nickelates. Using extensive first-principles calculations and unbiased large-scale DMRG simulations, we show that Dzyaloshinski-Moriya interaction (DMI)-arising from local inversion-symmetry breaking-is a common ingredient across these families. This DMI unifies hallmark observations in parent compounds-incommensurate orders, spin-wave gaps, and noncollinear textures. Under hole doping, strong DMI drives spin vortices to merge with pi-shifted hole stripes, forming hybrid vortex-hole stripe phases. These phases stabilize charge order while supporting, not suppressing, superconductivity. By contrast, under electron doping, these vortices pin holes and suppress long-range superconductivity. Our results establish DMI as a unifying link between noncollinear magnetism and superconductivity, identifying hole-strip-vortex coupling as a microscopic pairing engine. Given that DMI is common across major superconductor families, these findings challenge the prevailing pairing mechanism and offer an experimentally testable roadmap for materials optimization.

cond-mat.supr-con↗
arXiv2026

Digital-analog concept for superconducting perceptron-like neural networks

A promising route to superconducting artificial neural networks is a hybrid digital-Analog architecture that combines digital single-flux-quantum (SFQ) communication with compact Analog nonlinear processing. The study focused on the dynamic conversion of a discrete signal passing through a digital-to-Analog-to-digital (DAD) converter, in which the role of the Analog cell was performed by a $Σ$-neuron with a nonlinear transfer function -- the basic cell of perceptron-like neural networks. Furthermore, the DAD converter, the elementary functional block of the hybrid architecture, combines a digital-to-analog converter (DAC) and an Analog-to-digital converter (ADC), and re-encodes the Analog $Σ$-neuron waveforms as an SFQ pulse sequence. Circuit-level simulations demonstrate how input values encoded by SFQ pulse trains are converted into analog signal levels, transformed by the $Σ$-neuron, and mapped back to pulse-based outputs. As a key experimental step, we fabricated and characterised a redesigned $Σ$-neuron and measured a sigmoid-like transfer characteristic suitable for activation-function implementation. The extracted response was incorporated into system-level simulations to assess the influence of realistic device parameters on the conversion process. We delineate the operating-range matching requirements for the DAC, neuron, and ADC blocks, supporting the feasibility of the proposed interface as a building block for perceptron-like superconducting neural networks with digital inputs and outputs. Finally, we developed two perceptron networks, one using a mathematical sigmoid activation and the other the measured $Σ$-neuron transfer characteristic, which reached classification accuracies of $97.0\%$ and $91.9\%$, respectively, on the MNIST handwritten digit dataset.

cond-mat.supr-con↗