Pairing Symmetry Research Articles

Tusk metrics and pair symmetry in savannah elephants

The right and left tusks and from both genders from five separately culled savannah elephant clans were measured, recording weight (n = 2,453), overall length (n = 563), external length beyond the gingivae (n = 158), internal length within the alveolus (n = 158) and circumference at the lip (n = 158). The increase in tusk weights and lengths with age was reconfirmed as basically exponential in males and more linear in females up to their fifth decade. Between the right and left tusks, the five metrics were on average symmetrical (in the sense of being mirror images of one another), and predictive of both age and each other (i.e. from one the others can be deduced). Strikingly, however, pair length symmetry is less between within alveoli, where growth takes place, than between their corresponding external parts, where tusks are essentially dead tissue. Such greater external symmetry can only occur if the shorter tusk grows faster to catch up with its partner or the longer tooth is reduced through wear towards parity with its partner, or both.

Superconductivity in twisted bilayer graphene: Possible pairing symmetries, impurity-induced states, and Chern number

Superconductivity in twisted bilayer graphene: Possible pairing symmetries, impurity-induced states, and Chern number

Spin–orbit enabled unconventional Stoner magnetism

The Stoner instability remains a cornerstone for understanding metallic ferromagnets. This instability captures the interplay of Coulomb repulsion, Pauli exclusion, and twofold fermionic spin degeneracy. In materials with spin-orbit coupling, this fermionic spin is generalized to a twofold degenerate pseudospin which is typically believed to have symmetry properties as spin. Here, we identify a distinct symmetry of this pseudospin that forbids it to couple to a Zeeman field. This "spinless" property is required to exist in five nonsymmorphic space groups and has nontrivial implications for superconductivity and magnetism. With Coulomb repulsion, Fermi surfaces composed primarily of this spinless pseudospin property give rise to Stoner instabilities into magnetic states that are qualitatively different than ferromagnets. These spinless-pseudospin ferromagnets break time-reversal symmetry, have a vanishing magnetization, are noncollinear, and exhibit momentum-dependent energy band spin-splittings. In superconductors, for all pairing symmetries and field orientations, this spinless pseudospin extinguishes paramagnetic limiting. We discuss applications to superconducting UCoGe and magnetic NiS[Formula: see text]Se[Formula: see text].

Charge stripe manipulation of superconducting pairing symmetry transition

Charge stripes have been widely observed in many different types of unconventional superconductors, holding varying periods (P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal{P}}}$$\\end{document}) and intensities. However, a general understanding on the interplay between charge stripes and superconducting properties is still incomplete. Here, using large-scale unbiased numerical simulations on a general inhomogeneous Hubbard model, we discover that the charge-stripe period P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal{P}}}$$\\end{document}, which is variable in different real material systems, could dictate the pairing symmetries—d wave for P≥4,s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal{P}}}\\ge 4,s$$\\end{document} and d waves for P≤3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal{P}}}\\le 3$$\\end{document}. In the latter, tuning hole doping and charge-stripe amplitude can trigger a d-s wave transition and magnetic-correlation shift, where the d-wave state converts to a pairing-density wave state, competing with the s wave. These interesting phenomena arise from an unusual stripe-induced selection rule of pairing symmetries around on-stripe region and within inter-stripe region, giving rise to a critical point of P=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal{P}}}=3$$\\end{document} for the phase transition. In general, our findings offer important insights into the differences in the superconducting pairing mechanisms across many P\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathcal{P}}}$$\\end{document}-dependent superconducting systems, highlighting the decisive role of charge stripe.

The Superconducting Mechanism in BiS2-Based Superconductors: A Comprehensive Review with Focus on Point-Contact Spectroscopy.

The family of BiS2-based superconductors has attracted considerable attention since their discovery in 2012 due to the unique structural and electronic properties of these materials. Several experimental and theoretical studies have been performed to explore the basic properties and the underlying mechanism for superconductivity. In this review, we discuss the current understanding of pairing symmetry in BiS2-based superconductors and particularly the role of point-contact spectroscopy in unravelling the mechanism underlying the superconducting state. We also review experimental results obtained with different techniques including angle-resolved photoemission spectroscopy, scanning tunnelling spectroscopy, specific heat measurements, and nuclear magnetic resonance spectroscopy. The integration of experimental results and theoretical predictions sheds light on the complex interplay between electronic correlations, spin fluctuations, and Fermi surface topology in determining the coupling mechanism. Finally, we highlight recent advances and future directions in the field of BiS2-based superconductors, underlining the potential technological applications.

Magic angle of Sr2RuO4 : Optimizing correlation-driven superconductivity

Understanding of unconventional superconductivity is crucial for engineering materials with specific order parameters or elevated superconducting transition temperatures. However, for many materials, the pairing mechanism and symmetry of the order parameter remain unclear: reliable and efficient methods of predicting the order parameter and its response to tuning parameters are lacking. Here, we investigate the response of superconductivity in Sr2RuO4 to structural distortions via the random phase approximation (RPA) and functional renormalization group (FRG), starting from realistic models of the electronic structure. Our results suggest that RPA misses the interplay of competing fluctuation channels. FRG reproduces key experimental findings. We predict a magic octahedral rotation angle, maximizing the superconducting Tc and a dominant dx2−y2 pairing symmetry. To enable experimental verification, we provide calculations of the phase-referenced Bogoliubov Quasiparticle Interference imaging. Our work demonstrates a designer approach to tuning unconventional superconductivity with relevance and applicability for a wide range of quantum materials. Published by the American Physical Society 2024

Dualities of Paired Quantum Hall Bilayer States at ν_{T}=1/2+1/2.

Density-balanced, widely separated quantum Hall bilayers at ν_{T}=1 can be described as two copies of composite Fermi liquids (CFLs). The two CFLs have interlayer weak-coupling Bardeen-Cooper-Schrieffer instabilities mediated by gauge fluctuations, the resulting pairing symmetry of which depends on the CFL hypothesis used. If both layers are described by the conventional Halperin-Lee-Read (HLR) theory-based composite electron liquid (CEL), the dominant pairing instability is in the p+ip channel; whereas if one layer is described by CEL and the other by a composite hole liquid (CHL, in the sense of anti-HLR), the dominant pairing instability occurs in the s-wave channel. Using the Dirac composite fermion (CF) picture, we show that these two pairing channels can be mapped onto each other by particle-hole (PH) transformation. Furthermore, we derive the CHL theory as the nonrelativistic limit of the PH-transformed massive Dirac CF theory. Finally, we prove that an effective topological field theory for the paired CEL-CHL in the weak-coupling limit is equivalent to the exciton condensate phase in the strong-coupling limit.

“Quantum Geometric Nesting” and Solvable Model Flat-Band Systems

We introduce the concept of “quantum geometric nesting” (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence of an infinite class of local interactions that can be explicitly constructed and give rise to solvable ground states with various forms of possible fermion bilinear order, including flavor ferromagnetism, density waves, and superconductivity. For the ideal Hamiltonians constructed in this way, we show that certain aspects of the low-energy spectrum can also be exactly computed including, in the superconducting case, the phase stiffness. Examples of perfect QGN include flat bands with certain symmetries (e.g., chiral or time reversal) and non-symmetry-related cases exemplified with an engineered model for pair-density wave. Extending this approach, we obtain exact superconducting ground states with nontrivial pairing symmetry. Published by the American Physical Society 2024

THz optical response of Ba(Fe[formula omitted]Ni[formula omitted])[formula omitted]As[formula omitted] films analyzed within the three-band Eliashberg s[formula omitted]-wave model

The uncertainty of the nature of the normal state and superconducting condensate of unconventional superconductors continues to stimulate considerable speculation about the mechanism of superconductivity in these materials. Of particular interest are the type of symmetry of the order parameter and the basic electronic characteristics of the superconducting and normal states. We report the derivation of temperature dependences of the superconducting condensate plasma frequency, superfluid density, and London penetration depth by measuring terahertz spectra of conductivity and dielectric permittivity of the Ba(Fe1−xNix)2As2 thin films with different Ni concentrations. A comprehensive analysis of the experimental data was performed in the framework of the simple three-band Eliashberg model under the assumption that the superconducting coupling mechanism is mediated by antiferromagnetic spin fluctuations. The results of independent experiments support the choice of model parameters. Based on calculations of the temperature dependences of superconducting gaps, we may conclude that the obtained results are compatible with the scenario, in which Ba(Fe1−xNix)2As2 is a multiband superconductor with s±-wave pairing symmetry.

Pairing correlation of the kagome-lattice Hubbard model with the nearest-neighbor interaction

Abstract A recently discovered family of kagome lattice materials, AV3Sb5 (A = K,Rb,Cs), has attracted great interest, especially in the debate over their dominant superconducting pairing symmetry. To explore this issue, we study the superconducting pairing behavior within the kagome-lattice Hubbard model through the constrained path Monte Carlo method. It is found that doping around the Dirac point generates a dominant next-nearest-neighbor-d pairing symmetry driven by on-site Coulomb interaction U. However, when considering the nearest-neighbor interaction V, it may induce nearest-neighbor-p pairing to become the preferred pairing symmetry. Our results provide useful information to identify the dominant superconducting pairing symmetry in the AV3Sb5 family.

Noncommuting charges can remove non-stationary quantum many-body dynamics

Studying noncommuting conserved quantities, or ‘charges,’ has revealed a conceptual puzzle: noncommuting charges hinder thermalization in some ways yet promote it in others. While many quantum systems thermalize according to the Eigenstate Thermalization Hypothesis (ETH), systems with ‘dynamical symmetries’ violate the ETH and exhibit non-stationary dynamics, preventing them from equilibrating, much less thermalizing. We demonstrate that each pair of dynamical symmetries corresponds to a specific charge. We find that introducing new charges that do not commute with existing ones disrupts these symmetries, thereby eliminating non-stationary dynamics and facilitating thermalization. We illustrate this behavior across various models, including the Hubbard model and Heisenberg spin chains. Our findings demonstrate that noncommuting charges can enhance thermalization by reducing the number of local observables that thermalize according to the ETH.

YOLOv8n–CBAM–EfficientNetV2 Model for Aircraft Wake Recognition

In the study of aircraft wake target detection, as the wake evolves and develops, the detection area of the LiDAR often shows the presence of two distinct vortices, one on each side. Sometimes, only a single wake vortex may be present. This can lead to a reduction in the accuracy of wake detection and an increased likelihood of missed detections, which may have a significant impact on the flight safety. Hence, we propose an algorithm based on the YOLOv8n–CBAM–EfficientNetV2 model for wake detection. The algorithm incorporates the lightweight network of EfficientNetV2 and the Convolutional Block Attention Module (CBAM) based on the YOLOv8n model, which achieves the lightweight improvement in the YOLOv8n algorithm and the improvement in detection accuracy. First, this study classifies the wake vortices in the wake greyscale images obtained at Hong Kong International Airport, based on the Range–Height Indicator (RHI) scanning characteristics of the LiDAR and the symmetry of the wake vortex pairs. The classification is used to detect left and right vortices for more accurate wake detection in wind field images, which thereby improves the precision rate of target detection. Subsequently, experiments are conducted using a YOLOv8n–CBAM–EfficientNetV2 model for aircraft wake detection. Finally, the performance of the YOLOv8n–CBAM–EfficientNetV2 model is analysed. The results show that the algorithm proposed in this study can achieve a 96.35% precision rate, 93.58% recall rate, 95.06% F1-score, and 250 frames/s. The results show that the method proposed in this study can be effectively applied in aircraft wake detection.

High-TC superconductivity in La3Ni2O7 based on the bilayer two-orbital t-J model

The recently discovered high-Tc superconductor La3Ni2O7 has sparked renewed interest in unconventional superconductivity. Here we study superconductivity in pressurized La3Ni2O7 based on a bilayer two-orbital t−J model, using the renormalized mean-field theory. Our results reveal a robust s±-wave pairing driven by the inter-layer dz2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{z}^{2}}$$\\end{document} magnetic coupling, which exhibits a transition temperature within the same order of magnitude as the experimentally observed Tc ~ 80 K. We establish a comprehensive superconducting phase diagram in the doping plane. Notably, the La3Ni2O7 under pressure is found to be situated roughly in the optimal doping regime of the phase diagram. When the dx2−y2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{x}^{2}-{y}^{2}}$$\\end{document} orbital becomes close to half-filling, d-wave and d + is pairing can emerge from the system. We discuss the interplay between Fermi surface topology and different pairing symmetries. The stability of the s±-wave pairing against Hund’s coupling and other magnetic exchange couplings is discussed.

Disorder-dependent superconducting pairing symmetry in doped graphene

Disorder-dependent superconducting pairing symmetry in doped graphene

Phonon-mediated unconventional superconductivity in rhombohedral stacked multilayer graphene

Understanding the origin of superconductivity in correlated two-dimensional materials is a key step in leveraging material engineering techniques for next-generation nanoscale devices. While it is widely accepted that phonons fluctuations only mediate conventional (s-wave) superconductivity, the common phenomenology of superconductivity in Bernal bilayer and rhombohedral trilayer graphene, as well as in a large family of graphene-based moiré systems, suggests a common superconducting mechanism across these platforms. In particular, in all these platforms some superconducting regions violate the Pauli limit, indicating unconventional superconductivity, naively ruling out conventional phonon-mediated pairing as the underlying mechanism. Here we combine first principles simulations with effective low-energy theories to investigate the superconducting mechanism and pairing symmetry in rhombohedral stacked graphene multilayers. We find that phonon-mediated superconductivity explains the main experimental findings, namely the displacement field and doping level dependence of the critical temperature, and the presence of two superconducting regions with different pairing symmetries that depend on the parent normal state. In particular, we find that intra-valley phonon scattering favors a triplet f-wave pairing when combined with electronic correlations stabilizing a spin- and valley-polarized normal state. We also propose a so far unexplored superconducting region at higher hole doping densities nh ≈ 4 × 1012 cm−2, and demonstrate how this highly hole-doped regime can be reached in heterostructures consisting of monolayer α-RuCl3 and rhombohedral trilayer graphene. Our findings promote phonon-mediated pairing as a strong contender to explain superconductivity across a wide range of graphene platforms, and demonstrate that phonons can, in fact, stabilize unconventional superconducting orders.

Electromagnetic Response of Spinful Majorana Fermions

Abstract A remarkable feature of topological superconductors is the emergence of Majorana fermions in electron systems. Whereas the emergent Majorana fermions share the self-antiparticle property with Majorana fermions in particle physics, they may have essentially different electromagnetic properties. In this paper, we discuss the electromagnetic response of spinful Majorana fermions in topological superconductors. We present a general theory of the electromagnetic response of spinful Majorana fermions in topological superconductors and clarify how the pairing symmetry is encoded in the electromagnetic response. As an application, we predict the sublattice-dependent dipole (Ising)-type magnetic response of corner Majorana fermions in iron-based superconductors.

Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4

The pairing symmetry of Sr2RuO4 is a long-standing fundamental question in the physics of superconducting materials with strong electronic correlations. We use the functional renormalization group to investigate the behavior of superconductivity under uniaxial strain in a two-dimensional realistic model of Sr2RuO4 obtained with density functional theory and incorporating the effect of spin-orbit coupling. We find a dominant dx2−y2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{{{{\\rm{x}}}}}^{2}-{{{{\\rm{y}}}}}^{2}}$$\\end{document} superconductor mostly hosted by the dxy-orbital, with no other closely competing superconducting state. Within this framework, we reproduce the experimentally observed enhancement of the critical temperature under strain and propose a simple mechanism driven by the density of states to explain our findings. We also investigate the competition between superconductivity and spin-density wave ordering as a function of interaction strength. By comparing theory and experiment, we discuss constraints on a possible degenerate partner of the dx2−y2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{{{{{\\rm{x}}}}}^{2}-{{{{\\rm{y}}}}}^{2}}$$\\end{document} superconducting state.

Level statistics of the one-dimensional dimerized Hubbard model

The statistical properties of level spacings provide valuable insights into the dynamical properties of a many-body quantum systems. We investigate the level statistics of the Fermi–Hubbard model with dimerized hopping amplitude and find that after taking into account translation, reflection, spin and η pairing symmetries to isolate irreducible blocks of the Hamiltonian, the level spacings in the limit of large system sizes follow the distribution expected for hermitian random matrices from the Gaussian orthogonal ensemble. We show this by analyzing the distribution of the ratios of consecutive level spacings in this system, its cumulative distribution and quantify the deviations of the distributions using their mean, standard deviation and skewness.

Normal and Superconducting Properties of La3Ni2O7

Abstract This review provides a comprehensive overview of current research on the structural, electronic, and magnetic characteristics of the recently discovered high-temperature superconductor La3Ni2O7 under high pressures. We present the experimental results for synthesizing and characterizing this material, derived from measurements of transport, thermodynamics, and various spectroscopic techniques, and discuss their physical implications. We also explore theoretical models proposed to describe the electronic structures and superconducting pairing symmetry in La3Ni2O7, highlighting the intricate interplay between electronic correlations and magnetic interactions. Despite these advances, challenges remain in growing high-quality samples free of extrinsic phases and oxygen deficiencies and in developing reliable measurement tools for determining diamagnetism and other physical quantities under high pressures. Further investigations in these areas are essential to deepening our understanding of the physical properties of La3Ni2O7 and unlocking its superconducting pairing mechanism.

Evidences for d-wave symmetry of c-axis superconducting gap in atomically thin twisted flakes of bismuth-based HTS cuprates

c-axis Josephson tunnelling in atomically thin twisted flakes of quasi-two-dimensional cuprate superconductors is one of the experimental techniques which can be used to reveal the pairing symmetry in HTS cuprates. Until very recent experiments reported by Zhao et al. (Science382, 1422 (2023)), there was a widely accepted consensus that the c-axis Josephson currents, Ic(T), in twisted cuprate junctions manifest the s-wave gap symmetry for c-axis gap component. Here, I highlighted that this consensus was based on the analysis of the Ic(T) data by using the Ambegaokar-Baratoff equation, where the weak-coupling s-wave gap equation was utilized. In this study, I introduced a more accurate gap equation in the AB model and reanalyzed the Ic(T) data in atomically thin twisted Bi2Sr2-xLaxCuO6+y (Bi-2201) and Bi2Sr2CaCu2O8+x (Bi-2212) flakes. In the result, the analysis revealed evidences for d-wave pairing symmetry. Beside this, the analysis of the RnIc(T) data reported by Zhao et al. (Science382, 1422 (2023)) by a piecewise AB model, where a linear low-T dependence of the Ic(T) is used, and where the threshold temperature TM is a free-fitting parameter, confirmed the d-wave symmetry in these twisted Bi-2212 junctions.