Recent studies of unconventional superconductivity have focused on charge or spin fluctuation, instead of electron-phonon coupling, as an origin of attractive interaction between electrons. On the other hand, a multipole order, which represents electrons' degrees of freedom in strongly correlated and spin-orbit-coupled systems, has recently been attracting much attention. Stimulated by this background, we investigate multipole-fluctuation-mediated superconductivity, which proposes a new pairing mechanism of unconventional superconductivity. Indeed, previous works have shown spin-triplet superconductivity induced by fluctuations of odd-parity electric multipole orders in isotropic systems. In this study, we establish a general formulation of the multipole-fluctuation-mediated superconductivity for all multipole symmetries, in both isotropic and crystalline systems. As a result, we reveal various anisotropic pairings induced by odd-parity and/or higher-order multipole fluctuations, which are beyond the ordinary charge or spin fluctuations. Topological superconductivity due to the mechanism is also discussed. Based on the obtained results, we discuss unconventional superconductivity in doped SrTiO$_3$, PrTi$_2$Al$_{20}$, Li$_2$(Pd, Pt)$_3$B, and magnetic multipole metals.
Despite of many experimental and theoretical efforts, the pairing symmetry of superconductivity in Sr$_2$RuO$_4$ remains undecided. The accidentally degenerate $d_{x^2-y^2}+ig$ is consistent with most current experiments and seems to be one of the most probable candidates, but we still lack a satisfactory theoretical mechanism for its appearance. Here we construct a phenomenological model combining realistic electronic band structures and all symmetry-allowed multipole fluctuations as potential pairing glues, and make a systematic survey of major pairing states within the Eliashberg framework.…
A microscopic calculation and symmetry argument reveal superconductivity in the vicinity of parity-violating magnetic order. An augmented cluster magnetic multipole order in a crystal lacking local space inversion parity may break global inversion symmetry, and then, it is classified into an odd-parity multipole order. We investigate unconventional superconductivity induced by an odd-parity magnetic multipole fluctuation in a two-dimensional two-sublattice Hubbard model motivated by Sr$_2$IrO$_4$. We find that even-parity superconductivity is more significantly suppressed by a spin-orbit coupl…
In heavy fermion systems, higher-rank multipole operators are active thanks to the strong spin-orbit interaction (SOI), and the role of diverse multipole fluctuations on the pairing mechanism attracts a lot of attention. Here, we study a mechanism of superconductivity in heavy fermion systems, by focusing on the impact of vertex corrections (VCs) for the pairing interaction going beyond the Migdal approximation. In heavy fermion systems, strong interference between multipole fluctuations cause significant VCs, that represent many-body effects beyond mean-field-type approximations. Especially, …
Ultrasonic Observation of Slowing Down of Multipole Fluctuations in Sr$_2$RuO$_4$
Tokyo University of Science（东京科学大学）；Niigata University（新潟大学）；Toyama Prefectural University（富山県立大学）；National Institute of Advanced Industrial Science and Technology (AIST)（产业技术综合研究所）
In heavy-fermion superconductors, it is widely believed that the superconducting gap function has sign-reversal due to the strong electron correlation. However, recently discovered fully-gapped s-wave superconductivity in CeCu2Si2 has clarified that strong attractive pairing interaction can appear even in heavy-fermion systems. To understand the origin of attractive force, we develop the multipole fluctuation theory by focusing on the inter-multipole many-body interaction called the vertex corrections. By analyzing the periodic Anderson model for CeCu2Si2, we find that hexadecapole fluctuation…
We have applied the model-mapped RPA [H. Sakakibara et al., J. Phys. Soc. Jpn. 86, 044714 (2017)] to the cuprate superconductors La2CuO4 and HgBa2CuO4, resulting two-orbital Hubbard models. All the model parameters are determined based on first-principles calculations. For the model Hamiltonians, we perform fluctuation exchange calculation. Results explain relative height of Tc observed in experiment for La2CuO4 and HgBa2CuO4. In addition, we give some analyses for the interaction terms in the model, especially comparisons with those of the constrained RPA.
Recent experiments suggest that besides of antiferromagnetic fluctuations nematic fluctuations may contribute to the occurrence of superconductivity in iron pnictides. Motivated by this observation we study superconductivity from nematic fluctuations in a minimal two-band model. The employed band parameters are appropriate for iron pnictides and lead to four pockets for the Fermi line. It is shown that low-energy, long-wavelength nematic fluctuations within the pockets give rise to strong-coupling superconductivity whereas the large momenta density fluctuations between pockets are rather irrel…
In contrast to elementary Majorana particles, emergent Majorana fermions (MFs) in condensed-matter systems may have electromagnetic multipoles. We developed a general theory of magnetic multipoles for surface helical MFs on time-reversal-invariant superconductors. The results show that the multipole response is governed by crystal symmetry, and that a one-to-one correspondence exists between the symmetry of Cooper pairs and the representation of magnetic multipoles under crystal symmetry. The latter property provides a way to identify nonconventional pairing symmetry via the magnetic response …
We study the spin-fluctuation-mediated $s\pm$-wave superconductivity in the bilayer Hubbard model with vertical and diagonal interlayer hoppings. As in the two-leg ladder model with diagonal hoppings, studied previously by the present authors, superconductivity is strongly enhanced when one of the bands lies just below (or touches) the Fermi level, that is, when the band is incipient. The strong enhancement of superconductivity is because large weight of the spin fluctuations lies in an appropriate energy range, whereas the low energy, pair-breaking spin fluctuations are suppressed. The optimi…
We study the superconducting instability mediated by spin fluctuations in the Eliashberg theory for a minimal two-band model of iron-based superconductors. While antiferromagnetic spin fluctuations can drive superconductivity (SC) as is well established, we find that spin fluctuations necessarily contain a contribution to suppress SC even though SC can eventually occur at lower temperatures. This self-restraint effect stems from a general feature of the spin-fluctuation mechanism, namely the repulsive pairing interaction, which leads to phase frustration of the pairing gap and consequently the…
To understand the interplay between nematic fluctuation and superconductivity in iron-based superconductors, we performed a systematic study of the realistic two-orbital Hubbard model by using the constrained-path quantum Monte Carlo method. Our numerical results showed that the on-site nematic interaction induces a strong enhancement of nematic fluctuations at various momentums, especially at ($π$,$π$). Simultaneously, it was found that the on-site nematic interaction suppresses the ($π$,0)/(0,$π$) antiferromagnetic order and long-range electron pairing correlations for dominant pairing chann…
Nematic-fluctuation-mediated superconductivity in CuxTiSe2
Renmin University of China（中国人民大学）；Center for High Pressure Science and Technology Advanced Research（高压科学和技术先进研究中心）；Anhui University（安徽大学）；Beijing University of Posts and Telecommunications（北京邮电大学）
研究发现Cu x TiSe 2中易位波动与超导性之间的相互作用，揭示易位相变对超导性增强的作用机制。
Nematic superconductors possess unconventional superconducting order parameters that spontaneously break rotational symmetry of the underlying crystal. In this work we propose a mechanism for nematic superconductivity stabilized by strong density wave fluctuations in two dimensions. While the weak-coupling theory finds the fully gapped chiral state to be energetically stable, we show that strong density wave fluctuations result in an additional contribution to the free energy of a superconductor with multicomponent order parameters, which generally favors nematic superconductivity. Our theory …
We investigate the evolution of superconductivity with decreasing film thickness in ultrathin amorphous MoGe (a-MoGe) films using a combination of sub-Kelvin scanning tunneling spectroscopy, magnetic penetration depth measurements and magneto-transport measurements. We observe that superconductivity is strongly affected by quantum and classical phase fluctuations for thickness below 5 nm. The superfluid density is strongly suppressed by quantum phase fluctuations at low temperatures and evolves towards a linear-T dependence at higher temperatures. This is associated with a rapid decrease in th…
Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moiré potential. Superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to chiral unconventional superconductivity when the fluctuations are st…
In quantum materials, electrons that have strong correlations tend to localize, leading to quantum spins as the building blocks for low-energy physics. When strongly correlated electrons coexist with more weakly-correlated conduction electrons, multiple channels of effective interactions develop and compete with each other. The competition creates quantum fluctuations having a large spectral weight, with the associated entropies reaching significant fractions of $R\ln 2$ per electron. Advancing a framework to understand how the fluctuating local moments influence unconventional superconductivi…
Superconductivity arises mostly at energy and temperature scales that are much smaller than the typical bare electronic energies. Since the computational effort of diagrammatic many-body techniques increases with the number of required Matsubara frequencies and thus with the inverse temperature, phase transitions that occur at low temperatures are typically hard to address numerically. In this work, we implement a fluctuation exchange (FLEX) approach to spin fluctuations and superconductivity using the "intermediate representation basis" (IR) [Shinaoka et al., PRB 96, 2017] for Matsubara Green…
The interplay of orbital and spin degrees of freedom is the fundamental characteristic in numerous condensed matter phenomena, including high temperature superconductivity, quantum spin liquids, and topological semimetals. In iron-based superconductors (FeSCs), this causes superconductivity to emerge in the vicinity of two other instabilities: nematic and magnetic. Unveiling the mutual relationship among nematic order, spin fluctuations, and superconductivity has been a major challenge for research in FeSCs, but it is still controversial. Here, by carrying out 77Se nuclear magnetic resonance (…
Herman Rietschel纪念会议的组织者要求我回顾超导性和自旋涨落相互作用的一些历史。最初，Berk和Schrieffer展示了顺磁自旋涨落如何抑制近铁磁材料中的超导性。在此之后，Rietschel和其他同事写了一些论文，研究自旋涨落在降低各种电子-声子超导体T_c中的作用。副磁振子自旋涨落也被认为提供了负责$^3He$超流相的p波配对机制。最近，反铁磁自旋涨落被认为是重费米子超导体和某些有机材料以及高T_c铜氧化物中d波配对的机制。在这里，我将回顾一些早期的历史，并讨论我们最近从数值模拟中学到的一些东西。
Non-Fermi-Liquid Transport Phenomena and Superconductivity Driven by Orbital Fluctuations in Iron Pnictides: Analysis by Fluctuation-Exchange Approximation
Coexistence of Antiferromagnetic Spin Fluctuations and Superconductivity in La2SmNi2O7 Thin Films
ShanghaiTech University（上海科技大学）；Shanghai Advanced Research Institute, Chinese Academy of Sciences（中国科学院上海高等研究院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）
We review recent studies for superconductivity using diagrammatic extensions of dynamical mean field theory. These approaches take into account simultaneously both, the local correlation effect and spatial long-range fluctuations, which are essential to describe unconventional superconductivity in a quasi-two-dimensional plane. The results reproduce and predict the experimental phase diagrams of strongly correlated system such as cuprates and nickelates. Further studies reveal that the dynamical screening effect of the pairing interaction vertex has dramatic consequences for the transition tem…
Unconventional Superconductivity Induced by Quantum Critical Fluctuations in Hydrate Cobaltate Na$_{x}$(H$_3$O)$_{z}$CoO$_{x}\cdot$ $y$H$_{2}$O -- Relationship between Magnetic Fluctuations and the Superconductivity Revealed by a Co Nuclear Quadrupole Resonance --
Motivated by recent experiments reporting superconductivity only at very low temperature in a class of heavy fermion compounds, we study the impact of energy fluctuations with small momentum transfer on the pairing instability near an antiferromagnetic quantum critical point. While these fluctuations, formed by composite spin fluctuations, were proposed to explain the thermodynamic and transport properties near the quantum critical point of compounds such as YbRh$_{2}$Si$_{2}$ and CeCu$_{6-x}$Au$_{x}$ at $x\approx0.1$, here they are found to strongly suppress $T_{c}$ of the $d$-wave pairing of…
Superconductivity in low carrier density metals challenges the conventional electron-phonon theory due to the absence of retardation required to overcome Coulomb repulsion. In quantum critical polar metals, the Coulomb repulsion is heavily screened, while the critical transverse optic phonons decouple from the electron charge. In the resulting vacuum, the residual interactions between quasiparticles are carried by energy fluctuations of the polar medium, resembling the gravitational interactions of a dark matter universe. Here we demonstrate that pairing inevitably emerges from "gravitational'…
Simultaneous emergence of superconductivity, inter-pocket scattering and nematic fluctuation in potassium-coated FeSe superconductor
超导性起源于电子配对。因此，费米面上的配对沟道和配对胶是理解超导体的两个关键问题。最近，在电子掺杂的FeSe超导体中发现了超过40 K的高温超导性，包括K $_x$ Fe $_{2-y}$ Se $_2$、Li $_{0.8}$ Fe $_{0.2}$ OHFeSe和单层FeSe薄膜。然而，它们的配对机制仍然存在争议。本文研究了包钾FeSe单晶电子结构的系统演化。通过在样品表面上原位蒸发钾来精确控制掺杂水平。我们发现当费米面的Lifshitz跃迁使两个电子袋之间的袋间散射打开时，超导性就出现了。在相同的掺杂浓度下，电子有序度显著降低，在较宽的掺杂范围内，电子有序度仍有较大的涨落。我们的研究结果表明，在电子掺杂的FeSe超导体的超导电性，袋间散射，和涨落之间的潜在的相关性。
We study the contribution of the electron-spin fluctuation coupling to the superconducting state of the two dimensional Hubbard model within dynamical cluster approximation (DCA) using a numerical exact continuous time Monte Carlo solver. By analyzing the frequency dependence of the self energy, we show that only about half of the superconductivity can be attributed to a "pairing glue" arising from treating spin fluctuations as a pairing boson in the standard one-loop theory.
We present $^{77}$Se-NMR measurements on FeSe$_{1-x}$S$_x$ samples with sulfur content $x=0,9,15$ and $29\%$. Twinned nematic domains are observed in the NMR spectrum for all samples except $x=29\%$. The NMR spin-lattice relaxation rate shows that magnetic fluctuations are initially enhanced between $x=0\%$ and $x=9\%$, but are strongly suppressed for higher $x$ values. The observed behavior of the magnetic fluctuations parallels the superconducting transition temperature $T_c$ in these materials, providing strong evidence for the primary importance of magnetic fluctuations for superconductivi…
