Sr $_2$ RuO $_4$中的非常规超导机制在本质上更接近于超流体$^3$ He，还是更接近于铜酸盐、磷属元素化物和有机超导体？我们挑战在这一领域的主流假设，并使用良好的控制微扰重整化群计算，我们认为，超导性的Sr $_2$ RuO $_4$更接近于准一维有机超导体。我们的理论有某些现象学的结论，与实验观察到的现象是一致的。
英文摘要：
Is the mechanism of unconventional superconductivity in Sr$_2$RuO$_4$ closer in spirit to superfluid $^3$He, or to the cuprates, pnictides, and organic superconductors? We challenge prevailing assumptions in this field and using well-controlled perturbative renormalization group calculations, we suggest that superconductivity in Sr$_2$RuO$_4$ resembles more closely the quasi-one dimensional organic superconductors. Our theory has certain phenomenological consequences that are consistent with the experimentally observed phenomena.
Single crystals of the Sr$_2$RuO$_4$-Ru eutectic system are known to exhibit enhanced superconductivity at 3~K, in addition to the bulk superconductivity of Sr$_2$RuO$_4$ at 1.5~K. The 1.5-K phase is believed to be a spin-triplet, chiral $p$-wave state with the multi-component order parameter, giving rise to chiral domain structure. In contrast, the 3-K phase is attributable to enhanced superconductivity of Sr$_2$RuO$_4$ in the strained interface region between Ru inclusion of a few to tens of micrometers in size and the surrounding Sr$_2$RuO$_4$. We investigate the dynamic behavior of a topol…
Sr$_{2}$RuO$_{4}$ is one of the most promising candidates of a topological superconductor with broken time-reversal symmetry, because a number of experiments have revealed evidences for a spin-triplet chiral $p$-wave superconductivity. In order to clarify the time-reversal symmetry of Sr$_{2}$RuO$_{4}$, we introduce a novel test that examines the invariance of the Josephson critical current under the inversion of both the current and magnetic fields, in contrast to the detection of a spontaneous magnetic field employed in past experiments. Analyses of the transport properties of the planar and…
We use functional renormalization group method to study a three-orbital model for superconducting Sr$_2$RuO$_4$. Although the pairing symmetry is found to be chiral $p$-wave, the atomic spin-orbit coupling induces near-nodes for quasiparticle excitations. Our theory explains a major experimental puzzle between $d$-wave-like feature observed in thermal experiments and the chiral $p$-wave triplet pairing revealed in nuclear-magnetic-resonance and Kerr effect.
By tuning the physical and chemical pressures of layered perovskite materials we can realize the quantum states of both superconductors and insulators. By reducing the thickness of a layered crystal to a nanometer level, a nanofilm crystal can provide novel quantum states that have not previously been found in bulk crystals. Here we report the realization of high-temperature superconductivity in Ca$_2$RuO$_4$ nanofilm single crystals. Ca$_2$RuO$_4$ thin film with the highest transition temperature $T_c$ (midpoint) of 64~K exhibits zero resistance in electric transport measurements. The superco…
Sr$_2$RuO$_4$ is a leading candidate for chiral $p$-wave superconductivity. The detailed mechanism of superconductivity in this material is still the subject of intense investigations. Since superconductivity is sensitive to the topology of the Fermi surface (the contour of zero-energy quasi-particle excitations in the momentum space in the normal state), changing this topology can provide a strong test of theory. Recent experiments tuned the Fermi surface topology efficiently by applying planar anisotropic strain. Using functional renormalization group theory, we study the superconductivity a…
We propose a general scheme to probe the compatibility of arbitrary pairing states with a given normal state Hamiltonian by the introduction of a concept called superconducting fitness. This new quantity gives a direct measure of the suppression of the superconducting critical temperature in presence of key symmetry breaking fields. A merit of the superconducting fitness is that it can be used as a tool to identify non-trivial mechanisms to suppress superconductivity under various external influences, in particular, magnetic fields or distortions, even in complex multi-orbital systems. In the …
Despite much effort for over the two decades, the paring symmetry of a Sr$_2$RuO$_4$ superconductor has been still unclear. In this Rapid Communication, motivated by the recent rapid progress in fabrication techniques for Sr$_2$RuO$_4$ thin-films, we propose a promising strategy for identifying the spin-triplet superconductivity in the thin-film geometry by employing an antisymmetric spin-orbit coupling potential and a Zeeman potential due to an external magnetic field. We demonstrate that a spin-triplet superconducting thin-film undergoes a phase transition from a helical state to a chiral st…
Muon-spin rotation measurements of the vortex state in Sr$_2$RuO$_4$: type-1.5 superconductivity, vortex clustering and a crossover from a triangular to a square vortex lattice
We provide results for the leading superconducting instabilities for a model pertaining to Sr$_2$RuO$_4$ obtained within spin-fluctuation mediated superconductivity in the very weak-coupling limit. The theory incorporates spin-orbit coupling (SOC) effects both in the band structure and in the pairing kernel in the form of associated magnetic anisotropies. The leading superconducting phase is found to be $d_{x^2-y^2}$ and a nodal $s$-wave state. However, the odd-parity helical solution can become leading either for small SOC and Hund's coupling $J$ in the weak $U$-limit, or in the opposite limi…
We establish the existence of bulk odd-frequency superconductivity in Sr$_2$RuO$_4$ and show that an intrinsic Kerr effect is a direct evidence of this state. We use both general two- and three-orbital models, as well as a realistic tight-binding description of Sr$_2$RuO$_4$ to demonstrate that odd-frequency pairing arises due to finite hybridization between different orbitals in the normal state, and is further enhanced by finite inter-orbital pairing.
The superconducting pairing in Sr$_2$RuO$_4$ is widely considered to be chiral $p$-wave with $\vec{d}_{\boldsymbol k} \sim (k_x + ik_y)\hat{z}$, which belongs to the $E_u$ representation of the crystalline $D_{4h}$ group. However, this superconducting order appears hard to reconcile with a number of key experiments. In this paper, based on symmetry analysis we discuss the possibility of odd-parity pairing with inherent three-dimensional (3D) character enforced by the inter-orbital interlayer coupling and the sizable spin-orbit coupling (SOC) in the material. We focus on a yet unexplored $E_u$ …
Applying in-plane uniaxial pressure to strongly correlated low-dimensional systems has been shown to tune the electronic structure dramatically. For example, the unconventional superconductor Sr$_2$RuO$_4$ can be tuned through a single Van Hove singularity which results in a strong enhancement of both $T_\text{c}$ and $H_\text{c2}$. Out-of-plane ($c$ axis) uniaxial pressure is expected to tune the quasi-two-dimensional structure even more strongly, causing it to approach two Van Hove singularities simultaneously. Here we achieve a record value of $3.2$ GPa compression along the $c$ axis of Sr$…
Sr$_{2}$RuO$_{4}$ (SRO) is the prime candidate for chiral $p$-wave superconductor with critical temperature $T_{c}(SRO)\sim$1.5 K. Chiral domains with opposite chiralities $p_{x}\pm ip_{y}$ were proposed, but yet to be confirmed. We measure the field dependence of the point contact (PC) resistance between a tungsten tip and the SRO-Ru eutectic crystal, where micrometer-sized Ru inclusions are embedded in SRO with atomic sharp interface. Ruthenium is an $s$-wave superconductor with $T_{c}(Ru)\sim$0.5 K, flux pinned near the Ru inclusions can suppress its superconductivity as reflected from the …
Despite of many experimental and theoretical efforts, the pairing symmetry of superconductivity in Sr$_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.…
There is intense controversy around the unconventional superconductivity in strontium ruthenate, where the various theoretical and experimental studies suggest diverse and mutually exclusive pairing symmetries. Currently, the investigation is solely focused on only one material, Sr2RuO4, and the field suffers from the lack of comparison targets. Here, employing a density functional theory based analysis, we show that the heterostructure composed of SrRuO3 and SrTiO3 is endowed with all the key characteristics of Sr2RuO4, and, in principle, can host superconductivity. Furthermore, we show that …
Conditions for orbital selective altermagnetism in Sr$_2$RuO$_4$: tight binding model, similarities with cuprates and implications on superconductivity
The superconducting state of Sr$_2$RuO$_4$ was once thought to be a leading candidate for $p$-wave superconductivity. A constant Knight shift below the transition temperature provided evidence for spin-triplet pairing, and a $π$ phase shift observed in Josephson junction tunneling experiments suggested odd-parity pairing, both of which are described by $p$-wave states. However, with recent experiments observing a significant decrease in the Knight shift below the transition temperature, signifying a spin-singlet state, the odd-parity results are left to be reconciled. In this work, we show tha…
Unambiguous identification of the superconducting order parameter symmetry of Sr$_2$RuO$_4$ has remained elusive for more than a quarter century. While a chiral $p$-wave ground state analogue to superfluid $^3$He-$A$ was ruled out only very recently, other proposed $p$-wave scenarios are still viable. Here, field-dependent $^{17}$O Knight shift measurements are compared to corresponding specific heat measurements, previously reported. We conclude that the shift results can be accounted for by the expected field-induced quasiparticle response only. An upper bound for the condensate magnetic res…
Motivated by the success of experimental manipulation of the band structure through biaxial strain in Sr$_2$RuO$_4$ thin film grown on a mismatched substrate, we investigate theoretically the effects of biaxial strain on the electronic instabilities, such as superconductivity (SC) and spin density wave (SDW), by functional renormalization group. According to the experiment, the positive strain (from lattice expansion) causes charge transfer to the $γ$-band and consequently Lifshitz reconstruction of the Fermi surface. Our theoretical calculations show that within a limited range of positive st…
The polar Kerr effect in superconducting Sr$_2$RuO$_4$ implies finite ac anomalous Hall conductivity. Since intrinsic anomalous Hall effect (AHE) is not expected for a chiral superconducting pairing developed on the single Ru $d_{xy}$ orbital, multiorbital chiral pairing actively involving the Ru $d_{xz}$ and $d_{yz}$ orbitals has been proposed as a potential mechanism. Here we propose that AHE could still arise even if the chiral superconductivity is predominantly driven by the $d_{xy}$ orbital. This is demonstrated through two separate models which take into account subdominant orbitals in t…
Strontium ruthenate (Sr$_2$RuO$_4$) has long been thought to host a spin-triplet chiral $p$-wave superconducting state. However, the singletlike response observed in recent spin-susceptibility measurements casts serious doubts on this pairing state. Together with the evidence for broken time-reversal symmetry and a jump in the shear modulus $c_{66}$ at the superconducting transition temperature, the available experiments point towards an even-parity chiral superconductor with $k_z(k_x\pm ik_y)$-like $E_g$ symmetry, which has consistently been dismissed based on the quasi-two-dimensional electr…
Under various conditions of the growth process, when the presumably unconventional superconductor Sr$_2$RuO$_4$ (SRO) contains micro-inclusions of Ru metal, the superconducting critical temperature increases significantly. An STEM study shows a sharp interface geometry which allows crystals of SRO and of Ru-metal to grow side by side by forming a commensurate superlattice structure at the interface. In an attempt to shed light as to why this happens, we investigated the atomic structure and electronic properties of the interface between the oxide and the metal micro-inclusions using density fu…
The unconventional superconductivity in Sr$_2$RuO$_4$ continues to attract considerable interest. While many measurements can be interpreted on the basis of chiral $p$-wave pairing with intriguing topological character, a number of exceptions hinder an unambiguous verification of such pairing. The pairing mechanism also remains under debate. In this paper, with effects of the sizable spin-orbit coupling accounted for, we reexamine the superconducting instabilities in Sr$_2$RuO$_4$ through systematic microscopic analysis within random phase approximation. Our calculations show that the odd-pari…
We propose to realize second-order topological superconductivity in bilayer spin-polarized Fermi gas superfluids. We focus on systems with intralayer chiral $p$-wave pairing and with tunable interlayer hopping and interlayer interactions. Under appropriate circumstances, an interlayer even-parity $s$- or $d$-wave pairing may coexist with the intralayer $p$-wave. Our model supports localized Majorana zero modes not only at the corners of the system geometry, but also at the terminations of certain one-dimensional defects, such as lattice line defects and superfluid domain walls. We show how suc…
Origins of spontaneous magnetic fields in Sr$_2$RuO$_4$
PSI Center for Neutron and Muon Sciences CNM（瑞士保罗谢尔研究所中子与μ子科学中心）；STFC-ISIS Facility, Rutherford Appleton Laboratory（英国科学与技术设施委员会- ISIS设施，鲁瑟福阿普尔顿实验室）；National Institute for Materials Science（日本国立材料研究所）；Toyota Riken - Kyoto-Univ. Research Center (TRiKUC)（丰田理研-京都大学研究中心）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）
Sr$_2$RuO$_4$ is a prototypical multi-band superconductor with three bands crossing the Fermi level. These bands exhibit distinct dimensional characteristics, with one quasi-2D $γ$-band and two quasi-1D $α$- and $β$-bands. This leads to the expectation that the superconductivity on the $γ$-band may be only weakly Josephson-coupled to that on the other two bands. Based on an explicit microscopic weak coupling calculation appropriate for Sr$_2$RuO$_4$, we study the collective Leggett modes associated with the relative phase oscillations between the bands and show that a relatively soft Leggett m…
One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning, leading to experiments that have advanced our understanding of the fas…
In the light of the recently discussed mechanism for suppression of superconductivity in multi-orbital systems called inter-orbital effect, here we extend our analysis of the upper critical field in Sr$_2$RuO$_4$ now under strain. We show that the presence of the standard orbital effect and the new mechanism can consistently account for the qualitative changes observed in the upper critical field for the strained system, in particular, combining the overall enhancement of the critical field with the reduction in the anisotropy. The proposed picture holds for a triplet superconducting state, sh…
Among unconventional superconductors, Sr$_2$RuO$_4$ has become a benchmark for experimentation and theoretical analysis because its normal-state electronic structure is known with exceptional precision, and because of experimental evidence that its superconductivity has, very unusually, a spontaneous angular momentum, i.e. a chiral state. This hypothesis of chirality is however difficult to reconcile with recent evidence on the spin part of the order parameter. Measurements under uniaxial stress offer an ideal way to test for chirality, because under uniaxial stress the superconducting and chi…
High-quality single crystals are essentially needed for the investigation of the novel bulk properties of unconventional superconductors. The availability of such crystals grown by the floating-zone method has helped to unveil the unconventional superconductivity of the layered perovskite Sr$_2$RuO$_4$, which is considered as a strong candidate of a topological spin-triplet superconductor. Yet, recent progress of investigations urges further efforts to obtain ultimately high-quality crystalline samples. In this paper, we focus on the method of preparation of feed rods for the floating-zone mel…
The binary ruthenate, RuO$_2$, has been the subject of intense interest due to its itinerant antiferromagnetism and strain-induced superconductivity. The strain mechanism and its effect on the microscopic electronic states leading to the normal and superconducting state, however, remain undisclosed. Here, we investigate highly-strained epitaxial (110) RuO$_2$ films using polarization-dependent oxygen K-edge X-ray absorption spectroscopy (XAS). Through the detection of pre-edge peaks, arising from O:$2p$ - Ru:$4d$ hybridization, we uncover the effects of epitaxial strain on the orbital/electron…
The ruthenate family of layered perovskites has been a topic of intense interest with much work dedicated to understanding the superconducting state of the single layer, Sr$_2$RuO$_4$. Another longstanding puzzle is the lack of superconductivity in its sister compound, Sr$_3$Ru$_2$O$_7$, which constrains the possible superconducting mechanisms of Sr$_2$RuO$_4$. Here we address a microscopic mechanism that unifies superconducting and spin-density wave order in this family of materials. Beginning from a model of Sr$_2$RuO$_4$ featuring intraband pseudospin-singlet superconductivity originating f…
