三维超导体泡利顺磁极限中的双阶段连续-不连续超导相变：URu $%_{2}$ Si $_{2}$情况
Double-stage continuous-discontinuous superconducting phase transition in the Pauli paramagnetic limit of a 3D superconductor: the URu$%_{2}$Si$_{2}$ case
在重费米子化合物URu $_{2}$ Si $% _{2}$的混合超导（SC）态中观察到的de-Haas van-Alphen振荡的急剧抑制证实了在3D顺磁限制的超导体中由波动模糊的窄的双级SC相变的理论预测。二阶过渡到非均匀（FFLO）状态，然后通过一阶过渡到均匀的SC状态，通过使用非微扰的方法获得的预测的情况下，也被发现是一致的，最近的热导率测量上进行的这种材料。
英文摘要：
The sharp suppression of the de-Haas van-Alphen oscillations observed in the mixed superconducting (SC) state of the heavy fermion compound URu$_{2}$Si$% _{2}$ is shown to confirm a theoretical prediction of a narrow double-stage SC phase transition, smeared by fluctuations, in a 3D paramagnetically-limitted superconductor. The predicted scenario of a second order transition to a nonuniform (FFLO) state followed by a first order transition to a uniform SC state, obtained by using a non-perturbative approach, is also found to be consistent with recent thermal conductivity measurements performed on this material.
Pauli Paramagnetic Effects on Vortices in Superconducting TmNi2B2C
从理论和实验上研究了TmNi_2B_2C在顺磁相时涡旋周围的磁场分布。的漩涡形状因子，测量小角中子散射，被发现是独立的字段高达0.6 HC 2，然后在较高的字段急剧下降。的数据拟合好的解决方案的Eilenberger方程的顺磁效应时，由于交换相互作用与本地化的4f Tm时刻。涡核周围的感应顺磁矩用于保持由形状因子探测的场对比度。
We performed $^{59}$Co nuclear magnetic resonance (NMR) measurements of single-crystalline U$_6$Co. There is a small decrease in the Knight shift in the superconducting (SC) state, but this change mainly arises from the SC diamagnetic effect. The negligible change of the spin part of the Knight shift, together with the absence of the Pauli-paramagnetic effect in the SC U$_6$Co, is understood as a consequence of the small spin susceptibility. The nuclear spin-lattice relaxation rate $1/T_1$ is also measured in the SC state under the magnetic field, and exhibits a tiny Hebel-Slichter peak just b…
Bulk evidence for a time reversal symmetry broken superconducting state in URu2Si2
URu $_2$ Si $_2$被认为是一种手征\emph{d}波超导体，其库珀对波函数具有$k_z (k_x \pm ik_y)$时间反演对称破缺轨道分量，其中包含节点和节点线\cite{kasahara, kasahara2}。为了研究这种非常规状态的磁响应，通过大量的，热力学探针，我们测量了磁转矩$τ$在非常高的质量，良好的特性URu $_2$ Si $_2$单晶\cite{altarawneh,altarawneh2}在高磁场$H$和在非常低的温度$T$。URu $_2$ Si $_2$的磁化强度$M(H) \propto τ(H) /H$，在其超导状态下，并且对于从\emph{ab}平面的$15^{\circ}$内的角度，揭示了接近$H_{c2}$的$H$的符号的变化：从由涡旋的钉扎主导的明显的抗磁性响应到具有较小但“类顺磁性”滞后响应的状态，这意味着它与超导态有内在的联系。我们认为，这种异常的，角度依赖的行为是一个时间反转对称破缺超导状态的证据在URu $_2$ Si $_2$，虽然不一定是$k_z (k_x \pm ik_y)$状态。
We study the intrinsic anisotropy of the superconducting state in KFe$_2$As$_2$, using small-angle neutron scattering to image the vortex lattice as the applied magnetic field is rotated towards the FeAs crystalline planes. The anisotropy is found to be strongly field dependent, indicating multiband superconductivity. Furthermore, the high field anisotropy significantly exceeds that of the upper critical field, providing further support for Pauli limiting in KFe$_2$As$_2$ for field applied in the basal plane. The effect of Pauli paramagnetism on the unpaired quasiparticles in the vortex cores …
Superconductivity and the normal-state properties of NbN films can be tuned in a wide range, supplying a suitable platform to investigate the systematical evolution of the superconducting performances. Herein, we report the upper critical field of NbN films in both the vertical ($B\perp$ film) and parallel ($B\parallel$ film) orientations over a wide temperature range. Eight samples with the superconducting critical temperature $T_c$ ranging from 2.5 K to 9.8 K are studied. Meanwhile, the normal-state resistivity is tuned by more than six times by changing the conditions of the film growth. It…
Recently, 12442 system of Fe-based superconductors has attracted considerable attention owing to its unique double-FeAs-layer structure. A steep increase in the in-plane upper critical field with cooling has been observed near the superconducting transition temperature, $T_c$, in KCa$_2$Fe$_4$As$_4$F$_2$ single crystals. Herein, we report a high-field investigation on upper critical field of this material over a wide temperature range, and both out-of-plane ($H\|c$, $H_{c2}^{c}$) and in-plane ($H\|ab$, $H_{c2}^{ab}$) directions have been measured. A sublinear temperature-dependent behavior is …
The $g$-factor anisotropy of the heavy quasiparticles in the hidden order state of URu$_2$Si$_2$ has been determined from the superconducting upper critical field and microscopically from Shubnikov-de Haas (SdH) oscillations. We present a detailed analysis of the $g$-factor for the $α$, $β$ and $γ$ Fermi-surface pockets. Our results suggest a strong $g$-factor anisotropy between the $c$ axis and the basal plane for all observed Fermi surface pockets. The observed anisotropy of the $g$-factor from the quantum oscillations is in good agreement with the anisotropy of the superconducting upper cri…
We have studied the temperature dependence of the upper critical fields, $μ_{0}H_{c2}$, of K$_{x}$Fe$_{2-y}$Se$_{2-z}$S$_{z}$ single crystals up to 60 T. The $μ_{0}H_{c2}$ for $H\parallel ab$ and $H\parallel c$ decrease with increasing sulfur content. The detailed analysis using Werthamer-Helfand-Hohenberg (WHH) theory including the Pauli spin-paramagnetic effect shows that $μ_{0}H_{c2}$ for $H\parallel ab$ is dominated by the spin-paramagnetic effect, which diminishes with higher S content, whereas $μ_{0}H_{c2}$ for $H\parallel c$ shows a linear temperature dependence with an upturn at high f…
The putative spin-triplet superconductor UTe2 has an Ising-like magnetic anisotropy, indicating the Cooper pair spins parallel to the easy-axis. However, the upper critical field for the hard-axis direction is much larger than that for the easy-axis, implying the strong suppression of the Pauli depairing effect even for the hard-axis direction. This observation is consistent with the recent NMR measurements which show the tiny decrease of the Knight shift below the transition temperature Tc for hard-axis magnetic fields. We clarify that these behaviors are naturally understood as a result of m…
Two-dimensional materials are ideal candidates to host Charge density waves (CDWs) that exhibit paramagnetic limiting behavior, similarly to the well known case of superconductors. Here we study how CDWs in two-dimensional systems can survive beyond the Pauli limit when they are subjected to a strong magnetic field by developing a generalized mean-field theory of CDWs under Zeeman fields that includes incommensurability, imperfect nesting and temperature effects and the possibility of a competing or coexisting Spin density wave (SDW) order. Our numerical calculations yield rich phase diagrams …
We investigate quasiparticle relaxation dynamics in URu$_{2-x}$Fe$_{x}$Si$_{2}$ single crystals using ultrafast optical-pump optical-probe (OPOP) spectroscopy as a function of temperature ($T$) and Fe substitution ($x$), crossing from the hidden order (HO) phase ($x$ = 0) to the large moment antiferromagnet (LMAFM) phase ($x$ = 0.12). At low $T$, the dynamics for $x$ = 0 and $x$ = 0.12 are consistent with the low energy electronic structure of the HO and LMAFM phases that emerge from the high $T$ paramagnetic (PM) phase. In contrast, for $x$ = 0.1, two transitions occur over a narrow $T$ range…
Paramagnetic Effects on the Vortex Lattice of the Unconventional Superconductor CeCoIn_5
在临界场主要由泡利极限决定，超流主要来自电子自旋与局域磁场的顺磁相互作用的情况下，分析了具有d波配对的高kappa超导体Abrikosov晶格中的磁场分布.在广义Clem变分法框架下得到的结果与CeCoIn_5的形状因子随磁场的增加而增加，然后在接近H_c2时减小的观察结果是一致的。（A. D. Bianchi等人，Science第319卷，177（2008））。
Ambient-pressure-grown LaO$_{0.5}$F$_{0.5}$BiS$_2$ with a superconducting transition temperature $T_{c}\sim$3K possesses a highly anisotropic normal state. By a series of electrical resistivity measurements with a magnetic field direction varying between the crystalline $c$-axis and the $ab$-plane, we present the first datasets displaying the temperature dependence of the out-of-plane upper critical field $H_{c2}^{\perp}(T)$, the in-plane upper critical field $H_{c2}^{\parallel}(T)$, as well as the angular dependence of $H_{c2}$ at fixed temperatures for ambient-pressure-grown LaO$_{0.5}$F$_{0…
An Experimental and Semi-Empirical Method to Determine the Pauli-Limiting Field in Quasi 2D Superconductors as applied to $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$: Strong Evidence of a FFLO State
We theoretically investigate the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state by using the microscopic quasi-classical Eilenberger equation. The Pauli paramagnetic effects and the orbital depairing effects due to vortices are treated in an equal footing for three dimensional spherical Fermi surface model and $s$-wave pairing. The field evolution of the LO state is studied in detail, such as the $H$-$T$ phase diagram, spatial structures of the order parameter, the paramagnetic moment, and the internal filed. Field-dependences of various thermodynamic quantities: the paramagnetic moment, entrop…
The upper critical field is a fundamental measure of the strength of superconductivity in a material. It is also a cornerstone for the realization of superconducting magnet applications. The critical field arises because of the Copper pair breaking at a limiting field, which is due to the Pauli paramagnetism of the electrons. The maximal possible magnetic field strength for this effect is commonly known as the Pauli paramagnetic limit given as $μ_0 H_{\rm Pauli} \approx 1.86{\rm [T/K]} \cdot T_{\rm c}$ for a weak-coupling BCS superconductor. The violation of this limit is only rarely observed.…
Pauli-limited upper critical field and anisotropic depairing effect of La2.82Sr0.18Ni2O7 superconducting thin film
Southeast University（东南大学）；National Laboratory of Solid State Microstructures, Jiangsu Key Laboratory of Artificial Functional Materials, College of Engineering and Applied Sciences, Nanjing University（南京大学工程与应用科学学院）；Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学先进微结构协同创新中心）；Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology（华中科技大学物理学院）；Purple Mountain Laboratories（紫金山实验室）；Jiangsu Physica Science Research Center（江苏物理科学研究中心）
La2.82Sr0.18Ni2O7 超薄 films 的 Pauli 限制临界磁场和各向异性配对破坏效应研究显示，其超导性在低温下表现出三维 bulk 特征，且自旋-顺磁效应显著影响高场超导相图。
Hidden Crossover Phenomena in Strongly Pauli Limited Multiband Superconductors ---Application to CeCu$_2$Si$_2$
基于最近对重费米子材料CeCu $_2$ Si $_2$和UBe $_{13}$的实验研究，我们建立了一个框架来描述具有强泡利顺磁效应（PPE）的多带超导体的一般性质.与单带情况相比，即使在强PPE情况下，上临界场$H_{\rm c2}$仍能保持二级跃迁。预期的一阶跃迁隐藏在$H_{\rm c2}$内部，并由于多频带的相互作用而成为交叉。本文基于微观Eilenberger理论的完全自洽解，解释了最近在CeCu $_2$ Si $_2$上的STM实验中观察到的与交叉和“空”涡核态有关的几种神秘异常现象。
The full H-T phase diagram in the nematic superconductor FeSe is mapped out using specific-heat and thermal-expansion measurements down to 0.7 K and up to 30 T for both field directions. A clear thermodynamic signal of an underlying vortex-melting transition is found in both datasets and could be followed down to low temperatures. The existence of significant Gaussian thermal superconducting fluctuations is demonstrated by a scaling analysis, which also yields the mean-field upper critical field Hc2(T). For both field orientations, Hc2(T) shows Pauli-limiting behavior. Whereas the temperature …
We have recently reported the first direct calorimetric observation of a magnetic-field-induced first-order phase transition into a high-field FFLO superconducting state at the Clogston-Chandrasekar `Pauli' paramagnetic limit $H_p$ in a 2D superconductor $κ-{\textrm{(BEDT-TTF)}}_2{\textrm{Cu}}{\textrm{(NCS)}}_2$. The high-field state is both higher entropy and strongly paramagnetic, as thermodynamically required for the FFLO state. Here we compare our results with theoretical predictions for the field dependence of the high-field FFLO state in the 2D limit, revealing tentative evidence for tra…
We present a study of the upper critical field, H$_{c2}$, of pristine and proton-irradiated RbEuFe$_4$As$_4$ crystals in pulsed magnetic fields of up to 65 T. The data for H$_{c2}$ reveal pronounced downwards curvature, particularly for the in-plane field orientation, and a superconducting anisotropy that decreases with decreasing temperature. These features are indicative of Pauli paramagnetic limiting. For the interpretation of these data, we use a model of a clean single-band superconductor with an open Fermi surface in the shape of a warped cylinder, which includes strong paramagnetic limi…
We investigate the response of a doped topological insulator Bi$_2$Se$_3$ with spin-triplet nematic superconductivity to external magnetization. We calculate the Zeeman part of magnetic susceptibility for nematic and chiral superconducting phases near T$_c$ in Ginzburg-Landau formalism. Superconducting order parameter from $E_u$ representation has non-trivial coupling with the transversal Zeeman field that results in a paramagnetic response to a magnetization. The topology of a Fermi surface has a strong influence on magnetic susceptibility. Lifshitz transition from closed to open Fermi surfac…
The fluctuation conductivity of a moderately clean type II superconductor with strong Pauli paramagnetic pair-breaking (PPB) is studied by focusing on the quantum regime at low temperatures and in high magnetic fields. First, it is pointed out that, as the PPB effect becomes stronger, the quantum superconducting fluctuation is generally enhanced so that the Aslamasov-Larkin (AL) fluctuation conductivity tends to vanish upon cooling. Further, by examining other (the DOS and the Maki-Thompson (MT)) terms of the fluctuation conductivity, the field dependence of the resulting total conductivity is…
We report magnetic torque measurements on iron-pnictide superconductors Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($x \approx$ 0.69 and 0.76) up to an applied field of $B_a$ = 45 T. The peak effect is observed in torque-vs-field curves below the irreversibility field. It is enhanced and becomes asymmetric as the field is tilted from the $c$ axis. For field directions close to the $ab$ plane, increasing- and decreasing-field curves peak at markedly different fields, and exhibit a sharp jump, suggestive of a first-order phase transition, on the high- and the low-field side of the peak, respectively. Complicat…
The Pauli limiting field represents fundamental magnetic field at which superconducting state collapses due to the spin-paramagnetic Cooper pair-breaking effect. Cao et al [1] reported that the upper critical field (i.e., the magnetic field at which the superconducting state collapses in experiment) in magic-angle twisted trilayer graphene (MATNG, N=3) in 2-3 times exceeds the Pauli limiting field in this material. This observation was interpreted as a violation of the Pauli-limiting field in MAT3G. Similar conclusions were recently reported by the same research group in MATNG (N=4,5) superlat…
We report the synthesis, crystal structure, and superconductivity of Ti$_4$Ir$_2$O. The title compound crystallizes in an $η$-carbide type structure of the space group $Fd\overline{3}m$ (No. 227), with lattice parameters $a=b=c=11.6194(1)$ Å. The superconducting $T_c$ is found to be 5.1 $\sim$ 5.7 K. Most surprisingly, Ti$_4$Ir$_2$O hosts an upper critical field of 16.45 T, which is far beyond the Pauli paramagnetic limit. Strong coupled superconductivity with evidences for multigap is revealed by the measurements of heat capacity and upper critical field. First-principles calculations suggest…
Superconducting critical field far above the Pauli limit in one-dimensional Li$_{0.9}$Mo$_6$O$_{17}$
发现紫色青铜Li $_{0.9}$ Mo $_6$ O $_{17}$的上临界场$H_{c2}$具有大的各向异性，与从观察到的电阻率各向异性所预期的定量一致。随着磁场沿最导电的轴排列，$H_{c2}$随着温度的降低而单调增加，达到比估计的顺磁对断裂场大五倍的值。增强$H_{c2}$调用自旋轨道散射或强耦合超导性的理论被证明是不足以解释所观察到的行为，这表明在Li $_{0.9}$ Mo $_6$ O $_{17}$的配对状态是非常规的，可能是自旋三重态。
The recent observation of superconductivity in thin film infinite-layer nickelates$^{1-3}$ offers a different angle to investigate superconductivity in layered oxides$^{4}$. A wide range of candidate models have been proposed$^{5-10}$, emphasizing single- or multi-orbital electronic structure, Kondo or Hund's coupling, and analogies to cuprates. Clearly, further experimental characterization of the superconducting state is needed to develop a full understanding of the nickelates. Here we use magnetotransport measurements to probe the superconducting anisotropy in Nd$_{0.775}$Sr$_{0.225}$NiO$_{…
In this paper we introduce an exactly solvable Kondo lattice model without any fine-tuning local gauge symmetry. This model describes itinerant electrons interplaying with a localized magnetic moment via only longitudinal Kondo exchange. Its solvability results from conservation of the localized moment at each site, and is valid for arbitrary lattice geometry and electron filling. A case study on square lattice shows that the ground state is a Néel antiferromagnetic insulator at half-filling. At finite temperature, paramagnetic phases including a Mott insulator and correlated metal are found. …
Ising superconductivity in noncentrosymmetric bulk NbSe2
Pavol Jozef Šafárik University in Košice（科希策帕沃尔·约瑟夫·沙法里克大学）；Institute of Experimental Physics, Slovak Academy of Sciences（斯洛伐克科学院实验物理研究所）；Univ. Grenoble Alpes, CNRS, Grenoble INP*, Institut Néel（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔理工学院、内耳研究所）；Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG, Pheliqs（格勒诺布尔阿尔卑斯大学、法国原子能和替代能源委员会、格勒诺布尔理工学院、IRIG、Pheliqs）；Institut des Matériaux Jean Rouxel, Université de Nantes and CNRS-UMR 6502（让·鲁克斯尔材料研究所、南特大学和法国国家科学研究中心联合研究单位6502）
The upper critical field in type II superconductors is limited by the Pauli paramagnetic limit. In superconductors with strong Rashba spin-orbit coupling this limit can be overcome by forming a helical state. Here we quantitatively study the magnetic field-temperature phase diagram of finite-size superconductors with Rashba spin-orbit coupling. We discuss the effect of finite size and shape anisotropy. We demonstrate that the critical field is controllable by intrinsic parameters such as spin-orbit coupling strength and tunable parameters such as sample geometry and applied field direction. Ou…
