对非常规超导性的研究一直集中在具有强自旋轨道耦合和独特晶格的材料上。掺杂的硒化铋（Bi $_2$ Se $_3$）是考虑到母体化合物的拓扑绝缘体性质及其三角晶格的强有力的候选物。超导态的物理性质与其潜在的晶体对称性之间的耦合是对非常规超导性的关键测试。在本文中，我们报告的直接证据表明，超导磁响应强烈耦合到潜在的三重晶体对称性在最近发现的超导体与三角晶体结构，铌（Nb）掺杂硒化铋（Bi $_2$ Se $_3$）。更重要的是，我们观察到，磁响应大大增强沿一个首选方向自发打破旋转对称性。超导磁滞回线不是简单的三重晶体对称，而是主要的二重和四重对称。这一观测结果证实了旋转对称性的破缺，并表明Nb掺杂Bi $_2$ Se $_3$的超导基态中存在有序。此外，热容测量显示在超导状态下的指数衰减，并建议在超导能隙中没有线节点。这些观测结果为奇宇称拓扑超导性提供了强有力的证据。
英文摘要：
The search for unconventional superconductivity has been focused on materials with strong spin-orbit coupling and unique crystal lattices. Doped bismuth selenide (Bi$_2$Se$_3$) is a strong candidate given the topological insulator nature of the parent compound and its triangular lattice. The coupling between the physical properties in the superconducting state and its underlying crystal symmetry is a crucial test for unconventional superconductivity. In this paper, we report direct evidence that the superconducting magnetic response couples strongly to the underlying 3-fold crystal symmetry in the recently discovered superconductor with trigonal crystal structure, niobium (Nb)-doped bismuth selenide (Bi$_2$Se$_3$). More importantly, we observed that the magnetic response is greatly enhanced along one preferred direction spontaneously breaking the rotational symmetry. Instead of a simple 3-fold crystalline symmetry, the superconducting hysteresis loop shows dominating 2-fold and 4-fold symmetry. This observation confirms the breaking of the rotational symmetry and indicates the presence of nematic order in the superconducting ground state of Nb-doped Bi$_2$Se$_3$. Further, heat capacity measurements display an exponential decay in superconducting state and suggest that there is no line node in the superconducting gap. These observations provide strong evidence of odd-parity topological superconductivity.
IrTe$_2$ with large spin-orbital coupling (SOC) shows a CDW-like first order structural phase transition from high-temperature trigonal phase to low-temperature monoclinic phase at 270 K, accompanying with a large jump in transport and magnetic measurement as well as in heat capacity. Here, the 3d element Ni has been doped into IrTe$_2$ by growing Ir$_{1-x}$Ni$_x$Te$_2$ single crystals. Both XRD and XPS results reveal that the Ni atoms have substituted for Ir, which is consistent with the calculation result. Like the CDW behaviour, the structural phase transition shows competition and coexiste…
With the discovery of strong coupling physics and superconductivity in Moiré superlattices, it's essential to have an understanding of strong coupling driven superconductivity in systems with trigonal symmetry. The simplest lattice model with trigonal symmetry is the triangular lattice Hubbard model. Although the triangular lattice spin model is a heavily studied model in the context of frustration, studies of the hole-doped triangular lattice Hubbard model are rare. Here we use density matrix renormalization group (DMRG) to investigate the domininant superconducting channels in the hole-doped…
Identification of nematic superconductivity from the upper critical field
最近的核磁共振和比热测量同时提供了掺杂拓扑绝缘体Cu $_x$ Bi $_2$ Se $_3$超导态旋转对称性自发破缺的证据。这表明配对对称性对应于$D_{3d}$晶体点群的二维表示，并且Cu $_x$ Bi $_2$ Se $_3$是超导体。本文在Ginzburg-Landau（GL）理论框架下对超导体的上临界场$H_{c2}$进行了全面的研究。与典型的GL理论相反，GL理论具有涌现的U（1）旋转对称性，掩盖了晶体的离散对称性，三角晶体中的双组分超导体理论反映了真正的$D_{3d}$晶体对称性。这对上临界场有直接的影响。首先，三角超导体的$H_{c2}$在基面上表现出六重各向异性。第二，当两个分量的简并度被提升时，例如，在单轴应变下，$H_{c2}$表现出具有特征角度和温度依赖性的双重各向异性。我们的深入研究表明，上临界场的测量是一种直接检测超导性的方法，它直接适用于最近发现的三角超导体Cu $_x$ Bi $_2$ Se $_3$，Sr $_x$ Bi $_2$ Se $_3$，Nb $_x$ Bi $_2$ Se $_3$，和Tl $_x$ Bi $_2$ Se $_3$。
Two-gap superconductivity in heavily n-doped graphene: ab initio Migdal-Eliashberg theory
石墨烯是从零维到三维材料的碳家族中唯一尚未观察到超导性的成员。目前尚不清楚对超导石墨烯的探索是否受到技术挑战的阻碍，或者是二维序参量的波动。在这一领域，从头计算是有用的，以指导实验工作，缩小搜索空间。本着这种精神，我们从第一原理研究了使用由Wannier-Fourier插值提供动力的完全各向异性Migdal-Eliashberg理论在掺杂石墨烯中诱导超导性的可能性。为了解决最好的情况下，我们考虑在高载流子密度的电子和空穴掺杂，以便对准费米能级的范霍夫奇点。在这些条件下，我们发现超导间隙的$s$波对称性，与轻微的各向异性引起的三角形翘曲，并在$n$掺杂的石墨烯的情况下，一个意想不到的两个间隙结构联想到MgB $_2$。我们的Migdal-Eliashberg计算表明，对于载流子密度超过$10^{15}$ cm $^{-2}$的$n$掺杂的石墨烯，在低温下观察到超导性应该是可能的。
Spontaneous rotational-symmetry breaking in the superconducting state of doped $\mathrm{Bi}_2\mathrm{Se}_3$ has attracted significant attention as an indicator for topological superconductivity. In this paper, high-resolution calorimetry of the single-crystal $\mathrm{Sr}_{0.1}\mathrm{Bi}_2\mathrm{Se}_3$ provides unequivocal evidence of a two-fold rotational symmetry in the superconducting gap by a \emph{bulk thermodynamic} probe, a fingerprint of nematic superconductivity. The extremely small specific heat anomaly resolved with our high-sensitivity technique is consistent with the material's …
Here we report the effect of structural and superconductivity properties on Ru doped CuIr2Te4 telluride chalcogenide. XRD results suggest that the CuIr2-xRuxTe4 maintain the disordered trigonal structure with space group P3m1 (No. 164) for x less than 0.3. The lattice constants, a and c, both decrease with increasing Ru content. Temperature-dependent resistivity, magnetic susceptibility and specific-heat measurements are performed to characterize the superconducting properties systematically. Our results suggest that the optimal doping level for superconductivity in CuIr2-xRuxTe4 is x = 0.05, …
The crystal structure, magnetic, electronic, and thermal properties of Mn-doped SrFe2As2 crystals have been systematically investigated. A miscibility gap is found in the system from x = 0.4362(4) to x = 0.9612(9). For x < 0.2055(2), the single crystals holding tetragonal structure (space group I4/mmm (no. 139)) have a continuously enlarged lattice parameter c, followed by a phase separation with crystals holding both tetragonal and trigonal structures up to x = 0.4362(4). Beyond the miscibility gap, the crystals with x > 0.9612(9) hold the trigonal structure (space group P-3m1 (no. 164)). Mor…
Nematic superconductivity is a novel class of superconductivity characterized by spontaneous rotational-symmetry breaking in the superconducting gap amplitude and/or Cooper-pair spins with respect to the underlying lattice symmetry. Doped Bi2Se3 superconductors, such as CuxBi2Se3, SrxBi2Se3, and NbxBi2Se3, are considered as candidates for nematic superconductors, in addition to the anticipated topological superconductivity. Recently, various bulk probes, such as nuclear magnetic resonance, specific heat, magnetotransport, magnetic torque, and magnetization, have consistently revealed two-fold …
We investigate the nature of the time-reversal breaking pairing state in the hole-doped monolayer MoS$_{2}$ on the basis of the realistic three-orbital attractive Hubbard-like model with the atomic spin-orbit coupling. Due to the multi-band features arising from the Mo $d$ orbitals in the noncentrosymmetric crystal structure, the Lifshitz transition takes place upon hole doping. Across the Lifshitz transition point, the sign of the relative phase between the Cooper-pair components drastically changes, leading to the emergence of the time-reversal breaking phase with complex gap functions. It i…
Local breaking of four-fold rotational symmetry by short-range magnetic order in heavily overdoped Ba(Fe$_{1-x}$Cu$_{x}$)$_{2}$As$_{2}$
研究了Cu掺杂Ba（Fe $_{1-x}$ Cu $_x$）$_2$ As $_2$的输运、磁化率和弹性中子散射。在重Cu掺杂区，BaFe $_2$ As $_2$的长程条纹型反铁磁有序被抑制，Ba（Fe $_{1-x}$ Cu $_x$）$_2$ As $_2$（0.145 $\leq x \leq$ 0.553）样品的磁化率表现出类似自旋玻璃的行为，电输运表现出类似绝缘的温度依赖性.利用弹性中子散射，我们发现条纹型短程磁序的自旋玻璃区确定的磁化率测量。在Ba（Fe $_{1-x}$ Cu $_x$）$_2$ As $_2$中，短程磁有序在大的掺杂范围内的持久性可能来自于有利于磁有序的Fe和Cu的局部排列，其中Cu充当空位缓解磁挫挫和简并。这些结果表明，局部破缺的四重旋转对称性，表明条纹型磁性是普遍存在的铁磷属元素。
Quantum Geometry and Pair Breaking in Intra- and Intervalley Superconductivity of Rhombohedral Graphene
Theoretical Division, Los Alamos National Lab（洛斯阿拉莫斯国家实验室理论部）；Department of Physics and Astronomy, University of Tennessee, Knoxville, Tennessee 37996, USA（田纳西大学诺克斯维尔分校物理与天文系）；Min H. Kao Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, Tennessee 37996, USA（田纳西大学诺克斯维尔分校明浩高电气与计算机科学系）；Theoretical Division, T-4, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA（洛斯阿拉莫斯国家实验室T-4理论部）；Center for Integrated Nanotechnologies (CINT), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA（洛斯阿拉莫斯国家实验室集成纳米技术中心）
By measuring the polarization changes in THz, infrared, and visible radiation over an extended energy range (3-2330 meV), we observe symmetry-breaking in cuprate high temperature superconductors over wide energy, doping, and temperature ranges. We measure the polarization rotation and ellipticity of transmitted radiation though thin films as the sample is rotated. We observe a two-fold rotational symmetry in the Faraday angle, which is associated with linear dichroism (LD) and occurs when electromagnetic radiation polarized along one direction is absorbed more strongly than radiation polarized…
Odd-parity superconductors with two-component order parameters: nematic and chiral, full gap and Majorana node
最近的实验表明，掺杂拓扑绝缘体Cu $_x$ Bi $_2$ Se $_3$中的超导性具有奇宇称对对称性和旋转对称性破缺，基于这一实验，我们研究了三角晶系和六方晶系中具有双组分序参量的奇宇称超导体.在强自旋-轨道相互作用的存在下，我们发现了两个可能的超导相低于$T_c$，一个时间反演破缺（即，手性）相和各向异性（即，相位，并从动量空间中的能隙函数确定它们的相对能量。手征超导体通常具有完整的准粒子带隙，而具有三维（3D）费米表面的手征超导体具有提升自旋简并的点节点，导致体块中的巡回马约拉纳费米子和表面上的拓扑马约拉纳弧。
Probing bulk superconductivity in centrosymmetric Te-doped PtBi$_2$ single crystals
Leibniz Institute for Solid State and Materials Research（莱布尼茨固体和材料研究所）；Max Planck Institute for Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）；Centro Atómico Bariloche, CNEA-CONICET（巴里洛切原子中心，CNEA-CONICET）；B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine（乌克兰国家科学院B.维尔金低温物理与工程研究所）；Kyiv Academic University（基辅学术大学）
Deviating band symmetries and many-body interactions in a model hole doped iron pnictide superconductor
本文用角分辨光电子能谱研究了最佳掺杂的铁磷属元素化物超导体Ba $_{0.6}$ K $_{0.4}$ Fe $_2$ As $_2$（T $_c$ = 37 K）的低能能带结构.偏振对比测量被用来识别和跟踪所有三个低能量的类空穴带预测局域密度近似（LDA）计算。光发射的电子揭示了不一致的LDA预测的对称性沿$Γ$ -X高对称动量轴，由于电子动力学的意外强大的旋转各向异性。我们评估的多体效应，如莫特-哈伯德相互作用，可能是异常的基础，并讨论如何观察到的LDA能带结构的偏差影响铁磷属元素化物库珀配对的空穴掺杂制度的能量。
We investigate the superconducting properties and possible nematic superconductivity of self-doped BiCh2-based (Ch: S, Se) superconductor CeOBiS1.7Se0.3 through the measurements of in-plane anisotropy of magnetoresistance. Single crystals of CeOBiS1.7Se0.3 were grown using a flux method. Single-crystal structural analysis revealed that the crystal structure at room temperature is tetragonal (P4/nmm). Bulk superconductivity with a transition temperature of 3.3 K was observed through electrical resistivity and magnetization measurements. Investigation of anisotropy of upper critical field sugges…
If the topological insulator Bi$_{2}$Se$_{3}$ is doped with electrons, superconductivity with $T_{\rm c}\approx3-4\:{\rm K}$ emerges for a low density of carriers ($n\approx10^{20}{\rm cm}^{-3}$) and with a small ratio of the superconducting coherence length and Fermi wave length: $ξ/λ_{F}\approx2\cdots4$. These values make fluctuations of the superconducting order parameter increasingly important, to the extend that the $T_{c}$-value is surprisingly large. Strong spin-orbit interaction led to the proposal of an odd-parity pairing state. This begs the question of the nature of the transition i…
Topological superconductors are exotic gapped phases of matter hosting Majorana mid-gap states on their boundary. In conventional topological superconductors, Majorana in-gap states appear in the form of either localized zero-dimensional modes or propagating spin-1/2 fermions with a quasi-relativistic dispersion relation. Here we show that unconventional propagating Majorana states can emerge on the surface of three-dimensional topological superconductors protected by rotational symmetry. The unconventional Majorana surface states fall into three different categories: a spin-$S$ Majorana fermi…
Electronic nematicity, a consequence of rotational symmetry breaking, is an emergent phenomenon in various new materials. In order to fully utilize the functions of these materials, ability of tuning them through a knob, the nematic director, is desired. Here we report a successful manipulation of the nematic director, the vector order-parameter (d-vector), in the spin-triplet superconducting state of CuxBi2Se3 by magnetic fields. At H = 0.5 T, the ac susceptibility related to the upper critical field shows a two-fold symmetry in the basal plane. At H = 1.5 T, however, the susceptibility shows…
Thermodynamic evidence for nematic superconductivity in Cu$_x$Bi$_2$Se$_3$
非常规超导的特征在于宏观超导波函数的自发对称性破缺，以及规范对称性破缺，例如相对于基本晶格对称性的旋转对称性破缺。特别是，超导性与自发的旋转对称性破缺的波函数振幅，从而在体的性质，尚未报告以前，是有趣的，可以被称为“双”超导性的类比，以双液晶相。在这里，基于比热测量的单晶Cu $_x$ Bi $_2$ Se $_3$精确的磁场方向控制下，我们报告的热力学证据的超导性，即，明确的双重对称行为的三角晶格。结果表明，实现了一个“奇宇称”的状态，只有宏观量子凝聚体和不同的液晶中的双态。结果也证实了Cu $_x$ Bi $_2$ Se $_3$的拓扑非平凡超导电性。
We present a novel experimental evidence for the odd-parity nematic superconductivity in high-quality single crystals of doped topological insulator Sr$_x$Bi$_2$Se$_3$. The X-ray diffraction shows that the grown single crystals are either weakly stretched or compressed uniaxially in the basal plane along one of the crystal axis. We show that in the superconducting state, the upper critical magnetic field $H_{c2}$ has a two-fold rotational symmetry and depends on the sign of the strain: in the stretched samples, the maximum of $H_{c2}$ is achieved when the in-plane magnetic field is transverse …
Recent experiments show the spontaneous breaking of rotational symmetry in the superconducting topological insulators M$_{x}$Bi$_{2}$Se$_{3}$ (M represents Cu, Sr, or Nd), suggesting that the pairing belongs to a two-dimensional representation of the $D_{3d}$ symmetry group of the crystal. Motivated by these progresses, we construct an exhaustive list of possible two-component pairings of the M$_{x}$Bi$_{2}$Se$_{3}$ superconductors, both for the odd-parity $E_{u}$ representation and for the even-parity $E_{g}$ representation. Starting from a tight-binding model for the normal phase of Bi$_{2}$…
The doped topological insulator $A_{x}\mathrm{Bi_{2}Se_{3}}$, with $A=\{\mathrm{Cu},\mathrm{Sr},\mathrm{Nb}\}$, becomes a nematic superconductor below $T_{c}\sim3-4\,\mathrm{K}$. The associated electronic nematic director is described by an angle $α$ and is experimentally manifested in the elliptical shape of the in-plane critical magnetic field $H_{c2}$. Because of the threefold rotational symmetry of the lattice, $α$ is expected to align with one of three high-symmetry directions corresponding to the in-plane nearest-neighbor bonds, consistent with a $Z_{3}$-Potts nematic transition. Here, w…
Overshadowing the superconducting dome in hole-doped cuprates, the pseudogap state is still one of the mysteries that no consensus can be achieved. It has been suggested that the rotational symmetry is broken in this state and may result in a nematic phase transition, whose temperature seems to coincide with the onset temperature of the pseudogap state $T^*$ around optimal doping level, raising the question whether the pseudogap results from the establishment of the nematic order. Here we report results of resistivity measurements under uniaxial pressure on several hole-doped cuprates, where t…
Possible emergence of nematic superconductivity that breaks its underlying lattice symmetry in doped topological insulator Bi$_2$Se$_3$,establishes this system as a unique candidate of topological superconductors. Exclusion of possible extrinsic causes for the two-fold superconductivity is essential to clarify its topological nature. Here, we present electrical transport on Sr$_x$Bi$_2$Se$_3$ superconductors with rectangular and circular geometries. The occurrence of the two-fold symmetric in-plane upper critical field $H_{c2}$ is found to be weakly geometry dependent. However, the anisotropic…
High temperature superconductivity emerges in the vicinity of competing strongly correlated phases. In the iron-based superconductor $Ba(Fe_{1-x}Co_{x})_{2}As_{2}$, the superconducting state shares the composition-temperature phase diagram with an electronic nematic phase and an antiferromagnetic phase that break the crystalline rotational symmetry. Symmetry considerations suggest that anisotropic strain can enhance these competing phases and thus suppress the superconductivity. Here we study the effect of anisotropic strain on the superconducting transition in single crystals of $Ba(Fe_{1-x}C…
Unconventional superconductivity often intertwines with various forms of order, such as the "nematic" order which breaks the rotational symmetry of the lattice. Investigation of these ordered phases sheds crucial light on the superconductivity itself. Here we report a low-temperature scanning tunneling microscopy (STM) study on RbFe2As2, a heavily hole-doped Fe-based superconductor (FeSC). We observe significant symmetry breaking in its electronic structure and magnetic vortex which differentiates the (π, π) and (π, -π) directions of the unfolded Brillouin zone (BZ). It is thus a novel nematic…
Electronic nematicity, a correlated state that spontaneously breaks rotational symmetry, is observed in several layered quantum materials. In contrast to their liquid-crystal counterparts, the nematic director cannot usually point in an arbitrary direction (XY nematics), but is locked by the crystal to discrete directions (Ising nematics),resulting in strongly anisotropic fluctuations above the transition. Here, we report on the observation of nearly isotropic XY-nematic fluctuations, via elastoresistance measurements, in hole-doped Ba$_{1-x}$Rb$_{x}$Fe$_{2}$As$_{2}$ iron-based superconductors…
Experiments carried over the last years on the underdoped cuprates have revealed a variety of symmetry-breaking phenomena in the pseudogap state. Charge-density waves, breaking of $C_{4}$ rotational symmetry as well as time-reversal symmetry breaking have all been observed in several cuprate families. In this regard, theoretical models where multiple non-superconducting orders emerge are of particular interest. We consider the recently introduced (Phys. Rev. B 93, 085131 (2016)) spin-fermion model with overlapping 'hot spots' on the Fermi surface. Focusing on the particle-hole instabilities we…
