13 pages, 7 figures and 1 table; Extensive revision and expansion, including a new section on classifying the quasiparticles and a new section on an alternative Chern--Simons Lagrangian
A Chern--Simons theory for the doped spin-1/2 kagomé system is constructed, from which it is shown that the system is an exotic superconductor that breaks time-reversal symmetry. It is also shown that the system carries minimal vortices of flux $hc/4e$ (as opposed to the usual $hc/2e$ in conventional superconductors) and contains fractional quasiparticles (including fermionic quasiparticles with \emph{semionic} mutual statistics and spin-1/2 quasiparticles with \emph{bosonic} self-statistics) in addition to the usual spin-1/2 fermionic Bougoliubov quasiparticle. Two Chern--Simons theories--one with an auxiliary gauge field kept and one with the auxiliary field and a redundant matter field directly eliminated--are presented and shown to be consistent with each other.
Spin-orbit coupling induced semi-metallic state in the 1/3 hole doped hyper-kagome Na3Ir3O8
以单晶形式合成了具有B位有序尖晶石结构的复合氧化铱Na 3 Ir 3 O 8，其中确定了在自旋液体候选物Na 4 Ir 3 O 8中观察到的Ir原子的手性超kagome晶格。Ir的平均价态为4.33+，因此，Na 3 Ir 3 O 8可以被看作是具有Ir 4+的超可戈姆自旋液体的掺杂类似物。输运测量表明，Na_3 Ir_3 O_8实际上是一种半金属。电子结构计算表明，Ir的强自旋-轨道耦合使其从带绝缘态转变为半金属态，这可能是超kagome晶格中的奇异拓扑效应.
We address the problem of a lightly doped spin-liquid through a large-scale density-matrix renormalization group (DMRG) study of the $t$-$J$ model on a Kagome lattice with a small but non-zero concentration, $δ$, of doped holes. It is now widely accepted that the undoped ($δ=0$) spin 1/2 Heisenberg antiferromagnet has a spin-liquid groundstate. Theoretical arguments have been presented that light doping of such a spin-liquid could give rise to a high temperature superconductor or an exotic topological Fermi liquid metal (FL$^\ast$). Instead, we infer that the doped holes form an insulating cha…
Neutron scattering measurements have been performed on deuterated powder samples of claringbullite and Zn-doped claringbullite (Zn$_x$Cu$_{4-x}$(OD)$_{6}$FCl). At low temperatures, claringbullite Cu$_4$(OD)$_{6}$FCl forms a distorted pyrochlore lattice with long-range magnetic order and spin-wave-like magnetic excitations. Partial Zn doping leads to the nominal ZnCu$_3$(OD)$_{6}$FCl compound, a geometrically frustrated spin-1/2 kagome antiferromagnet that shows no transition to magnetic order down to 1.5 K. The magnetic excitations form a gapless continuum, a signature of fractional excitation…
Exploration of exotic transport behavior for quantum materials is of great interest and importance for revealing exotic orders to bring new physics. In this Letter, we report the observation of exotic prominent planar Hall effect (PHE) and planar anisotropic magnetoresistivity (PAMR) in strange kagome metal KV$_3$Sb$_5$. The PHE and PAMR, which are driven by an in-plane magnetic field and display sharp difference from other Hall effects driven by an out-of-plane magnetic field or magnetization, exhibit exotic higher-order oscillations in sharp contrast to those following empirical rule only al…
Whether the doped t-J model on the Kagome lattice supports exotic superconductivity has not been decisively answered. In this paper, we propose a new class of variational states for this model and perform large-scale variational Monte Carlo simulation on it. The proposed variational states are parameterized by the SU(2)-gauge-rotation angles, as the SU(2)-gauge structure hidden in the Gutzwiller-projected mean-field ansatz for the undoped model is broken upon doping. These variational doped states smoothly connect to the previously studied U(1) $π$-flux or $0$-flux states, and energy minimizat…
We present a successful synthesis method of the series Ga$_{x}$Cu$_{4-x}$(OD)$_{6}$Cl$_{2}$ with substitutions up to $x=0.8$. The compound remains a frustrated kagome system with an insulating ground state similar to herbertsmithite for these substitutions, as the additional charge of Ga$^{3+}$ is most likely bound to additional OH$^{-}$ and Cl$^{-}$. Besides infrared measurements, we present magnetic and specific-heat data down to 2 K for selected samples with $0\leq x\leq0.8$. With increasing $x$ the long-range magnetic order is suppressed, similar to what was observed in the series Zn$_{x}$…
Impurity-doped Kagome Antiferromagnet: A Quantum Dimer Model Approach
在广义量子二聚体模型（QDM）的框架下，研究了非磁性杂质对可果美晶格上量子海森堡反铁磁体的掺杂.遵循Ralko等人的方法[Phys.Rev.Lett. 101，117204（2008）]，我们在Kagome晶格上引入QDM的（最小）扩展，以解释在有限磁场下自发产生S=1/2自旋子。调制的二聚体密度（在零或有限的磁场）和在附近的杂质的局部场诱导的磁化强度的计算使用Lanczos精确对角化技术的小集群（48和75网站）。的VBC是清楚地揭示从其钉扎杂质，而在二聚体液体中，杂质周围的结晶只涉及两个相邻的二聚体。我们还发现，次近邻铁磁耦合有利于VBC秩序。出乎意料的是，一个小尺寸的自旋杂质束缚态出现在二聚体液相的某些区域。相反，在VBC相的自旋离域在一个大的区域内的杂质，揭示了VBC限制势的弱点。最后，我们观察到，杂质浓度小至4%，大大提高二聚。这些结果与价键玻璃方案[R. R. P. Singh，Phys. Rev. Lett. 104，177203（2010）]，并概述了对解释该Herbertsmithite化合物的核磁共振谱的影响。
We review recent density-matrix renormalization group (DMRG) studies of lightly doped quantum spin liquids (QSLs) on the kagome lattice. While a number of distinct conducting phases, including high-temperature superconductivity, have been theoretically anticipated we find instead a tendency toward fractionalized insulating charge-density-wave (CDW) states. In agreement with earlier work (Jiang, Devereaux, and Kivelson, Phys. Rev. Lett. ${\bf 119}$, 067002 (2017)), results for the $t$-$J$ model reveal that starting from a fully gapped QSL, light doping leads to CDW long-range order with a patte…
Disorder-induced spin-cluster magnetism in a doped kagome spin liquid candidate
Georgia Institute of Technology（佐治亚理工学院）；Naval Research Laboratory（海军研究实验室）；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）；University of Virginia（弗吉尼亚大学）；Songshan Lake Materials Laboratory（松山湖材料实验室）；Massachusetts Institute of Technology（麻省理工学院）
Observation of ubiquitous charge correlations and hidden quantum critical point in hole-doped kagome superconductors
Brown University（布朗大学）；Università di Parma（帕尔马大学）；Brown Center for Theoretical Physics and Innovation, BCTPI, Brown University（布朗大学理论物理与创新中心）；Università di Bologna（博洛尼亚大学）；Università di Modena e Reggio Emilia（摩德纳和雷焦艾米利亚大学）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）；Université Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Laboratoire National des Champs Magnétiques Intenses（强磁场国家实验室）；CNRS（法国国家科学研究中心）；Université de Toulouse（图卢兹大学）；INSA Toulouse（图卢兹国立应用科学学院）；European Magnetic Field Laboratory（欧洲强磁场实验室）
Herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$, is a two dimensional kagomé lattice realization of a spin liquid, with evidence for fractionalized excitations and a gapped ground state. Such a quantum spin liquid has been proposed to underlie high temperature superconductivity and is predicted to produce a wealth of new states, including a Dirac metal at $1/3$rd electron doping. Here we report the topochemical synthesis of electron-doped ZnLi$_x$Cu$_3$(OH)$_6$Cl$_2$ from $x$ = 0 to $x$ = 1.8 ($3/5$th per Cu$^{2+}$). Contrary to expectations, no metallicity or superconductivity is induced. Instead, we…
Direct Evidence of Unconventional Superconductivity in Doped Kagome system RV$_3$Sb$_5$
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；University of California Santa Barbara（加州大学圣塔芭芭拉分校）
Fermi-liquid-like phase driven by next-nearest-neighbor couplings in a lightly doped kagome-lattice $t$-$J$ model
School of Physics, Beihang University（北京航空航天大学物理学院）；School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；Department of Physics and Astronomy, California State University Northridge（加州州立大学北岭分校物理与天文学系）；School of Physical Sciences, Great Bay University（大湾区大学物理科学学院）；Great Bay Institute for Advanced Study（大湾区高等研究院）
Electronic states with non-trivial topology host a number of novel phenomena with potential for revolutionizing information technology. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. We introduce a new strategy for realizing these effects, namely by hole and electron doping kagome lattice Mott insulators through, for instance, chemical substitution. As an example, we apply this new approach …
The flat band has attracted a lot of attention because it gives rise to many exotic phases, as recently demonstrated in magic angle twisted bilayer graphene. Here, based on first-principles calculations, we identify a metal-insulator transition in boron triangular Kagome lattice with a spin-polarized flat band at 2/3-filling. This phase transition is accompanied by the formation of a Wigner crystal, which is driven by Fermi surface nesting effect and thereby strong electron-phonon interactions, keeping ferromagnetism. Our calculation results suggest that boron triangular Kagome lattices with p…
Herbertsmithite and Zn-doped barlowite are two compounds for experimental realization of twodimensional gapped kagome spin liquid. Theoretically, it has been proposed that charge doping a quantum spin liquid gives rise to exotic metallic states, such as high-temperature superconductivity. However, one recent experiment about herbertsmithite with successful Li-doping shows surprisingly the insulating state even under the heavy doped scenario, which can hardly be explained by many-body physics. Using first-principles calculation, we performed a comprehensive study about the Li intercalated dopin…
Exotic charge density waves and superconductivity on the Kagome Lattice
CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；Institut für Theoretische Physik und Astrophysik, Universität Würzburg（维尔茨堡大学理论与天体物理研究所）；Institute for Theoretical Physics, ETH Zürich（苏黎世联邦理工学院理论物理研究所）；New Cornerstone Science Laboratory（新基石科学实验室）；Department of Physics, Boston College（波士顿学院物理系）
The spin-$\frac{1}{2}$ kagome antiferromagnet is an archetypal frustrated system predicted to host a variety of exotic magnetic states. We show using neutron scattering measurements that deuterated vesignieite BaCu$_{3}$V$_{2}$O$_{8}$(OD)$_{2}$, a fully stoichiometric $S=1/2$ kagome magnet with $<$1% lattice distortion, orders magnetically at $T_{\mathrm{N}}=9$K into a multi-k coplanar variant of the predicted triple-k octahedral structure. We find this structure is stabilized by a dominant antiferromagnetic 3$^{\mathrm{rd}}$-neighbor exchange $J_3$ with minor 1$^{\mathrm{st}}$- or 2$^{\mathrm…
Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge order, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to non-kagome surface layers. Here we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifes a 2x2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin-mapping across steps of unit-cell-height demonstrates that this charge order emerges from spin-polarized electrons with an antiferr…
Exploration of rare-earth (RE)-based Kagome lattice magnets with spin-orbital entangled jeff=1/2 moments will provide new platform for investigating the exotic magnetic phases. Here, we report a new family of RE3BWO9 (RE=Pr,Nd,Gd-Ho) boratotungstates with magnetic RE3+ ions arranged on Kagome lattice, and perform its structure and magnetic characterizations. This serial compounds crystallize in hexagonal coordinated structure with space group P63 (No.173), where magnetic RE3+ ions have distorted Kagomé lattice connections within the ab plane and stacked in a AB-type fashion along c axis. The i…
Unconventional ferromagnetism and superconductivity in the imbalanced kagome-lattice Hubbard model are investigated by the mean-field theory and determinant quantum Monte Carlo method. Due to the asymmetric band structure of kagome lattice, the spin-$z$ ferromagnetic order intrinsically exists in the system, which is first enhanced by the interaction, and then continuously destructed after reaching a maximum at a moderate interaction strength. In contrast, the $xy$-plane ferromagnetism develops only above a critical interaction, which is estimated to be $U_c/t=3.65 \pm 0.05$ by finite-size sca…
We present a microscopic study of a doped quantum spin liquid candidate, the hyperkagome Na$_3$Ir$_3$O$_8$ compound by using $^{23}$Na NMR. We determine the intrinsic behavior of the uniform \textbf{q} $ = 0$ susceptibility via shift measurements and the dynamical response by probing the spin-lattice relaxation rate. Throughout the studied temperature range, the susceptibility is consistent with a semimetal behavior, though with electronic bands substantially modified by correlations. Remarkably, the antiferromagnetic fluctuations present in the insulating parent compound Na$_4$Ir$_3$O$_8$ sur…
The kagome lattice is a two-dimensional network of corner-sharing triangles known as a platform for exotic quantum magnetic states. Theoretical work has predicted that the kagome lattice may also host Dirac electronic states that could lead to topological and Chern insulating phases, but these have evaded experimental detection to date. Here we study the d-electron kagome metal Fe$_3$Sn$_2$ designed to support bulk massive Dirac fermions in the presence of ferromagnetic order. We observe a temperature independent intrinsic anomalous Hall conductivity persisting above room temperature suggestiv…
Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition temperature TC up to 7K. Recently, certain kagome superconductors have been found to exhibit an exotic charge order, which intertwines with superconductivity and persists to a temperature being one order of magnitude higher than TC. In this work, we use scanning tunneling microscopy (STM) to study the charge order in kagome superconductor RbV3Sb5. We observe both a 2x2 chiral charge order and nematic surface superlattices (predominantly 1x4). We find that the 2x2 charge order exhibits…
Search for a new quantum state of matter emerging in a crystal is one of recent trends in condensed matter physics. For magnetic materials, geometrical frustration and high magnetic field are two key ingredients to realize it: a conventional magnetic order is possibly destroyed by competing interactions (frustration) and is replaced by an exotic state that is characterized in terms of quasiparticles, that are magnons, and the magnetic field can control the density and chemical potential of the magnons. Here we show that a synthetic copper mineral, Cd-kapellasite, comprising a kagome lattice ma…
We present the results of neutron diffraction studies on polycrystals of a metallic kagome lattice, Tb3Ru4Al12, reported recently to undergo reentrant magnetism, with the onset of long range antiferromagnetic order below (TN=) 22 K and spin-glass features below about 17 K. The present results reveal long-range antiferromagnetic order of an incommensurate type with the moments oriented along c-axis at all temperatures below TN. There are however notable changes in the T dependence of propagation vector along b-axis across 17 K. An observation of interest is that there is no decrease of intensit…
