Using finite-temperature determinantal quantum Monte Carlo calculations, we re-examine the pairing susceptibilities in the Hubbard model on the honeycomb lattice, focusing on doping levels onto and away from the van Hove singularity (VHS) filling. For this purpose, electronic densities of $0.75$ (at the hole-doping VHS) and $0.4$ (well below the VHS) are considered in detail, where due to a severe sign problem at strong coupling strengths, we focus on the weak interaction region of the Hubbard model Hamiltonian. From analyzing the temperature dependence of pairing susceptibilities in various symmetry channels, we find the singlet $d$+$id$-wave to be the dominant pairing channel both at and away from the VHS filling. We furthermore investigate the electronic susceptibility to a specific chiral spin density wave (SDW) order, which we find to be similarly relevant at the VHS, while it extenuates upon doping away from the VHS filling.
We report magnetometry data obtained on twin-free single crystals of Na3Co2SbO6, which is considered a candidate material for realizing the Kitaev honeycomb model for quantum spin liquids. Contrary to a common belief that such materials can be modeled with the symmetries of an ideal honeycomb lattice, our data reveal a pronounced two-fold symmetry and in-plane anisotropy of over 200%, despite the honeycomb layer's tiny orthorhombic distortion of less than 0.2%. We further use magnetic neutron diffraction to elucidate a rich variety of field-induced phases observed in the magnetometry. These ph…
We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half-filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional Renormalization Group scheme which allows for highly resolved calculations of wavevector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure $n$-th nearest neighbor repulsiv…
Charge instabilities and topological phases in the extended Hubbard model on the honeycomb lattice with enlarged unit cell
我们研究了蜂窝晶格中无自旋费米子系统的自发对称性破缺，特别强调了增大的单胞对时间反演对称性破缺相位的作用。我们使用一个紧束缚模型与最近邻跳跃t和Hubbard相互作用V1和V2，并提取作为电子密度和相互作用的函数在平均场变分方法的相图。该分析完成了以前在Phys. Rev. Lett. 107，106402（2011），其中在不存在电荷重叠的情况下，发现具有非平凡拓扑性质的相仅具有最近邻相互作用V1。我们看到，拓扑相位抑制金属电荷密度波动的存在。添加次近邻相互作用V2恢复拓扑非平凡相位。
The impact of local and nonlocal density-density interactions on the electronic instabilities in the honeycomb lattice is widely investigated. Some early studies proposed the emergence of interaction-induced topologically nontrivial phases, but recently, it was denied in several works including renormalization group calculations with refined momentum resolution. We use the truncated unity functional renormalization group to study the many-body instabilities of electrons on the half-filled honeycomb lattice, focusing on the effect of the exchange interaction. We show that varying the next-neare…
Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physi…
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behaviour in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group…
The search for topological superconductors is one of the most pressing and challenging questions in condensed matter and material research. Despite some early suggestions that doping a topological insulator might be a successful recipe to find topological superconductors, until today there is no general understanding of the relationship of the topology of the superconductor and the topology of its underlying normal state system. One of the major obstacles is the strong effect of the Fermi surface and its subsequent pairing tendencies within the Hubbard model framework, usually preventing a det…
Na2Co2TeO6 is a proposed approximate Kitaev magnet, yet its actual magnetic interactions are elusive due to a lack of knowledge on the full excitation spectrum. Here, using inelastic neutron scattering and single crystals, we determine the system's temperature-dependent magnetic excitations over the entire Brillouin zone. Without committing to specific models, we unveil a distinct signature of the third-nearest-neighbor coupling in the spin waves, which signifies the associated distance as an emerging "soft link" in the ordered state. The presence of at least six non-overlapping spin-wave bran…
Proposals for superconductivity emerging from correlated electrons in the doped Hubbard model on the honeycomb lattice range from chiral $d+id$ singlet to $p+ip$ triplet pairing, depending on the considered range of doping and interaction strength, as well as the approach used to analyze the pairing instabilities. Here, we consider these scenarios using large-scale dynamic cluster approximation (DCA) calculations to examine the evolution in the leading pairing symmetry from weak to intermediate coupling strength. These calculations focus on doping levels around the van Hove singularity (VHS) a…
We investigate the doping effects of magnetic and nonmagnetic impurities injected to the honeycomb iridate sample of Na2IrO3 . Both the doping result in changing the ordering temperature as well as the Curie-Weiss temperature of the parent sample as a consequence of enhancement of the lattice frustration, screening of the Ir atoms and spin-orbit effects that reflects in the susceptibility and specific heat measurements. Our findings are corroborated by a detailed comparative study of various magnetic and nonmagnetic impurity atoms that have notable effects on different electronic properties of…
Topological spin textures, such as a skyrmion crystal, are a source of unusual physical phenomena owing to the interplay between magnetism and topology. Since physical phenomena depend on the topological property and the symmetry of underlying spin structures, the search for new topological spin textures and emergent phenomena is one of the challenges in condensed matter physics. In this letter, we theoretically explore new topological spin textures arising from the synergy between spin, charge, and sublattice degrees of freedom in an itinerant magnet. By performing simulated annealing for an …
Geometric Approach to the High-Throughput Identification of Honeycomb Materials
Stewart Blusson Quantum Matter Institute, University of British Columbia（不列颠哥伦比亚大学斯特瓦特·布拉斯量子物质研究所）；Department of Physics & Astronomy, University of British Columbia（不列颠哥伦比亚大学物理与天文系）；Canadian Institute for Advanced Research (CIFAR)（加拿大高级研究院）
Fermions hopping on a hexagonal lattice represent one of the most active research field in condensed matter since the discovery of graphene in 2004 and its numerous applications. Another exciting aspect of the interplay between geometry and quantum mechanical effects is given by the Haldane model (F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988)) where spinless fermions experiencing a certain flux pattern on the honeycomb lattice leads to the stabilization of a topological phase of matter, distinct from a Mott insulator and dubbed Chern insulator nowadays. In this context, it is crucial to u…
We study the many-body instabilities of correlated electrons on the half-filled honeycomb lattice with enhanced exchange coupling. The system is described by an extended Hubbard model including the next-nearest-neighbor Coulomb repulsion ($V_2$) and the nearest-neighbor exchange interaction ($J$). We use the truncated unity functional renormalization group approach to determine a schematic ground-state phase diagram with higher resolution in the parameter space of $V_2$ and $J$. In the absence of the on-site repulsion and presence of sizable next-nearest-neighbor repulsion and enhanced nearest…
We propose an experimental setup using ultracold atoms to implement a bilayer honeycomb lattice with Bernal stacking. In presence of a potential bias between the layers and at low densities, Fermions placed in this lattice form an annular Fermi sea. The presence of two Fermi surfaces leads to interesting patterns in Friedel oscillations and RKKY interactions in presence of impurities. Furthermore, a repulsive fermion-fermion interaction leads to a Stoner instability towards an incommensurate spin-density-wave order with a wave vector equal to the thickness of the Fermi sea. The instability occ…
Recent advances in ultracold atoms in optical lattices and developments in surface science have allowed for the creation of artificial lattices as well as the control of many-body interactions. Such systems provide new settings to investigate interaction-driven instabilities and non-trivial topology. In this paper, we explore the interplay between molecular electric dipoles on a two-dimensional triangular lattice with fermions hopping on the dual decorated honeycomb lattice which hosts Dirac and flat band states. We show that short-range dipole-dipole interaction can lead to ordering into vari…
We study the quantum many-body ground states of electrons on the half-filled honeycomb lattice with short- and long-ranged density-density interactions as a model for graphene. To this end, we employ the recently developed truncated-unity functional renormalization group (TU-fRG) approach which allows for a high resolution of the interaction vertex' wavevector dependence. We connect to previous lattice quantum Monte Carlo (QMC) results which predict a stabilization of the semimetallic phase for realistic \emph{ab initio} interaction parameters and confirm that the application of a finite biaxi…
We study the spin-one Kitaev model on the honeycomb lattice in the presence of single-ion anisotropies. We consider two types of single ion anisotropies: A $D_{111}$ anisotropy which preserves the symmetry between $X$, $Y$, and $Z$ bonds but violates flux conservation and a $D_{100}$ anisotropy that breaks the symmetry between $X$, $Y$, and $Z$ bonds but preserves flux conservation. We use series expansion methods, degenerate perturbation theory, and exact diagonalization to study these systems. Large positive $D_{111}$ anisotropy leads to a simple product ground state with conventional magnon…
Magnetoelastic honeycomb fragmentation in VI$_{3}$
University of Edinburgh（爱丁堡大学）；NIST Center for Neutron Research（美国国家标准与技术研究院中子研究中心）；University of Maryland, College Park（马里兰大学帕克分校）；ISIS Facility, Rutherford Appleton Laboratory（卢瑟福·阿普尔顿实验室 ISIS 设施）；European Synchrotron Radiation Facility（欧洲同步辐射装置）
We expand the concept of frustration in Mott insulators and quantum spin liquids to metals with flat bands. We show that when inter-orbital hopping $t_2$ dominates over intra-orbital hopping $t_1$, in a multiband system with strong spin-orbit coupling $λ$, electronic states with a narrow bandwidth $W\sim t_2^2/λ$ are formed compared to a bandwidth of order $t_1$ for intra-orbital hopping. We demonstrate the evolution of the electronic structure, Berry phase distributions for time-reversal and inversion breaking cases, and their imprint on the optical absorption, in a tight binding model of $d$…
We explore superconductivity in strongly interacting electrons on a decorated honeycomb lattice (DHL). An easy-plane ferromagnetic interaction arises from spin-orbit coupling in the Mott insulating phase, which favors a triplet resonance valence bond spin liquid state. Hole doping leads to partial occupation of a flat band and to triplet superconductivity. The order parameter is highly sensitive to the doping level and the interaction parameters, with $p+ip$, $f$ and $p+f$ superconductivity found, as the flat band leads to instabilities in multiple channels. Typically, first order transitions …
Plasmon excitations in half-filled graphene: A Comparative study between Quantum Monte Carlo and Random Phase Approximation
Institut für Theoretische Physik und Astrophysik, Universität Würzburg（维尔茨堡大学理论与天体物理研究所）；Department of Physics, Faculty of Science, Mahidol University（马希多尔大学理学院物理系）
Topologically ordered states of matter are generically characterized by excitations with quantum number fractionalization. A prime example is the spin liquid realized in Kitaev's honeycomb-lattice compass model where spin-flip excitations fractionalize into Majorana fermions and Ising gauge fluxes. While numerous compounds have been proposed to be proximate to such a spin-liquid phase, clear-cut evidence for fractionalized excitations is lacking. Here we employ microwave absorption measurements to study the low-energy excitations in $α$-RuCl$_3$ over a wide range of frequencies, magnetic field…
Layered quasi two dimensional systems have garnered huge interest both in the advancement of technology and in understanding emergent physics such as unconventional superconductivity, topological phases. In particular, the study of topological properties in some bilayer systems like transition metal chalcogenides and iridates has been the point of attraction due to comparatively strong spin orbit coupling of transition metal ions. In this paper, we analyze the topological phases induced by the interplay of electron correlation and spin orbit coupling in different stacking orders of bilayer hon…
Starting from a realistic extended Hubbard model for a $p_{x,y}$-orbital tight-binding model on the Honeycomb lattice, we perform a thorough investigation on the possible electron instabilities in the MA-TBG near the van Hove (VH) dopings. Here we focus on the interplay between the approximate SU(2)$\times$SU(2) symmetry and the $D_3$ symmetry, which leads to intriguing quantum states relevant to recent experiments, as revealed by our systematic RPA based calculations followed by a succeeding mean-field energy minimization for the ground state energy. At the SU(2)$\times$SU(2) symmetric point,…
We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal (DSM) and a symmetry-preserving band insulator (BI). The electronic dispersion at this critical point is anisotropic ($E_{\mathbf k}=\pm \sqrt{v^2 k^2_x + b^2 k^{2n}_y}$ with $n=2$), which results in unconventional scaling of physical observables. Due to the vanishing density of states ($\varrho(E) \sim |E|^{1/n}$), this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions t…
Relativistic Mott transition and high-order van Hove singularity in twisted double bilayer WSe${}_2$: mean-field and functional renormalization group study
