In single sheets of graphene, vacancy-induced states have been shown to host an effective spin-1/2 hole that can be Kondo-screened at low temperatures. Here, we show how these vacancy-induced impurity states survive in twisted bilayer graphene (TBG), which thus provides a tunable system to probe the critical destruction of the Kondo effect in pseudogap hosts. Ab-initio calculations and atomic-scale modeling are used to determine the nature of the vacancy states in the vicinity of the magic angle in TBG, demonstrating that the vacancy can be treated as a quantum impurity. Utilizing this insight, we construct an Anderson impurity model with a TBG host that we solve using the numerical renormalization group combined with the kernel polynomial method. We determine the phase diagram of the model and show how there is a strict dichotomy between vacancies in the AA/BB versus AB/BA tunneling regions. In AB/BA vacancies, the Kondo temperature at the magic angle develops a broad distribution with a tail to vanishing temperatures due to multifractal wavefunctions at the magic angle. We argue that scanning tunneling microscopy in the vicinity of the vacancy can act as a probe of both the critical single-particle states and the underlying many-body ground state in magic-angle TBG.
We study a magnetic impurity intercalated in bilayer graphene. A representative configuration generates a hybridization function with strong dependence on the conduction-electron energy, including a full gap with one hard and one soft edge. Shifts of the chemical potential via gating or doping drive the system between non-Kondo (free-moment) and Kondo-screened phases, with strong variation of the Kondo scale. Quantum phase transitions near the soft edge are of Kosterlitz-Thouless type, while others are first order. Near the hard edge, a bound-state singlet appears inside the gap; although of s…
We study the local moment formation and the Kondo effect at single-atom vacancies in Graphene. We develop a model accounting for the vacancy reconstruction as well as non-planarity effects induced by strain and/or temperature. Thus, we find that the dangling $σ$ orbital localized at the vacancy is allowed to strongly hybridize with the $π$-band since the scattering with the vacancy turns the hybridization into singular function of the energy ($\sim [|ε| \ln^2 ε/D]^{-1}$, $D\sim$ the bandwidth). This leads to several new types of impurity phases, which control the magnitude of the vacancy magne…
Electron correlation effects caused by the topological zero mode of a hydrogenated graphene vacancy, $V_{111}$, with three adsorbed hydrogen atoms is discussed theoretically. A Kondo model is derived from the multi-reference representation of the density functional theory, where exchange scattering processes between the zero mode and low-energy modes in the Dirac cones are estimated. Even when the Dirac cone is slightly off from the charge neutral point, a finite on-site correlation energy, $U_0$, for the zero mode of an isolated $V_{111}$ allows the half-filling of the localized level giving …
We use quantum Monte Carlo method to study a magnetic impurity located next to a vacancy in bilayer graphene with Bernal stacking. Due to the broken symmetry between two sublattices in bilayer system, there exist two different types of vacancy induced localized state. We find that the magnetic property of the adatom located on the adjacent site of the vacancy depends on whether the vacancy belongs to A or B sublattice. In general, local moment is more strongly suppressed if the vacancy belongs to the sublattice A when $μ\sim 0$. We switch the values of the chemical potential and study the basi…
We perform a general group-theoretical study of the Kondo problem in monolayer and bilayer graphene around the charge neutrality point. Utilizing the group representation theory, we derive from symmetry considerations a family of the Kondo models for all symmetric placements with either 3- or 6-fold rotational axis of an impurity atom in an arbitrary orbital state. We find six possible classes of the partially anisotropic four-channel Kondo model. As the key result, we argue several possibilities to realize the regime of the dominant channel-symmetric two-channel Kondo effect, protected by the…
Bilayer Kondo systems present interesting models to illustrate the competition between the Kondo effect and intermoment exchange. Such bilayers can exhibit two sharply distinct Fermi liquid phases which are distinguished by whether or not the local moments participate in the Fermi sea. We study these phases and the evolution from one to the other upon changing Kondo coupling. We argue that an ordered state with spontaneous interlayer phase coherence generically intervenes between the two Fermi liquids. Such a condensate phase breaks a U(1) symmetry and is bounded by a finite-temperature Koster…
A bilayer system comprising a Kondo insulator coupled to a simple metal (KI-M) is considered. Employing the framework of dynamical mean field theory, the model system is shown to exhibit a surface of quantum critical points (QCPs), that separates a Kondo screened, Fermi liquid phase from a local moment, Mott insulating phase. The quantum critical nature of these Mott transitions is characterized by the vanishing of (a) the coherence scale on the Fermi liquid side, and (b) the Mott gap on the MI side. In contrast to the usual `large to small' Fermi surface (FS) QCPs in heavy fermion systems, th…
Strong electron correlations have long been recognized as driving the emergence of novel phases of matter. A well recognized example is high-temperature superconductivity which cannot be understood in terms of the standard weak-coupling theory. The exotic properties that accompany the formation of the two-channel Kondo effect including the emergence of an unconventional metallic state in the low-energy limit also originate from strong electron interactions. Despite its paradigmatic role for the formation of non-standard metal behavior, the stringent conditions required for its emergence have m…
The true topological nature of the Kondo insulator SmB$_6$ remains to be unveiled. Our previous tunneling study not only found evidence for the existence of surface Dirac fermions, but it also uncovered that they inherently interact with the spin excitons, collective excitations in the bulk. We have extended such a spectroscopic investigation into crystals containing a Sm deficiency. The bulk hybridization gap is found to be insensitive to the deficiency up to 1% studied here, but the surface states in Sm-deficient crystals exhibit quite different temperature evolutions from those in stoichiom…
We study single hole dynamics in the bilayer Heisenberg and Kondo Necklace models. Those models exhibit a magnetic order-disorder quantum phase transition as a function of the interlayer coupling J_perp. At strong coupling in the disordered phase, both models have a single-hole dispersion relation with band maximum at p = (π,π) and an effective mass at this p-point which scales as the hopping matrix element t. In the Kondo Necklace model, we show that the effective mass at p = (π,π) remains finite for all considered values of J_perp such that the strong coupling features of the dispersion rela…
The nature of superconductivity in heavy-fermion materials is a subject under intense debate, and controlling this many-body state is central for its eventual understanding. Here, we examine how proximity effects may change this phenomenon, by investigating the effects of an additional metallic layer on the top of a Kondo-lattice, and allowing for pairing in the former. We analyze a bilayer Kondo Lattice Model with an on-site Hubbard interaction, $-U$, on the additional layer, using a mean-field approach. For $U=0$, we notice a drastic change in the density-of-states due to multiple-orbital si…
Paramagnetic impurities in a quantum spin-liquid can result in Kondo effects with highly unusual properties. We have studied the effect of locally exchange-coupling a paramagnetic impurity with the spin-1/2 honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases respectively. The ground state in the strong coupl…
Low-temperature electronic conductance in nanocontacts, scanning tunneling microscopy (STM), and metal break junctions involving magnetic atoms or molecules is a growing area with important unsolved theoretical problems. While the detailed relationship between contact geometry and electronic structure requires a quantitative ab initio approach such as density functional theory (DFT), the Kondo many-body effects ensuing from the coupling of the impurity spin with metal electrons are most properly addressed by formulating a generalized Anderson impurity model to be solved with, for example, the …
The cooperative behavior of quantum impurities on 2D materials, such as graphene and bilayer graphene, is characterized by a non-trivial competition between screening (Kondo effect), and Ruderman-Kittel-Kasuya-Yosida (RKKY) magnetism. In addition, due to the small density of states at the Fermi level, impurities may not couple to the conduction electrons at all, behaving as free moments. Employing a recently developed {\em{exact}} numerical method to study multi-impurity lattice systems, we obtain non-perturbative results that dramatically depart from expectations based on the conventional RKK…
Emergence of a symmetry-broken Chern insulator near a moiré Kondo breakdown
Shanghai Jiao Tong University（上海交通大学）；Cornell University（康奈尔大学）；Kavli Institute at Cornell for Nanoscale Science（康奈尔纳米科学卡弗里研究所）；Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；National Institute for Materials Science（国立材料研究所）；Hefei National Laboratory（合肥国家实验室）；Max Planck Institute for the Structure and Dynamics of Matter（马克斯·普朗克物质结构动力学研究所）
We investigate Kondo physics in a host with a strongly diverging density of states. This study is motivated by a recent work on vacancies in the graphene honeycomb lattice, whose density of states is enhanced at low energies due to potential scattering. The generalized quantum impurity model describing the vacancy is shown to support a spin-1/2 (doublet) Kondo phase. The special role played by a diverging host density of states is examined in detail, with distinctive signatures associated with the powerlaw Kondo effect shown to appear in thermodynamic quantities and the scattering t matrix, wi…
We address the origin of the magnetic-field independent -|A| T^{1/2} term observed in the low-temperature resistivity of several As-based metallic systems of the PbFCl structure type. For the layered compound ZrAs_{1.58}Se_{0.39}, we show that vacancies in the square nets of As give rise to the low-temperature transport anomaly over a wide temperature regime of almost two decades in temperature. This low-temperature behavior is in line with the non-magnetic version of the two-channel Kondo effect, whose origin we ascribe to a dynamic Jahn-Teller effect operating at the vacancy-carrying As laye…
We consider a magnetic impurity in two different S=1/2 Heisenberg bilayer antiferromagnets at their respective critical inter-layer couplings separating N'eel and disordered ground states. We calculate the impurity susceptibility using a quantum Monte Carlo method. With intra-layer couplings in only one of the layers (Kondo lattice), we observe an anomalous Curie constant C*, as predicted on the basis of field-theoretical work [S. Sachdev et al., Science 286, 2479 (1999)]. The value C*=0.262 +/- 0.002 is larger than the normal Curie constant C=S(S+1)/3. Our low-temperature results for the symm…
Mott-Derived Local Moments and Kondo Hybridization in a d-electron Kagome lattice
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；University of Chinese Academy of Sciences（中国科学院大学）；State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University（清华大学物理系低维量子物理国家重点实验室）；National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理全国重点实验室及物理学院）；Technical Institute of Physics and Chemistry, Chinese Academy of Sciences（中国科学院化学物理研究所）
Motivated by experiments on the archetypal frustrated magnet SrCr$_{9p}$Ga$_{12-9p}$O$_{19}$ (SCGO), we study the classical Heisenberg model on the pyrochlore slab (Kagomé bilayer) lattice with site-dilution $x=1-p$. This allows us to address generic aspects of the physics of non-magnetic vacancies in a classical spin liquid. We explicitly demonstrate that the pure ($x=0$) system remains a spin-liquid down to the lowest temperatures, with an unusual {\em non-monotonic} temperature dependence of the susceptibility, which even turns diamagnetic for the apical spins between the two kagome layers.…
We describe the uniform and staggered magnetization distributions around a vacancy in a quantum critical two-dimensional S=1/2 antiferromagnet. The distributions are delocalized across the entire sample with a universal functional form arising from an uncompensated Berry phase. The numerical results, obtained using quantum Monte Carlo simulations of the Heisenberg model on bilayer lattices with up to approximately 10^5 spins, are in good agreement with the proposed scaling structure. We determine the exponent eta'=0.40 +/- 0.02, which governs both the staggered and uniform magnetic structure a…
We review the problem of electron-electron interactions in graphene. Starting from the screening of long range interactions in these systems, we discuss the existence of an emerging Dirac liquid of Lorentz invariant quasi-particles in the weak coupling regime, and strongly correlated electronic states in the strong coupling regime. We also analyze the analogy and connections between the many-body problem and the Coulomb impurity problem. The problem of the magnetic instability and Kondo effect of impurities and/or adatoms in graphene is also discussed in analogy with classical models of many-b…
We introduce a block Lanczos (BL) recursive technique to construct quasi-one-dimensional models, suitable for density-matrix renormalization group (DMRG) calculations, from single- as well as multiple-impurity Anderson models in any spatial dimensions. This new scheme, named BL-DMRG method, allows us to calculate not only local but also spatially dependent static and dynamical quantities of the ground state for general Anderson impurity models without losing elaborate geometrical information of the lattice. We show that the BL-DMRG method can be easily extended to treat a multi-orbital Anderso…
