We study spin excitations and Kondo effect in open-shell nanographenes, motivated by recent scanning tunneling inelastic spectroscopy experiments. Specifically, we consider three systems, the triangulene, the extended triangulene with rocket shape, both with an $S=1$ ground state, and a triangulene dimer with $S=0$ on account of intermolecular exchange. We focus on the consequences of hybridization of the nanographene zero-modes with a conducting substrate on the $dI/dV$ lineshapes associated with spin excitations. The partially filled nanographene zero-modes coupled to the conduction electrons in the substrate constitute multi-orbital Anderson impurity models that we solve in the one-crossing approximation which treats the coupling to the substrate to infinite order. We find that the coupling to the substrate leads to (i) renormalization of the spin flip excitation energies of the bare molecule, (ii) broadening of the spectral features and (iii) the emergence of zero bias Kondo peaks for the $S=1$ ground states. The calculated substrate induced shift of the spin excitation energies is found to be significantly larger than their broadening, which implies that this effect has to be considered when comparing experimental results and theory.
Inelastic spin flip excitations associated with single-ion magnetic anisotropy of quantum spins, can be strongly renormalized by Kondo exchange coupling to the conduction electrons in the substrate, as shown recently for the case of Co adatoms on CuN$_2$ islands. In this case differential conductance spectra show zero-bias anomalies due to a Kondo effect of the doubly degenerate ground state, and finite-bias step features due to spin flip excitations. Here I consider spin-1 quantum magnets with positive uniaxial anisotropy, where the ground state is non-degenerate and hence the Kondo effect do…
We investigate Kondo correlations in a quantum dot with normal and superconducting electrodes, where a spin bias voltage is applied across the device and the local interaction $U$ is either attractive or repulsive. When the spin current is blockaded in the large-gap regime, this nonequilibrium strongly-correlated problem maps into an equilibrium model solvable by the numerical renormalization group method. The Kondo spectra with characteristic splitting due to the nonequilibrium spin accumulation are thus obtained at high precision. It is shown that while the bias-induced decoherence of the sp…
Quantum phase transition in magnetic nanographenes on a lead superconductor
Shenyang National Laboratory for Materials Science, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学生物与医学工程学院）；East China University of Science & Technology（华东理工大学）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）
An effective model that describes the Kondo effect due to a point defect in graphene is developed, taking account of the electronic state and the lattice structure of the defect. It is shown that this model can be transformed into a single-channel pseudogap Anderson model with a finite chemical potential. On the basis of the numerical renormalization group method, it is clarified that the experimentally observed gate-voltage dependence of the Kondo temperature is understood in this framework.
Sensing a magnetic rare-earth surface alloy by proximity effect with an open-shell nanographene
Empa - Swiss Federal Laboratories for Materials Science and Technology（瑞士联邦材料科学与技术研究院）；Regensburg Center for Ultrafast Nanoscopy (RUN), University of Regensburg（雷根斯堡大学超快纳米科学中心）；Institute of Theoretical Physics, University of Regensburg（雷根斯堡大学理论物理研究所）；Department of Chemistry, University of Zurich（苏黎世大学化学系）；ALBA Synchrotron Light Source（阿尔巴同步辐射光源）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（伯尔尼大学生物化学与药学系）；Department of Condensed Matter Physics, Faculty of Mathematics and Physics, Charles University（查理大学数学与物理学院凝聚态物理系）
Two topological phases in exchange alternating spin-1 nanographene chains
International Iberian Nanotechnology Laboratory (INL)（伊比利亚纳米技术实验室）；University of Santiago de Compostela（圣地亚哥-德孔波斯特拉大学）；Centro de Física das Universidades do Minho e do Porto, Universidade do Minho（米尼奥与波尔图大学物理中心，米尼奥大学）；NOVA School of Science and Technology (FCT NOVA)（新里斯本科学与技术学院）
We apply a recently developed nonequilibrium real-time renormalization group method in frequency space to describe nonlinear quantum transport through a small fermionic quantum system coupled weakly to several reservoirs via spin and/or orbital fluctuations. We provide an analytic and well-controlled procedure to solve the RG equations in the weak-coupling regime. Within a 2-loop analysis, we derive analytic formulas for the nonlinear conductance and the kernel determining the time evolution of the reduced density matrix. Most importantly, we present a consistent formalism how the RG flow is c…
We present a theory for the Kondo spin-1/2 effect in strongly correlated quantum dots. The theory is applicable at any temperature and voltage. It is based on a quadratic Keldysh effective action parameterized by a universal function. We provide a general analytical form for the tunneling density of states through this universal function for which we propose a simple microscopic model. We apply our theory to the highly asymmetric Anderson model with $U=\infty$ and describe its strong coupling limit, weak coupling limit and crossover region within a single analytical expression. We compare our …
Many-body correlations and macroscopic quantum behaviors are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo model which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems and can be explored with tunable nanostructures. Although Kondo physics is usually associated with the hybridization of itinerant electrons with microscopic magnetic moments, theory predicts that it can arise whenever degenerate quantum states are coupled to a continuum. Here we demonstrate the previous…
In this work we analyze the nonequilibrium transport through a quantum impurity (quantum dot or molecule) attached to ferromagnetic leads by using a hybrid numerical renormalization group-time-dependent density matrix renormalization group thermofield quench approach.For this, we study the bias dependence of the differential conductance through the system, which shows a finite zero-bias peak, characteristic of the Kondo resonance and reminiscent of the equilibrium local density of states. In the non-equilibrium settings, the resonance in the differential conductance is also found to decrease w…
The spatial length of the Kondo screening is still a controversial issue related to Kondo physics. While renormalization group and Bethe Anzats solutions have provided detailed information about the thermodynamics of magnetic impurities, they are insufficient to study the effect on the surrounding electrons, i.e., the spatial range of the correlations created by the Kondo effect between the localized magnetic moment and the conduction electrons. The objective of this work is to present a quantitative way of measuring the extension of these correlations by studying their effect directly on the …
We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage $ϕ$ and a magnetic field $B$. We investigate the interplay between the shift ($ω_B$) of the Kondo peak in the spin-resolved density of states (DOS) and the one ($ϕ_B$) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of $B$ down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as $ϕ_B$ only for $|…
We consider iron impurities in the noble metals gold and silver and compare experimental data for the resistivity and decoherence rate to numerical renormalization group results. By exploiting non-Abelian symmetries we show improved numerical data for both quantities as compared to previous calculations [Costi et al., Phys. Rev. Lett. 102, 056802 (2009)], using the discarded weight as criterion to reliably judge the quality of convergence of the numerical data. In addition we also carry out finite-temperature calculations for the magnetoresistivity of fully screened Kondo models with S = 1/2, …
The influence of spin-orbit interactions on the Kondo effect has been under debate recently. Studies conducted recently on a system composed by an Anderson impurity on a 2DEG with Rashba spin-orbit have been shown that it can enhance or suppress the Kondo temperature ($T_{\rm K}$), depending on the relative energy level position of the impurity with respect to the particle-hole symmetric point. Here we investigate a system composed by a single Anderson impurity side-coupled to a quantum wire with spin-orbit coupling (SOC). We derive an effective Hamiltonian in which the Kondo coupling is modif…
Magnetic frustrations can enhance quantum zero-point motion in spin systems and lead to exotic topological insulating states. When coupled to mobile electrons, they may lead to unusual non-Fermi liquid or metallic spin liquid states whose nature has not been well explored. Here, we propose a spin current Kondo mechanism underlying a series of non-Fermi liquid phases on the border of Kondo and magnetic phases in a frustrated three-impurity Kondo model. This mechanism is confirmed by renormalization group analysis and describes movable Kondo singlets called "holons" induced by an effective coupl…
We study the interplay of strong correlations and coherent driving by considering the strong-coupling Kondo model driven by a time-periodic bias voltage. Combining a recent nonequilibrium renormalization group method with Floquet theory, we find that by the coherent dressing of the driving field side-replicas of the Kondo resonance emerge in the conductance, which are not completely washed out by the decoherence induced by the driving. We show that to accurately capture the interplay of driving and strong correlations one needs to go beyond simple phenomenological pictures, which underestimate…
The Kondo effect of a Co atom on Cu(100) was investigated with a low-temperature scanning tunneling microscope using a monoatomically sharp nickel tip. Upon a tip-Co contact, the differential conductance spectra exhibit a spin-split asymmetric Kondo resonance. The computed ab initio value of the exchange coupling is too small to suppress the Kondo effect, but sufficiently large to produce the splitting observed. A quantitative analysis of the line shape using the numerical renormalization group technique indicates that the junction spin polarization is weak.
We report on a novel exchange mechanism, mediating the Kondo screening, in a correlated double quantum dot structure in the proximity of superconductor, stemming from nonlocal Andreev reflection processes. We estimate its strength perturbatively and corroborate analytical predictions with accurate numerical renormalization group calculations using an effective model for the superconductor-proximized nanostructure. We demonstrate that superconductor-induced exchange leads to a two-stage Kondo screening. We determine the dependence of the Kondo temperature on the coupling to superconductor and p…
Transition metal impurities will yield zero bias anomalies in the conductance of well contacted metallic carbon nanotubes, but Kondo temperatures and geometry dependences have not been anticipated so far. Applying the density functional plus numerical renormalization group approach of Lucignano \textit{et al.} to Co and Fe impurities in (4,4) and (8,8) nanotubes, we discover a huge difference of behaviour between outside versus inside adsorption of the impurity. The predicted Kondo temperatures and zero bias anomalies, tiny outside the nanotube, turn large and strongly radius dependent inside,…
When individual quantum spins are placed in close proximity to conducting substrates, the localized spin is coupled to the nearby itinerant conduction electrons via Kondo exchange. In the strong coupling limit this can result in the Kondo effect - the formation of a correlated, many body singlet state - and a resulting renormalization of the density of states near the Fermi energy. However, even when Kondo screening does not occur, Kondo exchange can give rise to a wide variety of other phenomena. In addition to the well known renormalization of the g factor and the finite spin decoherence and…
Exchange interactions and intermolecular hybridization in a spin-1/2 nanographene dimer
Department of Chemistry, University of Zurich（苏黎世大学化学系）；Departamento de Polímeros y Materiales Avanzados: Física, Química y Tecnología, Universidad del País Vasco UPV/EHU（巴斯克国立大学先进聚合物与材料系：物理、化学与技术）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯克，巴斯克科学基金会）；Integrated Systems Laboratory, ETH Zürich（苏黎世联邦理工学院集成系统实验室）；International Iberian Nanotechnology Laboratory (INL)（国际伊比利亚纳米技术实验室）；Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern（伯尔尼大学化学、生物化学与药学系）
The prospect of using semiconductor quantum dots as an experimental tool to distinguish Majorana zero modes (MZMs) from other zero-energy excitations such as Kondo resonances has brought up the fundamental question of whether topological superconductivity and the Kondo effect can coexist in these systems. Here, we study the Kondo effect in a quantum dot coupled to a metallic contact and to a pair of MZMs. We consider a situation in which the MBS are spin polarized in opposite directions. By using numerical renormalization-group calculations and scaling analysis of the renormalization group equ…
Using the framework of the density-matrix renormalization group (DMRG), we study a quantum dot coupled to a superconducting nanowire with strong Rashba spin-orbit coupling. Regarding the singlet-to-doublet "0-$π$" transition that takes place when the Kondo effect is overcome by the superconducting gap, we show that the Rashba coupling modifies the critical values at which the transition occurs, favouring the doublet phase. In addition, using a generalized Haldane's formula for the Kondo temperature $T_K$, we show that it is lowered by the Rashba coupling. We benchmark our DMRG results comparin…
Identification and optimization of accurate spin models for Fermi-Hubbard ladders using matrix product states
Donostia International Physics Center (DIPC)（多诺斯蒂亚国际物理中心）；University of the Basque Country (UPV/EHU)（巴斯克大学）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯基奎，巴斯克科学基金会）
The properties of a local spin S=1/2 coupled to K independent wires is studied in the presence of bias voltages which drive the system out of thermal equilibrium. For K >> 1, a perturbative renormalization group approach is employed to construct the voltage dependent scaling function for the conductance and the T-matrix. In contrast to the single-channel case, the Kondo resonance is split even by bias voltages small compared to the Kondo temperature T_K, V << T_K. Besides the applied voltage V, the current induced decoherence rate Γ<< V controls the physical properties of the system. While the…
We investigate the resistivity and dephasing rate in the Kondo regime due to magnetic impurities in graphene with different chemial potentials ($μ$). The Kondo effect due to either carbon vacancies or magnetic adatoms in graphene is described by the single-orbital pseudo-gap asymmetric Anderson impurity model. We find that although the Anderson impurity model considered here is a mixed valence system, it can be drived into either the Kondo [$μ> μ_c$ (critical value) $>0$] or mixed valency ($μ\approx μ_c$) or empty orbital ($μ< μ_c$) regime by a gate voltage, giving rise to characteristic featu…
We develop a numerical method to compute the negativity, an entanglement measure for mixed states, between the impurity and the bath in quantum impurity systems at finite temperature. We construct a thermal density matrix by using the numerical renormalization group (NRG), and evaluate the negativity by implementing the NRG approximation that reduces computational cost exponentially. We apply the method to the single-impurity Kondo model and the single-impurity Anderson model. In the Kondo model, the negativity exhibits a power-law scaling at temperature much lower than the Kondo temperature a…
The effect of the Zeeman field on the defect-induced Kondo effect in graphene is investigated. The effective model of the Kondo effect is derived, and is analyzed on the basis of the numerical renormalization group method. It is found that, under the Zeeman field, at the border of the spin polarized state and the Kondo-Yosida singlet state, there is an unusual fixed point where the entropy of the defect is k_B ln2 and the expectation value of S^2_z is 1/8.
