We study the spatial distribution of the Kondo screening cloud. We find that in 3 D the spatial range of the cloud is limited to distances of the order of the Fermi wavelength due to angular dispersion effects. In lower dimensions this effect is less important and thus the Kondo length determines the localization of the cloud around the magnetic impurity. We clarify the role of the Kondo cloud in the impurity-impurity interactions: the hole coherence factor of the Kondo-doublet interaction is proportional to the amplitude of the Kondo cloud. We single out an experimental setup in which the Kondo cloud could be directly measured.
We analyze the single-channel Kondo model using the recently developed unitary renormalization group (URG) method, and obtain a comprehensive understanding of the Kondo screening cloud. The fixed-point low-energy Hamiltonian enables the computation of a plethora of thermodynamic quantities (specific heat, susceptibility, Wilson ratio, etc.) as well as spectral functions, all of which are found to be in excellent agreement with known results. By integrating out the impurity, we obtain an effective Hamiltonian for the excitations of the electrons comprising the Kondo cloud. This is found to cont…
The topological Kondo effect arises when conduction electrons in metallic leads are coupled to a mesoscopic superconducting island with Majorana fermions. Working with its minimal setup, we study the lead electron local tunneling density of states in its thermally smeared form motivated by scanning tunneling microscopy, focusing on the component $ρ_{2 k_F}$ oscillating at twice the Fermi wavenumber. As a function of temperature $T$ and at zero bias, we find that the amplitude of $ρ_{2 k_F}$ is nonmonotonic, whereby with decreasing $T$ an exponential thermal-length-controlled increase, potentia…
The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: "singlet weights", or projections onto particular entangled two-particle states. Using approximate theoretical arguments, w…
We show that the non-local polarization response in a multimode circuit-QED setup, devised from a Cooper pair box coupled to a long chain of Josephson junctions, provides an alternative route to access the elusive Kondo screening cloud. For moderate circuit impedance, we compute analytically the universal lineshape for the decay of the charge susceptibility along the circuit, that relates to spatial entanglement between the qubit and its electromagnetic environment. At large circuit impedance, we numerically find further spatial correlations that are specific to a true many-body state.
When a magnetic impurity exists in a metal, conduction electrons form a spin cloud that screens the impurity spin. This basic phenomenon is called the Kondo effect. Contrary to electric charge screening, the spin screening cloud occurs quantum coherently, forming spin-singlet entanglement with the impurity. Although the spins interact locally around the impurity, the cloud can spread out over micrometers. The Kondo cloud has never been detected to date, and its existence, a fundamental aspect of the Kondo effect, remains as a long-standing controversial issue. Here we present experimental evid…
We study the nonequilibrium formation of a spin screening cloud that accompanies the quenching of a local magnetic moment immersed in a Fermi sea at zero temperature. Based on high precision density matrix renormalization group results for the interacting single impurity Anderson model we discuss the real time evolution after a quantum quench in the impurity-reservoir hybridization using time evolving block decimation. We report emergent length and time scales in the spatiotemporal structure of non-local correlation functions in the spin- and the charge density channel. At equilibrium, our dat…
We propose a variational approach for computing the macroscopic entanglement in a many-body mixed state, based on entanglement witness operators, and compute the entanglement of formation (EoF), a mixed-state generalization of the entanglement entropy, in single- and two-channel Kondo systems at finite temperature. The thermal suppression of the EoF obeys power-law scaling at low temperature. The scaling exponent is halved from the single- to the two-channel system, which is attributed, using a bosonization method, to the non-Fermi liquid behavior of a Majorana fermion, a "half" of a complex f…
Kondo effect in a side-coupled double-quantum-dot system embedded in a mesoscopic ring
利用大N从玻色子平均场论研究了双量子点系统中近藤屏蔽云的有限尺寸效应。在该设置中，一个点嵌入在具有有限尺寸$L$的封闭金属环中，另一个点经由具有强度K的反铁磁自旋-自旋交换耦合而侧耦合到嵌入的点。反铁磁耦合有利于局域自旋单态，抑制近藤屏蔽。Kondo有效温度T_k（与Kondo屏蔽云尺寸的倒数成正比）在有限尺寸下表现出Kosterlitz无标度（KT），表明Kondo屏蔽相之间存在KT型量子跃迁，< K_c and the local spin-singlet phase for K >K_c为热力学极限，K_c为临界值。当K < K_c（L= 4 n，4 n +1，4 n +3）和K>K_c（L= 4 n +2）时，Kondo和局域自旋单态基态之间存在交叉.为了更深入地研究量子点的交叉区，我们还计算了不同$K$值的量子点在有限尺寸下的局域态密度和持续电流。
We study the interaction between graphene and a single-molecule-magnet, [Fe4(L)2(dpm)6]. Focusing on the closest Iron ion in a hollow position with respect to the graphene sheet, we derive a channel selective tunneling Hamiltonian, that couples different d orbitals of the Iron atom to precise independent combinations of sublattice and valley degrees of freedom of the electrons in graphene. When looking at the spin-spin interaction between the molecule and the graphene electrons, close to the Dirac point the channel selectivity results in a channel decoupling of the Kondo interaction, with two …
Kondo screening by the surface modes of a strong topological insulator
我们考虑磁性杂质沉积在强拓扑绝缘体表面，通过近藤交换作用与表面模相互作用。考虑到表面模的费米线的翘曲，我们导出了一个映射到一个有效的一维模型，并表明，杂质是完全屏蔽的表面电子，除了当费米能级正好位于狄拉克点。利用Abrikosov费米子平均场论，我们计算了近藤屏蔽云存在时电子密度Friedel振荡的形状。我们定量分析了两种原型化合物Bi $_2$ Se $_3$和Bi $_2$ Te $_3$的Friedel振荡中六重对称性的可观测性。
Correlated interaction between dilute localized impurity electrons with the itinerant host conduction electrons in metals gives rise to the conventional many-body Kondo effect below sufficiently low temperature. In sharp contrast to these conventional Kondo systems, we report an intrinsic, robust and high-temperature Kondo state in two-dimensional semiconducting phosphorene. While absorbed at a thermodynamically stable lattice defect, Cr impurity triggers an electronic phase transition in phosphorene to provide conduction electrons, which strongly interact with the localized moment generated a…
The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Whereas complete Kondo screening has been explored widely, realizations of the underscreened scenario - where only some of several Kondo channels participate in the screening - remain rare. Here we report the observation of fully screened and underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a unique platform for studying Kondo physi…
The Kondo effect is the many-body screening of a local spin by a cloud of electrons at very low temperature. It has been proposed as an explanation of the zero-bias anomaly in quantum point contacts where interactions drive a spontaneous charge localization. However, the Kondo origin of this anomaly remains under debate, and additional experimental evidence is necessary. Here we report on the first phase-sensitive measurement of the zero-bias anomaly in quantum point contacts using a scanning gate microscope to create an electronic interferometer. We observe an abrupt shift of the interference…
In normal metals, the magnetic-moment of impurity-spins disappears below a characteristic Kondo temperature, TK. This marks the formation of a polarized cloud of conduction band electrons that screen the magnetic moment . In contrast, moments embedded in insulators remain unscreened at all temperatures. This raises the question about the fate of magnetic-moments in intermediate, pseudogap systems, such as graphene. In these systems coupling between the local moment and the conduction band electrons is predicted to drive a quantum phase-transition between a local-moment phase and a Kondo-screen…
We propose a scheme to realize the Kondo model with tunable anisotropy using alkaline-earth atoms in an optical lattice. The new feature of our setup is Floquet engineering of interactions using time-dependent Zeeman shifts, that can be realized either using state-dependent optical Stark shifts or magnetic fields. The properties of the resulting Kondo model strongly depend on the anisotropy of the ferromagnetic interactions. In particular, easy-plane couplings give rise to Kondo singlet formation even though microscopic interactions are all ferromagnetic. We discuss both equilibrium and dynami…
The coherent superposition of non-orthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset,Comm. Math. Phys.,356 451 (2017)]. We present a practical approach for performing a variational calculation based on such states. Our method is based on approximate imaginary-time equations of motion that decouple the dynamics of each Gaussian state forming the ansatz. It is independent of the lattice connectivity of the model and the implementation is highly parallelizable. To benchmark our variational metho…
