Kondo Peak Splitting Research Articles

Fe-induced Kondo peak splitting in tip-functionalized scanning tunneling spectroscopy: A first-principles-based simulation

The spin-polarized scanning tunneling microscope (SP-STM) has been employed to enhance its capabilities of detecting the electronic and magnetic properties of organometallic molecules. Using a tip functionalized with a cobaltocene (Cc) molecule, recent SP-STM experiment performed on the Cu-tip/Cc/Fe/Cu(100) composite junction revealed an asymmetric Kondo resonance splitting in the differential conductance (dI/dV) spectrum. However, a systematic theoretical simulation of such system is lacking, and the important roles of the substrate spin-polarization and the Fe adatom still remain to be elucidated. In this work, by combining density functional theory and the hierarchical equations of motion methods, we achieve first-principles-based simulations of the tip control process of the Cu-tip/Cc/Fe/Cu(100) junction. We correctly reproduce the experimental results and demonstrate the influences of the Fe adatom on the spin-polarization of the substrate and on the Kondo resonance splitting in the dI/dV spectra.

Anisotropic Kondo screening induced by spin-orbit coupling in quantum wires

Using the numerical renormalization group (NRG) method we study a magnetic impurity coupled to a quantum wire with Rashba and Dresselhaus spin-orbit coupling (SOC) in an external magnetic field. We consider the low-filling regime with the Fermi energy close to the bottom of the band and report the results for local static and dynamic properties in the Kondo regime. In the absence of the field, local impurity properties remain isotropic in spin space despite the SOC-induced magnetic anisotropy of the conduction band. In the presence of the field, clear fingerprints of anisotropy are revealed through the strong field-direction dependence of the impurity spin polarization and spectra, in particular of the Kondo peak height. The detailed behavior depends on the relative magnitudes of the impurity and band $g$-factors. For the case of impurity $g$-factor somewhat lower than the band $g$-factor, the maximal Kondo peak suppression is found for field oriented along the effective SOC field axis, while for a field perpendicular to this direction we observe a compensation effect (``revival of the Kondo peak''): the SOC counteracts the Kondo peak splitting effects of the local Zeeman field. We demonstrate that the SOC-induced anisotropy, measurable by tunneling spectroscopy techniques, can help to determine the ratio of Rashba and Dresselhaus SOC strengths in the wire.

Kondo-peak splitting and resonance enhancement caused by interdot tunneling in coupled double quantum dots

In this paper, we report our recent work on the interdot tunneling-dependent Kondo effect for two serially coupled quantum dots (QDs) by adopting the hierarchical equations of motion approach. As is known, for such a system, when interdot tunneling $t$ increases, a continuous crossover from a Kondo singlet to a spin singlet is observed rather than a quantum phase transition, even though an induced antiferromagnetic interaction exists due to the interdot tunneling $t$. Our study focuses on the influence of the tunneling $t$ between two QDs at a finite temperature and especially on the smearing of the quantum phase transition. In this study, we find that, at small $t$, there is an enhanced Kondo effect, which results in the most noticeable Kondo effect appearing at finite $t$ rather than at $t=0$. When $t$ is larger, the Kondo peak splits into two subpeaks. Because of the weak coupling to the leads, the splitting space exactly corresponds to the energy difference between the original degenerated local spin singlet and the local spin triplet of the two isolated QDs. The Kondo peak can be preserved when the energy difference between the local spin singlet and the local spin triplet is smaller than the enhanced Kondo temperature. Finally, interdot tunneling also introduces a doubly occupied charge singlet, which causes charge fluctuations in the ground state at finite temperature and thus, therefore, smears the phase transition. This can also explain why no phase transition is observed in experiments in other QDs systems, even though the phase transition is always predicted in theory.

Anisotropy induced Kondo splitting in a mechanically stretched molecular junction: A first-principles based study.

The magnetic anisotropy and Kondo phenomena in a mechanically stretched magnetic molecular junction are investigated by combining the density functional theory (DFT) and hierarchical equations of motion (HEOM) approach. The system is comprised of a magnetic complex Co(tpy-SH)2 sandwiched between adjacent gold electrodes, which is mechanically stretched in experiments done by Parks et al. [Science 328, 1370 (2010)]. The electronic structure and mechanical property of the stretched system are investigated via the DFT calculations. The HEOM approach is then employed to characterize the Kondo resonance features, based on the Anderson impurity model parameterized from the DFT results. It is confirmed that the ground state prefers the S = 1 local spin state. The structural properties, the magnetic anisotropy, and corresponding Kondo peak splitting in the axial stretching process are systematically evaluated. The results reveal that the strong electron correlations and the local magnetic properties of the molecule magnet are very sensitive to structural distortion. This work demonstrates that the combined DFT+HEOM approach could be useful in understanding and designing mechanically controlled molecular junctions.

Kondo peak splitting and Kondo dip induced by a local moment.

Many features like spin-orbit coupling, bias and magnetic fields applied, and so on, can strongly influence the Kondo effect. One of the consequences is Kondo peak splitting. However, Kondo peak splitting led by a local moment has not been investigated systematically. In this research we study theoretically electronic transport through a single-level quantum dot exchange coupled to a local magnetic moment in the Kondo regime. We focus on the Kondo peak splitting induced by an anisotropic exchange coupling between the quantum dot and the local moment, which shows rich splitting behavior. We consider the cases of a local moment with S = 1/2 and S = 1. The longitudinal (z-component) coupling plays a role of multivalued magnetic fields and the transverse (x, y-components) coupling lifts the degeneracy of the quantum dot, both of which account for the fine Kondo peak splitting structures. The inter-level or intra-level transition processes are identified in detail. Moreover, we find a Kondo dip at the Fermi level under the proper parameters. The possible experimental observations of these theoretical results should deepen our understanding of Kondo physics.

Kondo peak splitting and Kondo dip in single molecular magnet junctions

Many factors containing bias, spin–orbit coupling, magnetic fields applied, and so on can strongly influence the Kondo effect, and one of the consequences is Kondo peak splitting (KPS). It is natural that KPS should also appear when another spin degree of freedom is involved. In this work we study the KPS effects of single molecular magnets (SMM) coupled with two metallic leads in low-temperature regime. It is found that the Kondo transport properties are strongly influenced by the exchange coupling and anisotropy of the magnetic core. By employing Green's function method in Hubbard operator representation, we give an analytical expression for local retarded Green's function of SMM and discussed its low-temperature transport properties. We find that the anisotropy term behaves as a magnetic field and the splitting behavior of exchange coupling is quite similar to the spin–orbit coupling. These splitting behaviors are explained by introducing inter-level or intra-level transitions, which account for the seven-peak splitting structure. Moreover, we find a Kondo dip at Fermi level under proper parameters. These Kondo peak splitting behaviors in SMM deepen our understanding to Kondo physics and should be observed in the future experiments.

Kondo effect and spin-active scattering in ferromagnet-superconductor junctions

We study the interplay of superconducting and ferromagnetic correlations on charge transport in different geometries with a focus on both a quantum point contact as well as a quantum dot in the even and the odd state with and without spin-active scattering at the interface. In order to obtain a complete picture of the charge transport we calculate the full counting statistics in all cases and compare the results with experimental data. We show that spin-active scattering is an essential ingredient in the description of quantum point contacts. This holds also for quantum dots in an even charge state whereas it is strongly suppressed in a typical Kondo situation. We explain this feature by the strong asymmetry of the hybridisations with the quantum dot and show how Kondo peak splitting in a magnetic field can be used for spin filtering. For the quantum dot in the even state spin-active scattering allows for an explanation of the experimentally observed mini-gap feature.

Quantitative determination of the discretization and truncation errors in numerical renormalization-group calculations of spectral functions

In the numerical renormalization-group (NRG) calculations of spectral functions of quantum impurity models, the results are always affected by discretization and truncation errors. The discretization errors can be alleviated by averaging over different discretization meshes (``$z$-averaging''), but since each partial calculation is performed for a finite discrete system, there are always some residual discretization and finite-size errors. The truncation errors affect the energies of the states and result in the displacement of the delta-peak spectral contributions from their correct positions. The two types of errors are interrelated: for coarser discretization, the discretization errors increase, but the truncation errors decrease since the separation of energy scales is enhanced. In this work, it is shown that by calculating a series of spectral functions for a range of the total number of states kept in the NRG truncation, it is possible to estimate the errors and determine the error bars for spectral functions, which is important when making accurate comparison to the results obtained by other methods and for determining the errors in the extracted quantities (such as peak positions, heights, and widths). The closely related problem of spectral broadening is also discussed: it is shown that the overbroadening contorts the results without, surprisingly, reducing the variance of the curves. It is thus important to determine the results in the limit of zero broadening. The method is applied to determine the error bounds for the Kondo peak splitting in an external magnetic field. For moderately strong fields, the results are consistent with the Bethe ansatz study by Moore and Wen [Phys. Rev. Lett. 85, 1722 (2000)]. We also discuss the regime of large $U/\ensuremath{\Gamma}$ ratio. It is shown that in the strong-field limit, a spectral step is observed in the spectrum precisely at the Zeeman frequency until the field becomes so strong that the step merges with the atomic spectral peak.

Scaling feature of magnetic field induced Kondo-peak splittings

By using the full density matrix approach to spectral functions within the numerical renormalization group method, we present a detailed study of the magnetic field induced splittings in the spin-resolved and the total spectral densities of a Kondo correlated quantum dot described by the single level Anderson impurity model. The universal scaling of the splittings with magnetic field is examined by varying the Kondo scale either by a change of local level position at a fixed tunnel coupling or by a change of the tunnel coupling at a fixed level position. We find that the Kondo-peak splitting $\ensuremath{\Delta}/{T}_{K}$ in the spin-resolved spectral function always scales perfectly for magnetic fields $B<8{T}_{K}$ in either of the two ${T}_{K}$-adjusted paths. Scaling is destroyed for fields $B>10{T}_{K}$. On the other hand, the Kondo peak splitting $\ensuremath{\delta}/{T}_{K}$ in the total spectral function does slightly deviate from the conventional scaling theory in whole magnetic field window along the coupling-varying path. Furthermore, we show the scaling analysis suitable for all field windows within the Kondo regime and two specific fitting scaling curves are given from which certain detailed features at low field are derived. In addition, the scaling dimensionless quantity $\ensuremath{\Delta}/2B$ and $\ensuremath{\delta}/2B$ are also studied and they can reach and exceed 1 in the large magnetic field region, in agreement with a recent experiment [T. M. Liu et al., Phys. Rev. Lett. 103, 026803 (2009)].

Kondo peak splitting on a single adatom coupled to a magnetic cluster

The Kondo resonance induced by a single cobalt adatom interacting with a ferromagnetic iron nanocluster is measured using low-temperature scanning tunneling microscopy. The persistence of the Kondo resonance is evidenced along with the predicted splitting of the spectral density peak for a Kondo impurity surrounded by a spin-polarized electron bath. Reversible quenching of the split feature is observed using atom manipulation between adjacent adsorption sites. Using a Green's-function formalism, we model a double Fano resonance leading to a quantitative insight of our observations.

Spin-polarized STM for a Kondo adatom

We investigate the bias dependence of the tunneling conductance between a spin-polarized(SP) scanning tunneling microscope (STM) tip and the surface conduction states of anormal metal with a Kondo adatom. Quantum interference between tip–host metal andtip–adatom–host metal conduction paths is studied in the full range of the Fano parameterq. The spin-polarized STM gives rise to a splitting of the Kondo peak and asymmetry in thezero-bias anomaly, depending on the lateral tip–adatom distance. For increasing lateraldistances, the Kondo peak splitting shows a strong suppression and the spin-polarizedconductance exhibits the standard Fano–Kondo profile.

Kondo-Peak Splitting and Coherent Transport in a Single-Electron Transistor

The peculiar behavior of Kondo-peak splitting under a magnetic field and bias can be explained by calculating the nonequilibrium retarded Green's function via the nonperturbative dynamical theory (NDT). In the NDT, the application of a lead-dot-lead system reveals that new resonant tunneling levels are activated near the Fermi level and the conventional Kondo peak at the Fermi level diminishes when a bias is applied. Magnetic field causes asymmetry in the spectral density and transforms the new resonant peak into a major peak whose behavior explains all the features of the nonequilibrium Kondo phenomenon. We also show the mechanism of coherent transport through the new resonant tunneling level.

Point-contact-spectroscopy investigation of the Kondo size effect in CuCr and AuFe alloys

Size effects in Kondo scattering are studied on CuCr and AuFe alloys (TK=2 K and 0.2 K, respectively) by applying point-contact spectroscopy in break-junction type contacts. It is shown that as the contact diameter is decreased under the condition of ballistic electron transport, the size effect enhances the interaction of the conduction electrons with the Kondo impurity (as compared to the phonons) and increases the Kondo temperature in the contact region. In an external magnetic field the size effect decreases the negative magnetoresistance in CuCr and suppresses the Kondo peak splitting in AuFe.