Single Magnetic Impurity Research Articles

Yu-Shiba-Rusinov States in s-Wave Kagome Superconductors: Self-Consistent Bogoliubov-de Gennes Calculations.

Significant research has recently been conducted into the Yu-Shiba-Rusinov (YSR) states in kagome superconductors through theoretical modeling and experimental investigations. However, additional efforts are still needed to further understand the local superconductivity near magnetic impurities in the kagome lattice and clarify how relevant quantities depend on the interaction strength, J, between such impurities and electrons. In this study, we explore a self-consistent numerical solution of the Bogoliubov-de Gennes equations for an s-wave superconducting Kagome model with a single classical magnetic impurity. Our study reveals that with increasing J, the local pair potential is systematically depressed in the vicinity of the impurity, similar to previous results obtained for the square and triangular lattices. Moreover, when J is further increased, the system undergoes a first-order phase transition with the appearance of stable and metastable states, reflecting the presence of the hysteresis loop in the pertinent quantities. As a consequence of this transition, the minimal energy of the stable YSR state is nonzero at any J, contrary to the expectations based on the assumption of a constant pair potential. A distinctive feature of the kagome lattice is that characteristics of the first-order transition are very sensitive to the position of the chemical potential within the kagome energy spectrum.

Theory of a single magnetic impurity on a thin metal film in proximity to a superconductor

Theory of a single magnetic impurity on a thin metal film in proximity to a superconductor

Tunable correlation effects of magnetic impurities by cubic Rashba spin-orbit coupling

We theoretically study the influence of the $k$-cubic Rashba spin-orbit coupling (SOC) on the correlation effects of magnetic impurities by combining the variational method and the Hirsch-Fye quantum Monte Carlo (HFQMC) simulations. Markedly different from the normal $k$-linear Rashba SOC, even a small cubic Rashba term can greatly alter the band structure and induce a Van Hove singularity in a wide range of energy; thus, the single impurity local moment becomes largely tunable. The cubic Rashba SOC adopted in this paper breaks the rotational symmetry, but the host material is still invariant under the operations ${\mathcal{R}}^{z}(\ensuremath{\pi}), {\mathcal{IR}}^{z}(\ensuremath{\pi}/2), {\mathcal{M}}_{xz}, {\mathcal{M}}_{yz}$, where ${\mathcal{R}}^{z}(\ensuremath{\theta})$ is the rotation of angle $\ensuremath{\theta}$ about the $z$ axis, $\mathcal{I}$ is the inversion operator, and ${\mathcal{M}}_{xz}$ (${\mathcal{M}}_{yz}$) is the mirror reflection about the $x\text{\ensuremath{-}}z$ ($y\text{\ensuremath{-}}z$) principal plane. Saliently, various components of spin-spin correlation between the single magnetic impurity and the conduction electrons show three- or sixfold rotational symmetry. This unique feature is due to the triple winding of the spins with a $2\ensuremath{\pi}$ rotation of $\mathbf{k}$, which is a hallmark of the cubic Rashba effect, and can possibly be an identifier to distinguish the cubic Rashba SOC from the normal $k$-linear Rashba term in experiments. Although the cubic Rashba term drastically alters the electronic properties of the host, we find that the spatial decay rate of the spin-spin correlation function remains essentially unchanged. Moreover, the carrier-mediated Ruderman-Kittel-Kasuya-Yosida interactions between two magnetic impurities show twisted features, the ferromagnetic diagonal terms dominate when two magnetic impurities are very close, but the off-diagonal terms become important at long distances.

RKKY interaction at helical edges of topological superconductors

We study spin configurations of magnetic impurities placed close to the edge of a two-dimensional topological superconductor both analytically and numerically. First, we demonstrate that the spin of a single magnetic impurity close to the edge of a topological superconductor tends to align along the edge. The strong easy-axis spin anisotropy behind this effect originates from the interaction between the impurity and the gapless helical Majorana edge states. We then compute the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between two magnetic impurities placed close to the edge. We show that, in the limit of large interimpurity distances, the RKKY interaction between the two impurities is mainly mediated by the Majorana edge states and leads to a ferromagnetic alignment of both spins along the edge. This effect can be used to detect helical Majorana edge states.

Magnetic impurities in a charge-ordered background

We investigate how magnetic impurities may affect a system exhibiting a charge-density wave (CDW) in its ground state. We consider a disordered Hubbard-Holstein model with a homogeneous electron-phonon interaction but with a (randomly chosen) fraction of sites displaying a nonzero Coulomb repulsion $U$ and perform state-of-the-art finite-temperature quantum Monte Carlo simulations. For a single magnetic impurity, charge-charge correlations hamper the spin-spin ones around the repulsive site, thus requiring a strong enough value of $U$ to create nonnegligible antiferromagnetic (AFM) correlations. As the number of magnetic impurities increases, these AFM correlations become deleterious to CDW order and its features. First, the critical temperature is drastically reduced and seems to vanish $\ensuremath{\sim}40%$ of impurities (for fixed $U/\ensuremath{\lambda}=2$), which we correlate with the classical percolation threshold. We also notice that just a small amount of disorder suffices to create a bad insulating state, with the suppression of both Peierls and spin gaps, even within the charge-ordered phase. Finally, we have also found that pairing correlations are enhanced at large doping, driven by the competition between CDW and AFM tendencies.

Kondo screening of single magnetic impurity doped type-II Ising superconductors

We theoretically study the Kondo effect in type-II Ising superconductors with a single magnetic impurity. Type-II Ising superconductivity was found in two-dimensional centrosymmetric materials with multiple degenerate orbitals, such as in few-layer stanene [Falson et al., Science 367, 1454 (2020)] and ultrathin ${\mathrm{PdTe}}_{2}$ films [Liu et al., Nano Lett. 20, 5728 (2020)]. The type-II Ising spin-orbit coupling (SOC) in these materials generates out-of-plane effective Zeeman fields orienting opposite directions for opposing orbitals, which strongly protects the interorbital superconducting pairing states against in-plane magnetic fields. We show that the SOC-induced band splitting and the chemical potential significantly influence the formation of a localized magnetic moment, with particle-hole asymmetry in the phase boundary between magnetic and nonmagnetic states. The behaviors of spin-induced Yu-Shiba-Rusinov bound states and low-temperature magnetic susceptibility demonstrate that the SOC suppresses the Kondo screening of the magnetic moment, while the interorbital mixing weakens the SOC at finite momentum, then enhances the Kondo effect. The quantum phase transition between magnetic doublet and Kondo singlet ground states can be tuned through chemical potential in experiments.

Single magnetic impurity effects in graphene based superconductors

The magnetic impurity effects and the existence of bound states (i.e. Yu-Shiba-Rusinov states) in superconductors have been a topic of great interest. Recently, the existence of Yu-Shiba-Rusinov states in graphene-based superconducting materials has been successfully observed in the laboratory. In this work, an effective Hamiltonian in real space is established to describe the superconducting state of graphene materials by considering a single magnetic impurity. Thus the Bogoliubov-de Gennes (BdG) equation is constructed and the self-consistency calculations of the superconducting order parameter are conducted. On this basis, the effects of magnetic impurities on graphene-like superconductors are investigated theoretically. The numerical results show that the Yu-Shiba-Rusinov state can only appear in the symmetry of the superconducting pair of the traditional <i>s</i>-wave coupling. The position and strength of the bound state are related to the magnetic moment of the impurity, showing a notable electron-hole asymmetry. There are no bound states in the energy gap for other pairing symmetries. This theoretical calculation not only provides a reasonable explanation for experimental phenomena, but also demonstrates that the heterojunction system composed of graphene and traditional superconductors has an <i>s</i>-wave superconducting pairing induced by the proximity effect in the graphene layer.

Electron scattering by magnetic impurity in Weyl semimetals

Weyl semimetals are prominent examples of topologically protected quantum matter. These materials are the three-dimensional counterparts of graphene and great efforts are being devoted to achieve a thorough understanding of their fundamental physics. In this work, we aim at contributing to this end by discussing the effect of a single magnetic impurity in Weyl semimetals as a first step towards considering a larger number of point-like impurities. We find that resonances appear in the local density of states (LDOS) with a Friedel-like behaviour, oscillating as a function of distance. By studying the spin-resolved LDOS, we can observe non-trivial and anisotropic spin textures where the spin components perpendicular to the spin of the impurity wind around the latter, until the spin becomes completely parallel to the impurity right at the impurity’s location. Friedel oscillations also play a relevant role in the form of the spin textures, forming an oscillatory pattern. We believe our results can pave the way to further studies which consider the presence of a large number of random magnetic impurities.

Kondo screening regimes in multi-Dirac and Weyl systems

We have investigated the Kondo physics of a single magnetic impurity embedded in multi-Dirac (Weyl) node fermionic systems. By using a generic effective model for the host material and employing a numerical renormalization group approach we access the low temperature behavior of the system, identifying the existence of Kondo screening in single-, double-, and triple-Dirac (Weyl) node models. We find that in any multi-Dirac node systems the low-energy regime lies within one of the known classes of pseudogap Kondo problem, extensively studied in the literature. Kondo screening is also observed for time reversal symmetry broken Weyl systems. This is, however, possible only in the particle-hole symmetry broken regime obtained for finite chemical potential $\mu$. Although weakly, breaking time-reversal symmetry suppresses the Kondo resonance, especially in the single-node Weyl semimetals. More interesting Kondo screening regimes are obtained for inversion symmetry broken multi-Weyl fermions. In these systems the Kondo regimes of double- and triple-Weyl node models are much richer than in the single-Weyl node model. While in the single-Weyl node model the Kondo temperature increases monotonically with $|\mu|$ regardless the value of the inversion symmetry breaking parameter $Q_0$, in double- and triple-Weyl node models there are two distinct regimes: (i) For $Q_0< |\mu|$ the Kondo temperature depends strongly on $\mu$, while (ii) for $Q_0 > |\mu|$ the Kondo temperature depends very weakly on $\mu$, resembling the flat-band single impurity Anderson model.

First principles investigations of Fe3+ impurity and Fe3+ + V−Cd complex in strongly confined CdSe quantum dot

Solitary dopant or defect in a semiconductor is the basis of the emerging field of optoelectronics known as solotronics. It has been shown that the spin of a single magnetic ion impurity can be manipulated optically. Among the magnetic ions, Fe3+ has been proposed as a primary candidate for the design of quantum dots (QDs) for solotronics because of its zero nuclear spin in contrast to Mn2+ and larger magnetic moment compared to Fe2+. In this work, we performed density function theory calculations to determine optimal parameters for the colloidal synthesis of single FeCd3+over FeCd2+ in CdSe of 1 nm in radius. We also investigated Fe3+ plus Cd vacancy complex (FeCd3++VCd−). Transition energy level calculations show FeCd3+ to be a deep-level donor and VCd− to be a shallow acceptor. Charge difference plots show that the charge of the ionized electron is localized around FeCd3+. Tetrahedral symmetry is retained at the FeCd3+ site. The magnetic moment of Fe3+ is almost the same in the core and at the surface and is equal to ∼4.27 μB for passivated QD. The large moment can be manipulated for spin control in conjunction with unoccupied vacancy states of the triplet t2 level of the shallow VCd acceptor to create a hole spin current in a lithographically patterned surface.

Impurity-induced resonant spinon zero modes in Dirac quantum spin liquids

Quantum spin-liquids are strongly correlated phases of matter displaying a highly entangled ground state. Due to their unconventional nature, finding experimental signatures of these states has proven to be a remarkable challenge. Here we show that the effects of local impurities can provide strong signatures of a Dirac quantum spin-liquid state. Focusing on a gapless Dirac quantum spin-liquid state as realized in NaYbO$_2$, we show that single magnetic impurity coupled to the quantum spin-liquid state creates a resonant spinon peak at zero frequency, coexisting the original Dirac spinons. We explore the spatial dependence of this zero-bias resonance, and show how different zero modes stemming from several impurities interfere. We finally address how such spinon zero-mode resonances can be experimentally probed with inelastic spectroscopy and electrically-driven paramagnetic resonance with scanning tunnel microscopy. Our results put forward impurity engineering as a means of identifying Dirac quantum spin-liquids with scanning probe techniques, highlighting the dramatic impact of magnetic impurities in a macroscopically entangled many-body ground state.

Thermodynamics and Screening in the Ising–Kondo Model

A simplification of the symmetric single‐impurity Kondo model is introduced and studied. In the Ising–Kondo model, host electrons scatter off a single magnetic impurity at the origin whose spin orientation is dynamically conserved. This reduces the problem to potential scattering of spinless fermions that can be solved exactly using the equation‐of‐motion technique. The Ising–Kondo model provides an example for static screening. At low temperatures, the thermodynamics at finite magnetic fields resembles that of a free spin‐1/2 in a reduced external field. Alternatively, the Curie law is interpreted in terms of an antiferromagnetically screened effective spin. The spin correlations decay algebraically to zero in the ground state and display commensurate Friedel oscillations. In contrast to the symmetric Kondo model, the impurity spin is not completely screened, i.e., the screening cloud contains less than a spin‐1/2 electron. At finite temperatures and weak interactions, the spin correlations decay to zero exponentially with correlation length ξ(T) = 1/(2πT).

Transport Properties of Zigzag Ribbons Composed of Two-Dimensional Quantum Spin Hall Insulators with a Single Magnetic Impurity

We investigate the transport properties of a ribbon with zigzag-shaped edges, which is composed of a two-dimensional quantum spin Hall insulator and contains a single magnetic impurity near the edg...

In-gap states of magnetic impurity in quantum spin Hall insulator proximitized to a superconductor

We study in-gap states of a single magnetic impurity embedded in a honeycomb monolayer which is deposited on superconducting substrate. The intrinsic spin–orbit coupling induces the quantum spin Hall insulating (QSHI) phase gapped around the Fermi energy. Under such circumstances we consider the emergence of Shiba-like bound states driven by the superconducting proximity effect. We investigate their topography, spin-polarization and signatures of the quantum phase transition manifested by reversal of the local currents circulating around the magnetic impurity. These phenomena might be important for more exotic in-gap quasiparticles in such complex nanostructures as magnetic nanowires or islands, where the spin–orbit interaction along with the proximity induced electron pairing give rise to topological phases hosting the protected boundary modes.

Magneto-optical Kerr effect in spin split two-dimensional massive Dirac materials

Two-dimensional (2D) massive Dirac electrons possess a finite Berry curvature, with Chern number 1/2, that entails both a quantized dc Hall response and a subgap full-quarter Kerr rotation. The observation of these effects in 2D massive Dirac materials such as gapped graphene, hexagonal boron nitride or transition metal dichalcogenides (TMDs) is obscured by the fact that Dirac cones come in pairs with opposite sign Berry curvatures, leading to a vanishing Chern number. Here, we show that the presence of spin–orbit interactions, combined with an exchange spin splitting induced either by diluted magnetic impurities or by proximity to a ferromagnetic insulator, gives origin to a net magneto-optical Kerr effect in such systems. We focus on the case of TMD monolayers and study the dependence of Kerr rotation on frequency and exchange spin splitting. The role of the substrate is included in the theory and found to critically affect the results. Our calculations indicate that state-of-the-art magneto-optical Kerr spectroscopy can detect a single magnetic impurity in diluted magnetic TMDs.

Kondo temperature equation for the Fermi liquid and the non-Fermi liquid regime for a two-channel anderson model

Multichannel Kondo resonance causes non-Fermi liquid behavior in many systems, as nanostructured metallic quantum dots and metallic alloys. The Kondo effect occurs at low temperatures and its indicating parameter is the Kondo temperature TK. This parameter can be used to renormalize thermodynamic and transport properties. The Kondo temperature is an important quantity to analyze the antiferromagnetic interaction between a localized spin and itinerant ones in a fermionic bath. There are many different definitions of the Kondo temperature. One of them is that it universalizes magnetic impurity susceptibility. This version was created for the one-channel Anderson model, but it is also valid in two-channel Anderson models, where a single magnetic impurity interacts with the conduction band electrons by two different channels. If the two coupling parameters are different, the model exhibits the well known Fermi liquid regime. When the coupling parameters are equal, the model displays the non-Fermi liquid regime. Each one shows different universal magnetic susceptibility behavior with appropriate TK value. In this article, Numerical Renormalization Group method is applied to study the Kondo temperature systematically. Different values of the coupling parameters in a two-channel Anderson model are examined. Finally, a single analytic expression for the Kondo temperature, valid in the Fermi and non-Fermi liquid regime, is presented.

Electric field tuning of spin splitting in topological insulator quantum dots doped with a single magnetic ion

We investigate theoretically the electron spin states in a disk-shaped topological insulator quantum dot (TIQD) containing a single magnetic Mn2+ ion. We demonstrate that the energy spectra and the density distributions of the symmetry-protected edge states in a HgTe TIQD can be modulated effectively by a single magnetic impurity Mn2+. Additionally, when an in-plane external electric field is applied., it not only tunes the spin splittings of edge states via the s(p)-d exchange interaction between the electron (hole) and the magnetic Mn2+ ion respectively, but also gives rise to the bright-to-dark transitions in the optical transition spectrum. Such spin properties of TIQDs with single Mn2+ ion as illustrated in this work could offer a new platform for topological electro-optical devices.

Helical edge transport in the presence of a magnetic impurity: The role of local anisotropy

Helical edge modes of 2D topological insulators are supposed to be protected from time-reversal invariant elastic backscattering. Yet substantial deviations from the perfect conductance are typically observed experimentally down to very low temperatures. To resolve this conundrum we consider the effect of a single magnetic impurity with arbitrary spin on the helical edge transport. We consider the most general structure of the exchange interaction between the impurity and the edge electrons. Moreover, for the first time, we take into the account the local anisotropy for the impurity and show that it strongly affects the backscattering current in a wide range of voltages and temperatures. We show that the sensitivity of the backscattering current to the presence of the local anisotropy is different for half-integer and integer values of the impurity spin. In the latter case the anisotropy can significantly increase the backscattering correction to the current.

Molecular Kondo effect in flat-band lattices

The Kondo effect of a single magnetic impurity embedded in the Lieb lattice is studied by the numerical renormalization group. When the band flatness is present in the local density of states, it quenches the participation of all dispersive electrons in the Kondo singlet formation, and reduces the many-body Kondo problem to a two-electron molecular Kondo problem. The two-electron analog of the many-body Kondo singlet, a quantum entanglement of two spins, is stable at low temperature, and the impurity contributions to thermodynamical and dynamical quantities are qualitatively different from that obtained in the conventional Kondo effect in systems without flat bands. The existence conditions of the molecular Kondo effect in narrow band systems are also discussed.

Impurity bound states in mesoscopic topological superconducting loops

We study numerically the effect induced by magnetic impurities in topological s-wave superconducting loops with spin-orbit interaction based on spin-generalized Bogoliubov-de Gennes equations. In the case of a single magnetic impurity, it is found that the midgap bound states can cross the Fermi level at an appropriate impurity strength and the circulating spin current jumps at the crossing point. The evolution of the zero-energy mode can be effectively tuned by the located site of a single magnetic impurity. For the effect of many magnetic impurities, two independent midway or edge impurities cannot lead to the overlap of zero modes. The multiple zero-energy modes can be effectively realized by embedding a single Josephson junction with impurity scattering into the system, and the spin current displays oscillatory feature with increasing the layer thickness.