Impurity Spin Research Articles

Spin impurities, Wilson lines and semiclassics

We consider line defects with large quantum numbers in conformal field theories. First, we consider spin impurities, both for a free scalar triplet and in the Wilson-Fisher O(3) model. For the free scalar triplet, we find a rich phase diagram that includes a perturbative fixed point, a new nonperturbative fixed point, and runaway regimes. To obtain these results, we develop a new semiclassical approach. For the Wilson-Fisher model, we propose an alternative description, which becomes weakly coupled in the large spin limit. This allows us to chart the phase diagram and obtain numerous rigorous predictions for large spin impurities in 2 + 1 dimensional magnets. Finally, we also study 1/2-BPS Wilson lines in large representations of the gauge group in rank-1 mathcal{N} = 2 superconformal field theories. We contrast the results with the qualitative behavior of large spin impurities in magnets.

Internal decoherence in nano-object interferometry due to phonons

We discuss the coherent splitting and recombining of a nanoparticle in a mesoscopic “closed-loop” Stern–Gerlach interferometer in which the observable is the spin of a single impurity embedded in the particle. This spin, when interacting with a pulsed magnetic gradient, generates the force on the particle. We calculate the internal decoherence, which arises as the displaced impurity excites internal degrees of freedom (phonons) that may provide WelcherWeg information and preclude interference. We estimate the constraints this decoherence channel puts on future interference experiments with massive objects. We find that for a wide range of masses, forces, and temperatures, phonons do not inhibit Stern–Gerlach interferometry with micro-scale objects. However, phonons do constitute a fundamental limit on the splitting of larger macroscopic objects if the applied force induces phonons.

Rise and fall of Yu-Shiba-Rusinov bound states in charge-conserving s -wave one-dimensional superconductors

We re-examine the problem of a magnetic impurity coupled to a superconductor focusing on the role of quantum fluctuations. We study in detail a system that consists of a one-dimensional charge conserving spin-singlet superconductor coupled to a boundary magnetic impurity. Our main finding is that quantum fluctuations lead to the destruction of Yu-Shiba-Rusinov (YSR) intragap bound states in all but a narrow region of the phase diagram. We carry out our analysis in three stages, increasing the role of the quantum fluctuations at each stage. First we consider the limit of a classical impurity and study the bulk semiclassically, finding YSR states throughout the phase diagram, a situation similar to conventional BCS superconductors. In the second stage, we reintroduce quantum fluctuations in the bulk and find that the YSR state is suppressed over half of the phase diagram, existing only around the quantum critical point separating the unscreened and the partially screened phases. In the final stage we solve exactly the full interacting model with arbitrary coupling constants using the Bethe ansatz. We find that including both the quantum fluctuating bulk and quantum impurity destabilizes the YSR state over most of the phase diagram allowing it to exist only in a small region, the YSR regime, between a Kondo-screened and an unscreened regime. Within the YSR regime a first-order phase transition occurs between a spin singlet and doublet ground state. We also find that for large-enough impurity spin exchange interaction a renormalized Kondo-screened regime is established. In this regime, not found for BCS superconductors, there is no YSR state and a renormalized Kondo temperature scale is generated.

Analytical calculation of scattering from spin impurity and entanglement generation for edge states of Kane–Mele model

In this paper, the scattering from a spin impurity for the edge state of the Kane–Mele model has been calculated via the Lippmann–Schwinger approach. To solve this problem analytically, we first approximately calculate the edge states of the Kane–Mele model and use it to obtain Green’s function. We then calculate the scattering matrix of an electron from a spin impurity with Heisenberg interaction. Finally, we generalize this method to a double impurity model and use it to calculate the entanglement between two spins of two impurities. • The transmission and reflection coefficients by spin impurities of the edge states of Kane–Mele model are calculated in a 2D topological insulator . • The entanglement between impurities is investigated. • The scattering of electrons from two kondo impurities by Concurrence gauge is studied.

Orthogonality catastrophe and quantum speed limit for spin chain at finite temperature

We present an interesting relationship between the orthogonality catastrophe (OC) and the quantum speed limit (QSL) for a spin chain with uniform nearest neighbour couplings perturbed by an impurity spin. We thoroughly study the catastrophic QSL that specifies a bound on the evolution time between the initial and final states and in this respect, link it to the emerging OC effect. It is found that the speed of state evolution subtle but fundamental, and the bound characterized by QSL shows the same behaviours as the OC effect in the thermodynamic limit. It allows us to reveal some universal properties, in particular finite temperature effects. Significantly, the threshold of temperature and system size is clearly demonstrated for the QSL under finite temperature.

Thirty-Year Anniversary of κ-(BEDT-TTF)2Cu2(CN)3: Reconciling the Spin Gap in a Spin-Liquid Candidate

In 1991 the layered organic compound κ-(BEDT-TTF)2Cu2(CN)3 with a triangular lattice was synthesized for the first time. Although, originally, the focus was on the superconducting properties under pressure, this frustrated Mott insulator has been the most promising quantum-spin-liquid candidate for almost two decades, widely believed to host gapless spin excitations down to T→0. The recent observation of a spin gap rules out a gapless spin liquid with itinerant spinons and puts severe constraints on the magnetic ground state. This review evaluates magnetic, thermal transport, and structural anomalies around T⋆=6 K. The opening of a spin gap yields a rapid drop of spin susceptibility, NMR Knight shift, spin-lattice relaxation rate, and μ-SR spin fluctuation rate, but is often concealed by impurity spins. The concomitant structural transition at T⋆ manifests in thermal expansion, THz phonons and 63Cu NQR relaxation. Based on the field dependence of T⋆, a critical field of 30–60 T is estimated for the underlying spin-singlet state. Overall, the physical properties are remarkably similar to those of spin-Peierls compounds. Thus, a strong case is made that the ‘6K anomaly’ in κ-(BEDT-TTF)2Cu2(CN)3 is the transition to a valence-bond-solid state and it is suggested that such a scenario is rather the rule than the exception in materials with strong magnetic frustration.

Dynamic Friedel oscillations on the surface of a topological insulator

We study theoretically the dynamic Friedel oscillations of electrons at the surface of a topological insulator (TI) that are generated by the rotation of a localized impurity spin. We show that the spin-orbit interaction (SOI) in Rashba form, which is an integral part of the TI Hamiltonian, yields a highly anisotropic response to the localized spin rotation. As a result, the response to a flip of a localized spin $z$ projection involves the reaction of all $x$, $y$, and $z$ components of the local magnetization. Additionally, the dynamic spin moment (and thus also Friedel oscillations) emitted by the localized dynamical spin depends on the orientation in the TI plane. The resulting unusual dynamics is due to the interplay of SOI and Ruderman-Kittel-Kasuya-Yoshida interactions. This provides the basis for manipulation of the spin transport in topological insulators decorated with localized impurity spins, which may be important for technological applications.

Multi-impurity chiral Kondo model: Correlation functions and anyon fusion rules

The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for the multi-impurity chiral Kondo model, that scattering of an electron through the impurities depends on the anyon's total fusion channel. Here we study the correlation between impurity spins. We argue, based on a combination of conformal field theory, a perturbative limit with a large number of channels $k$, and the exactly solvable two-channel case, that the interimpurity spin correlation probes the anyon fusion of the pair of correlated impurities. This may allow, using measurement-only topological quantum computing protocols, to braid the multichannel Kondo anyons via consecutive measurements.

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension of exact diagonalization, it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in a many-body system. Based on the energies and the first and second-order correlation functions of yrast states, we identify different dynamical regimes and the transitions between them: The polaron regime, where the impurity’s motion is affected by the Bose gas through a renormalized effective mass; a regime of a gray soliton that is weakly correlated with a stationary impurity, and the depleton regime, where the impurity occupies a dark or gray soliton. Extracting the depleton effective mass reveals a super heavy regime where the magnitude of the (negative) depleton mass exceeds the mass of the finite Bose gas.

Transient dynamics of a magnetic impurity coupled to superconducting electrodes: Exact numerics versus perturbation theory

Impurities coupled to superconductors offer a controlled platform to understand the interplay between superconductivity, many-body interactions, and nonequilibrium physics. In the equilibrium situation, local interactions at the impurity induce a transition from the spin-singlet to the spin-doublet ground state, resulting in a supercurrent sign reversal ($0\text{\ensuremath{-}}\ensuremath{\pi}$ transition). In this work, we apply the exact time-dependent density matrix renormalization group method to simulate the transient dynamics of such superconducting systems. We also use a perturbative approximation to analyze their properties at longer times. These two methods agree for a wide range of parameters. In a phase-biased situation, the system gets trapped in a metastable state characterized by a lower supercurrent compared to the equilibrium case. We show that local Coulomb interactions do not provide an effective relaxation mechanism for the initially trapped quasiparticles. In contrast, other relaxation mechanisms, such as coupling to a third normal lead, make the impurity spin relax for parameter values corresponding to the equilibrium 0 phase. For parameters corresponding to the equilibrium $\ensuremath{\pi}$ phase the impurity converges to a spin-polarized stationary state. Similar qualitative behavior is found for a voltage-biased junction, which provides an effective relaxation mechanism for the trapped quasiparticles in the junction.

Heavy Fermion Emerging from the Singular Fermi Liquid in Underscreened Kondo Model for Eu Compounds

An underscreened Kondo model for the impurity spin S = 7/2 in a weak crystal field is studied to elucidate the Kondo effect in the Eu compounds. By utilizing the numerical renormalization group met...

Yu-Shiba-Rusinov Qubit

Magnetic impurities in $s$-wave superconductors lead to spin-polarized Yu-Shiba-Rusinov (YSR) in-gap states. Chains of magnetic impurities offer one of the most viable routes for the realization of Majorana bound states which hold a promise for topological quantum computing. However, this ambitious goal looks distant since no quantum coherent degrees of freedom have yet been identified in these systems. To fill this gap we propose an effective two-level system, a YSR qubit, stemming from two nearby impurities. Using a time-dependent wave-function approach, we derive an effective Hamiltonian describing the YSR qubit evolution as a function of distance between the impurity spins, their relative orientations, and their dynamics. We show that the YSR qubit can be controlled and read out using the state-of-the-art experimental techniques for manipulation of the spins. Finally, we address the effect of the spin noises on the coherence properties of the YSR qubit, and show a robust behaviour for a wide range of experimentally relevant parameters. Looking forward, the YSR qubit could facilitate the implementation of a universal set of quantum gates in hybrid systems where they are coupled to topological Majorana qubits.

Universal Thermal Entanglement of Multichannel Kondo Effects.

Quantum entanglement between an impurity and its environment is expected to be central in quantum impurity problems. We develop a method to compute the entanglement in spin-1/2 impurity problems, based on the entanglement negativity and the boundary conformal field theory (BCFT). Using the method, we study the thermal decay of the entanglement in the multichannel Kondo effects. At zero temperature, the entanglement has the maximal value independent of the number of the screening channels. At low temperature, the entanglement exhibits a power-law thermal decay. The power-law exponent equals two times of the scaling dimension of the BCFT boundary operator describing the impurity spin, and it is attributed to the energy-dependent scaling behavior of the entanglement in energy eigenstates. These agree with numerical renormalization group results, unveiling quantum coherence inside the Kondo screening length.

Probing Kondo spin fluctuations with scanning tunneling microscopy and electron spin resonance

We theoretically analyze a state-of-the-art experimental method based on a combination of electron spin resonance and scanning tunneling microscopy (ESR-STM), to directly probe the spin fluctuations in the Kondo effect. The Kondo impurity is exchange coupled to the probe spin, and the ESR-STM setup detects the small level shifts in the probe spin induced by the spin fluctuations of the Kondo impurity. We use the open quantum system approach by regarding the probe spin as the "system" and the Kondo impurity spin as the fluctuating "bath" to evaluate the resonance line shifts in terms of the dynamic spin susceptibility of the Kondo impurity. We consider various common adatoms on surfaces as possible probe spins and estimate the corresponding level shifts. It is found that the sensitivity is most pronounced for the probe spins with transverse magnetic anisotropy.

Kondo effect and spin\u2013orbit coupling in graphene quantum dots

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. Here we report on the interplay between spin–orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin–orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin–orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin–orbit interaction.

RKKY interaction in a spin-split superconductor

We determine theoretically the interaction between two magnetic impurities embedded in a spin-split $s$-wave superconductor. The spin-splitting in the superconductor gives rise to two different interaction types between the impurity spins, depending on whether their spins lie in the plane perpendicular to the spin-splitting field (Heisenberg) or not (Ising). For impurity separation distances exceeding $\xi_S$, we find that the magnitude of the spin-splitting can determine whether an antiferromagnetic or ferromagnetic alignment of the impurity spins is preferred by the RKKY interaction. Moreover, the Ising and Heisenberg terms of the RKKY interaction alternate on being the dominant term and their magnitudes oscillate as a function of distance between the impurities.

Magnetic impurities at quantum critical points: Large- N expansion and connections to symmetry-protected topological states

Motivated by recent studies of symmetry protected topological states that are stabilized even in the absence of an energy gap, the authors study analytically the interaction of a (0+1)$D$ impurity spin, which in some cases may be viewed as a topological state bound to a lattice defect, with a (2+1)$D$ strongly interacting bulk, composed of bosonic excitations tuned to a quantum critical point. The question of whether the spin is (partially) screened is addressed within the framework of four different models, using mainly the large-$N$ technique. The authors also point out intriguing connections with the physics of the Sachdev-Ye-Kitaev model.

Differentiating Hund from Mott physics in a three-band Hubbard-Hund model: Temperature dependence of spectral, transport, and thermodynamic properties

We study the interplay between Mott physics, driven by Coulomb repulsion U, and Hund physics, driven by Hund's coupling J, for a minimal model for Hund metals, the orbital-symmetric three-band Hubbard-Hund model (3HHM) for a lattice filling of 1/3. Hund-correlated metals are characterized by spin-orbital separation (SOS), a Hund's-rule-induced two-stage Kondo-type screening process, in which spin screening occurs at much lower energy scales than orbital screening. By contrast, in Mott-correlated metals, lying close to the phase boundary of a metal-insulator transition, the SOS window becomes negligibly small and the Hubbard bands are well separated. Using dynamical mean-field theory and the numerical renormalization group as real-frequency impurity solver, we identify numerous fingerprints distinguishing Hundness from Mottness in the temperature dependence of various physical quantities. These include ARPES-type spectra, the local self-energy, static local orbital and spin susceptibilities, resistivity, thermopower, and lattice and impurity entropies. Our detailed description of the behavior of these quantities within the context of a simple model Hamiltonian will be helpful for distinguishing Hundness from Mottness in experimental and theoretical studies of real materials.

Quantum chaos of the Bose-Fermi Kondo model at intermediate temperature

We study the quantum chaos in the Bose-Fermi Kondo model in which the impurity spin interacts with conduction electrons and a bosonic bath at the intermediate temperature in the large-$N$ limit. The out-of-time-ordered correlator is calculated based on the Bethe-Salpeter equation and the Lyapunov exponent ${\ensuremath{\lambda}}_{L}$ is extracted. Our calculation shows that the Lyapunov exponent monotonically increases as the Kondo coupling ${J}_{K}$ increases, and it can reach an order of ${\ensuremath{\lambda}}_{L}\ensuremath{\approx}T$ as ${J}_{K}$ approaches the multichannel Kondo fixed point ($MCK$). Furthermore, we also demonstrate that ${\ensuremath{\lambda}}_{L}$ decreases monotonically as the impurity and bosonic bath coupling $g$ increases, which is contrary to the general expectation that the most chaotic property occurs at the quantum critical point with the non-Fermi-liquid nature.

Electron spin and donor impurity effects on the absorption spectra of pseudo-elliptic quantum rings under magnetic field

ABSTRACT We investigated comparatively the electronic and optical properties of GaAs/GaAlAs pseudo-elliptic quantum rings with donor impurity under magnetic field in the absence and the presence of electron spin, taken into account through Rashba and Dresselhaus spin–orbit couplings and Zeeman effect. The energy and absorption spectra were computed for four representative positions of the donor impurity (edges and x(y)-middle of the ring). Both approaches demonstrate the important role played by the impurity position, with the strongest effects corresponding to the impurity placed in the middle of the ring. In the spin absence, the impurity position influences both the energies of the absorption peaks and their oscillatory behaviours in energy and amplitude. In the presence of electron spin, the absorption spectra of the pseudo-elliptic quantum ring become more complex at large magnetic fields as the number of transitions is increased by the splitting of the energy levels and present new distinct features at low and high energies that could be observed experimentally.