Kondo Singlet Research Articles

Coherent exchange-coupled nonlocal Kondo impurities

Quantum dots exhibit a variety of strongly correlated effects, e.g., they can emulate localized magnetic impurities that form a Kondo singlet with their surrounding environment. Interestingly, in double-dot setups, such magnetic impurities couple to each other by direct Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, which wins over the Kondo physics. In this work, we investigate a double-dot device where the dots are coupled via off-resonant ballistic modes, dubbed electronic cavity modes. Within this cavity-double-dot system, we study, using variational matrix product state techniques, the competition between Kondo formation and the combined coherent orbital hybridization and RKKY-like interaction that the cavity facilitates. Specifically, we find that Kondo can form on each dot individually whereby the cavity can either (i) destroy the Kondo via the RKKY that mediates a singlet state on the two dots, or (ii) lead to an exotic orbital macrsoscopic superposition of the Kondo forming on each of the dots. We dub the latter “Kondo cat”. En route to this key finding, we rigorously study the many-body phase diagram of the system, as well as compare it with the case of coupling the dots via an incoherent RKKY channel. The realization of a Kondo cat can facilitate applications in metrology, and reveal the spin coherence length in mesoscopic devices. Published by the American Physical Society 2024

Yu-Shiba-Rusinov states assisted by asymmetric Coulomb repulsion in a bipartite molecular device

Interfacing magnetism with superconducting condensates are promising candidates holding Majorana bound states with which fault-tolerant quantum computation could be implemented. Within this field, understanding the detailed dynamics is important both for fundamental reasons and for the development of innovative quantum technologies. Herein, motivated by a molecular magnet Tb2Pc3 interacting with a superconducting Pb(111) substrate, which results in spin-orbital Yu-Shiba-Rusinov (YSR) states, as is affirmed by a theoretical simulation with the aid of the numerical renormalization group technique (see Xia et al 2022 Nat. Commun. 13 6388), we study the YSR states and quantum phase transitions (QPTs) in a bipartite molecular device adsorbed on an wave superconducting substrate. We highlight the effect of asymmetric Coulomb repulsion by computing the spectrum function and spin correlation function in various parameter regimes. We demonstrate that if one impurity is non-interacting, there are no YSR states in both impurities with any repulsion value in the other impurity. Whereas if the repulsion in one impurity is strong, the YSR states are observed in both impurities, and a QPT arises as the repulsion in the other impurity sweeps, assisted by the competition between the superconducting singlet (Cooper pair) and the Kondo singlet. The evolution of YSR states distinguishes from the single impurity case and can be well interpreted by the energy scales of the isotropic superconducting gap parameter, as well as the two Kondo temperatures. Our findings provide theoretical insights into the phase diagram of two magnetic impurities on a superconducting host and shine light on the effects induced by asymmetric Coulomb repulsion on many-body interactions.

Theoretical Investigation of Localized- and Itinerant Character of 4f Electron in Ce Intermetallics by Means of 3d-4f Resonant Inelastic X-ray Scattering

In order to show characteristic features in core-level spectroscopy, reflecting the localized- or itinerant nature of 4f electrons in Ce intermetallics, 3d x-ray photoemission spectroscopy, 3d x-ray absorption spectroscopy and 3d-4f resonant inelastic x-ray scattering (RIXS) are theoretically investigated for CeIn3 and CeSn3 with the AuCu3-type crystal structure. In this study, considering energy-band effects based on first-principles calculation within local density approximation, we employ an impurity Anderson model with full multiplet coupling. Moreover, in order to make a quantitative discussion, the basis configurations describing electron–hole pair creation are also included in the calculation within the configuration interaction scheme, which have been often neglected as a first approximation in previous studies. By comparing the calculated results for CeIn3 and CeSn3, we find two advantages of 3d-4f RIXS for a quantitative investigation of Ce intermetallics: (i) we can observe directly a binding energy in Kondo singlet formation by choosing proper polarization geometry of incident photons, and (ii) we can investigate an itinerant component related to Kondo singlet formation of Ce intermetallics by adjusting energy and polarization of incident photons.

Towards a comprehensive theory of metal–insulator transitions in doped semiconductors

A review is given on the theory of metal–insulator transitions (MIT) in doped semiconductors. We focus in particular on reviewing theories of their anomalous magnetic properties, which emerge from the interplay of spin and charge correlations and disorder. Building on the review of these existing theories and experiments, we suggest that the finite temperature phase diagram can be structured into 1. a quantum spin liquid phase at subcritical doping and low temperature, as described by the Bhatt–Lee theory of random spin clusters, mostly random singlets. 2. a critical non-Fermi-liquid fan, originating at the MIT, which is dominated by random Kondo singlets with a universal tail of the distribution of their binding energies. This is caused by multifractality and results in an anomalous power law divergence of the magnetic susceptibility with a universal power and 3. a supercritical, low temperature phase. Rare events caused by the random placement of dopants do not allow to define strict phase boundaries. Remaining open problems are reviewed and outlined. Finally, the possibility of finite temperature delocalization transitions is reviewed, which are caused by the correlation induced temperature dependence of the spin scattering rate from magnetic moments. This review article is devoted to the memory of Konstantin B. Efetov.

Enhancement of the Kondo effect in a quantum dot formed in a full-shell nanowire

We analyze results of a recent experiment [D. Razmadze et al., Phys. Rev. Lett., 125, 116803 (2020)] on transport through a quantum dot between two full-shell nanowires and show that the observed effects are caused by the Kondo effect enhancement due to a nontrivial geometry (magnetic flux in a full-shell nanowire) rather than the presence of Majorana bound states. Moreover, we propose that such a setup presents a unique and convenient system to study the competition between superconductivity and the Kondo effect and has significant advantages in comparison to other known approaches, as the important parameter is controlled by the magnetic flux through the full-shell nanowire, which can be significantly varied with small changes of magnetic field, and does not require additional gates. This competition is of fundamental interest as it results in a quantum phase transition between an unscreened doublet and a many-body Kondo singlet ground states of the system.

Quantum spin liquid in an RKKY-coupled two-impurity Kondo system

We consider a 2-impurity Kondo system with spin-exchange coupling within the conduction band. Our numerical renormalization group calculations show that for strong intraband spin correlations the competition of these correlations with Kondo spin screening stabilizes a metallic spin-liquid phase of the localized spins without geometric frustration. For weak Kondo coupling the spin liquid and the Kondo singlet phase are separated by two quantum phase transitions and an intermediate RKKY spin-dimer phase, while beyond a critical coupling they are connected by a crossover. The results suggest how a quantum spin liquid may be realized in heavy-fermion systems near a spin-density wave instability.

Ferromagnetism in the SU( N ) Kondo lattice model: SU( N ) double exchange and supersymmetry

We study the ground-state properties of the SU(N)-generalization of the Kondo-lattice model in one dimension when the Kondo coupling J_K (both ferromagnetic and antiferromagnetic) is sufficiently strong. Both cases can be realized using alkaline-earth-like cold gases in optical lattices. Specifically, we first carry out the strong-coupling expansion and identify two insulating phases (one of which is the SU(N)-analogue of the well-known gapped Kondo singlet phase). We then rigorously establish that the ground state in the low-density (for J_K<0) or the high-density (for J_K>0) region is ferromagnetic. The results are accounted for by generalizing the double-exchange mechanism to SU(N) "spins". Possible realizations of Bose-Fermi supersymmetry SU(N|1) in the (generalized) SU(N) Kondo-lattice model are discussed as well.

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.

Low-temperature theory of inversion and quantum oscillations in Kondo insulators

The half-filled Kondo lattice model is studied at low temperatures on a simple cubic lattice using the self-consistent theory developed by Ram and Kumar [Phys. Rev. B 96, 075115 (2017)]. It is found to have three distinct insulating phases in the temperature-hopping plane, namely, the strong-coupling Kondo singlet (KS) phase, the inverted Kondo singlet (iKS) phase distinguished from the KS by inversion, and the antiferromagnetic (AFM) phase. The quasiparticle density of states across the inversion transition is noted to exhibit a dimensional reduction, which can differentiate between the KS and iKS insulators in experiments. Magnetic quantum oscillations obtained in the iKS and AFM phases are found to show a Lifshitz-Kosevich-like behavior with temperature as well as quantum fluctuations induced by the Kondo interaction.

Spin-orbit coupling and Kondo resonance in the Co adatom on the Cu(100) surface: DFT plus exact diagonalization study

We report density functional theory plus exact diagonalization of the multiorbital Anderson impurity model calculations for the Co adatom on the top of a Cu(001) surface. For the Co atom $d$-shell occupation ${n}_{d}\ensuremath{\approx}8$, a singlet many-body ground state and Kondo resonance are found, when the spin-orbit coupling is included in the calculations. The differential conductance is evaluated in good agreement with the scanning tunneling microscopy measurements. The results illustrate the essential role which the spin-orbit coupling is playing in the formation of a Kondo singlet for the multiorbital impurity in low dimensions.

Entanglement-based observables for quantum impurities

Quantum impurities exhibit fascinating many-body phenomena when the small interacting impurity changes the physics of a large noninteracting environment. The characterisation of such strongly correlated non-perturbative effects is particularly challenging due to the infinite size of the environment, and the inability of local correlators to capture the build-up of long-ranged entanglement in the system. Here, we harness an entanglement-based observable - the purity of the impurity - as a witness for the formation of strong correlations. We showcase the utility of our scheme by exactly solving the open Kondo box model in the small box limit, and thus describe all-electronic dot-cavity devices. Specifically, we conclusively characterise the metal-to-insulator phase transition in the system and identify how the (conducting) dot-lead Kondo singlet is quenched by an (insulating) intra-impurity singlet formation. Furthermore, we propose an experimentally feasible tomography protocol for the measurement of the purity, which motivates the observation of impurity physics through their entanglement build-up.

Entropy Measurement of a Strongly Coupled Quantum Dot.

The spin 1/2 entropy of electrons trapped in a quantum dot has previously been measured with great accuracy, but the protocol used for that measurement is valid only within a restrictive set of conditions. Here, we demonstrate a novel entropy measurement protocol that is universal for arbitrary mesoscopic circuits and apply this new approach to measure the entropy of a quantum dot hybridized with a reservoir. The experimental results match closely to numerical renormalization group (NRG) calculations for small and intermediate coupling. For the largest couplings investigated in this Letter, NRG calculations predict a suppression of spin entropy at the charge transition due to the formation of a Kondo singlet, but that suppression is not observed in the experiment.

Renormalization approach to the superconducting Kondo model

An approach to bound states based on unitary transformations of Hamiltonians is presented. The method is applied to study the interaction between electrons in a BCS s-wave superconductor and a quantum spin. It is shown that known results from the t-matrix method and numerical studies are reproduced by this new method. As a main advantage, the method can straightforwardly be extended to study the topological properties of combined bound states in chains of many magnetic impurities. It also provides a uniform picture of the interplay between the Yu-Shiba-Rusinov (YSR) bound states and the Kondo singlet state.

Kondo screening cloud in a superconductor with mixed s-wave and p-wave pairing states

We study the Kondo screening of a spin-1/2 magnetic impurity coupled to a superconductor, which is fabricated by combination of an s-wave superconductor, a ferromagnet and a semiconductor with Rashba spin–orbit coupling (RSOC). The proximity induced superconducting states include the s-wave and p-wave pairing components with the aids of RSOC, and the ferromagnet induces a Zeeman field which removes the spin degeneracy of the quasiparticles in the triplet states. Thus, the Kondo screening of magnetic impurity involves the orbital degrees of freedom, and is also affected by the Zeeman field. Using the variational method, we calculate the binding energy and the spin–spin correlation between the magnetic impurity and the electrons in the coexisting s-wave and p-wave pairing states. We find that Kondo singlet forms more easily with stronger RSOC, but Zeeman field in general decreases the binding energy. The spin–spin correlation decays fast in the vicinity of the magnetic impurity. Due to the RSOC, the spatial spin–spin correlation becomes highly anisotropic, and the Zeeman field can induce extra asymmetry to the off-diagonal components of the spin–spin correlation. Our study can offer some insights into the studies of extrinsic topological superconductors fabricated from the hybrid structures containing chains of magnetic impurities.

Dynamic transport characteristics of side-coupled double-quantum-impurity systems

A systematic study is performed on time-dependent dynamic transport characteristics of a side-coupled double-quantum-impurity system based on the hierarchical equations of motion. It is found that the transport current behaves like a single quantum dot when the coupling strength is low during tunneling or Coulomb coupling. For the case of only tunneling transition, the dynamic current oscillates due to the temporal coherence of the electron tunneling device. The oscillation frequency of the transport current is related to the step voltage applied by the lead, while temperature T, electron–electron interaction U and the bandwidth W have little influence. The amplitude of the current oscillation exists in positive correlation with W and negative correlation with U. With the increase in coupling t 12 between impurities, the ground state of the system changes from a Kondo singlet of one impurity to a spin singlet of two impurities. Moreover, lowering the temperature could promote the Kondo effect to intensify the oscillation of the dynamic current. When only the Coulomb transition is coupled, it is found that the two split-off Hubbard peaks move upward and have different interference effects on the Kondo peak at the Fermi surface with the increase in U 12, from the dynamics point of view.

Kondo effect in a spin-3/2 Fermi gas

We investigate the Kondo effect of a spin-3/2 Fermi gas and give a detailed calculation of the impurity resistance and ground state energy based on the s-d exchange model. It is found that the impurity resistance increases logarithmically with the decrease of temperature in the case of antiferromagnetic coupling similar to the spin-1/2 system but has a larger resistance minimum value due to the increase of spin scattering channels. In the case of antiferromagnetic interaction, the ground state is still the Kondo singlet state while the septuplet state has the lowest energy for ferromagnetic coupling. And with the same antiferromagnetic s-d coupling parameter, the energy of the Kondo singlet state is lower than spin-1/2, which indicates that the larger spin, the easier it is to enter the Kondo-screened phase. This provides some theoretical support for the realization of the Kondo effect with ultra-cold atoms.

Channel order in the two-channel Kondo lattice

We discuss the two-channel Kondo lattice model where a single localized spin per unit cell is coupled to two different conduction electron orbitals per unit cell. The calculation is done using the bond fermion formalism. For a Hamiltonian which is symmetric under exchange of the conduction channels we find a spontaneous breaking of this symmetry, i.e., the Kondo singlets are formed almost exclusively between the localized spin and only one of the two conduction orbitals. In addition to this channel-ferromagnetic phase we also find a channel-antiferromagnetic phase where the preferred conduction electron orbital alternates between sublattices. The parameter which determines the transition between these phases is the interchannel hybridization.

Two-impurity Kondo effect in potassium-doped single-layer p-sexiphenyl films

Herein, we show that a self-assembled phase of potassium (K)-doped single-layer para-sexiphenyl (PSP) film on a gold substrate is an excellent platform for studying the two-impurity Kondo model. On K-doped PSP molecules well separated from others, we observe a Kondo resonance peak close to EF with a Kondo temperature of 30 K. The Kondo resonance peak splits when another K-doped PSP molecule is present in the vicinity, and the splitting gradually increases with the decrease in intermolecular distance without signs of phase transition. Our data demonstrate how a Kondo singlet state gradually evolves into an antiferromagnetic singlet state due to the competition between Kondo screening and antiferromagnetic Ruderman-Kittel-Kasuya-Yosida coupling, as described in the two-impurity Kondo model. Intriguingly, the antiferromagnetic singlet is quickly destroyed on increasing temperature and transforms back to a Kondo singlet below the Kondo temperature. Our data provide a comprehensive picture and quantitative constraints on related theories and calculations of the two-impurity Kondo model.

Pressure-induced concomitant topological and metal-insulator quantum phase transitions in Ce3Pd3Bi4

The electronic property and magnetic susceptibility of Ce3Pd3Bi4 were systemically investigated from 18 to 290 K for varying values of cell volume using dynamic mean-field theory coupled with density functional theory. By extrapolating to zero temperature, the ground state of Ce3Pd3Bi4 at ambient pressure is found to be a correlated semimetal due to insufficient hybridization. Upon applying pressure, the hybridization strength increases and a crossover to the Kondo insulator is observed at finite temperatures. The characteristic temperature signaling the formation of Kondo singlet, as well as the characteristic temperature associated with f-electron delocalization–localization change, simultaneously vanishes around a critical volume of 0.992 V0, suggesting that such metal–insulator transition is possibly associated with a quantum critical point. Finally, Wilson’s loop calculations indicate that the Kondo insulating side is topologically trivial, thus a topological transition also occurs across the quantum critical point.

Spiral magnetism and chiral superconductivity in a Kondo-Hubbard triangular lattice model

Building on the results of Ref. \cite{faye2018phase}, which identified an antiferromagnetic and Kondo singlet phases on the Kondo-Hubbard square lattice, we use the variational cluster approximation (VCA) to investigate the competition between these phases on a two-dimensional triangular lattice with $120^{o}$ spin orientation. In addition to the antiferromagnetic exchange interaction $J_{\perp}$ between the localized (impurity) and conduction (itinerant) electrons, our model includes the local repulsion $U$ of the conduction electrons and the Heisenberg interaction $J_H$ between the impurities. At half-filling, we obtain the quantum phase diagrams in both planes $(J_{\perp}, U J_{\perp})$ and $(J_{\perp}, J_{H})$. We identify a long-range, three-sublattice, spiral magnetic order which dominates the phase diagrams for small $J_{\perp}$ and moderate $U$, while a Kondo singlet phase becomes more stable at large $J_{\perp}$. The transition from the spiral magnetic order to the Kondo singlet phase is a second-order phase transition. In the $(J_{\perp}, J_{H})$ plane, we observe that the effect of $J_H$ is to reduce the Kondo singlet phase, giving more room to the spiral magnetic order phase. It also introduces some small magnetic oscillations of the spiral magnetic order parameter. At finite doping and when spiral magnetism is ignored, we find superconductivity with symmetry order parameter $d+id$, which breaks time reversal symmetry. The superconducting order parameter has a dome centered at around $5\%$ hole doping, and its amplitude decreases with increasing $J_{\perp}$. We show that spiral magnetism can coexist with $d+id$ state and that superconductivity is suppressed, indicating that these two phases are in competition.