Two-channel Kondo Effect Research Articles

Many-Body Quantum Interference Route to the Two-Channel Kondo Effect: Inverse Design for Molecular Junctions and Quantum Dot Devices.

Molecular junctions-whether actual single molecules in nanowire break junctions or artificial molecules realized in coupled quantum dot devices-offer unique functionality due to their orbital complexity, strong electron interactions, gate control, and many-body effects from hybridization with the external electronic circuit. Inverse design involves finding candidate structures that perform a desired function optimally. Here we develop an inverse design strategy for generalized quantum impurity models describing molecular junctions, and as an example, use it to demonstrate that many-body quantum interference can be leveraged to realize the two-channel Kondo critical point in simple 4- or 5-site molecular moieties. We show that remarkably high Kondo temperatures can be achieved, meaning that entropy and transport signatures should be experimentally accessible.

Quantum-interference origin and magnitude of 1/f noise in Dirac nodal line IrO2 nanowires at low temperatures

We present 1/f noise measurements of IrO2 nanowires from 1.7 to 350 K. Results reveal that the noise magnitude (represented by Hooge parameter γ) increases at low temperatures, indicating low-frequency resistance noise from universal conductance fluctuations. The cause of this noise is determined to be due to oxygen vacancies in the rutile structure of IrO2. Additionally, the number density of these mobile defects can be calculated from the T resistance rise caused by the two-channel Kondo effect in the Dirac nodal line metal IrO2.

High-performance non-Fermi-liquid metallic thermoelectric materials

Searching for high-performance thermoelectric (TE) materials in the paradigm of narrow-bandgap semiconductors is hampered by a bottleneck. Here we report on the discovery of metallic compounds, TiFexCu2x−1Sb and TiFe1.33Sb, showing the thermopower exceeding many TE semiconductors and the dimensionless figure of merits zTs comparable with the state-of-the-art TE materials. A quasi-linear temperature (T) dependent electrical resistivity in 2–700 K and the logarithmic T-dependent electronic specific heat at low temperature coexist with the high thermopower, highlighting the strong intercoupling of the non-Fermi-liquid (NFL) quantum critical behavior of electrons with TE transports. Electronic structure analysis reveals a competition between the antiferromagnetic (AFM) ordering and Kondo-like spin compensation as well as a parallel two-channel Kondo effect. The T-dependent magnetic susceptibility agrees with the quantum critical scenario of strong local correlation. Our work demonstrates the correlation among high TE performance, NFL quantum criticality, and magnetic fluctuation, which opens up directions for future research.

Inelastic neutron scattering study of crystalline electric field excitations in the caged compounds NdT2Zn20 (T=Co, Rh, and Ir)

We have measured crystalline electric field (CEF) excitations of Nd3+ ions in the two-channel Kondo lattice candidates NdT2Zn20 (T = Co, Rh, and Ir) by means of inelastic neutron scattering (INS). In the INS measurements at 5 K, dispersionless excitations were observed at 3.8 and 7.2 meV for T = Co, 3.1 and 5.8 meV for T = Rh, and 3.0 and 5.3 meV for T = Ir. Analyses of the temperature dependence of the INS spectra confirm that the CEF ground states are the Gamma 6 doublet, that is a requisite for manifestation of the magnetic two-channel Kondo effect. For T = Co, a shoulder was observed at 7.7 meV close to the CEF excitation peak centered at 7.2 meV. The shoulder is attributed to a bound state of the CEF and low-lying optical phonon excitations.

Destructive interference and Fano antiresonance in T-shaped double quantum dots coupled to Luttinger liquid leads

We investigate the interplay of quantum interference effects and the electronic correlation on the transport through T-shaped spinless double quantum dots coupled to Luttinger liquid leads by using the nonequilibrium Green's function method. We find that the weak intralead Coulomb interaction leads to a zero-bias antiresonance dip in the differential conductance for small interdot tunneling coupling, which is distinct destructive interference characteristic. In particular, an intriguing Fano antiresonance profile for asymmetrically coupling to the Luttinger liquid leads is exhibited, consistent with the experiment findings but different physics screening origin. The strong intralead Coulomb interaction or large interdot coupling tunneling quenches the quantum interference effects, resulting in the disappearance of Fano antiresonance. The scaling behavior of differential conductance on temperature is presented for different intralead interactions. The relationship between destructive interference and two-channel Kondo effect is given. Our results provide a way of adjusting in and out of antiresonance to achieve quantum interference transistors and of switching by tuning the gate voltage controlling the interdot tunneling. • The interplay of interference and intralead Coulomb interaction on transport of T-shaped quantum dots is studied. • Weak intralead interaction leads to zero-bias dip in differential conductance for small interdot tunneling. • New physical mechanism is presented to explain for the antiresonance dip and Fano effect. • Scaling behavior of differential conductance on temperature is presented for different intralead interactions.

Emergence of orbital two-channel Kondo effect in epitaxial TiN thin films

The continual scaledown and stringent defect control in electronic devices are opening up frontiers in Kondo effect-a powerful testbed for probing magnetic impurity coupling to a continuum of electronic states. In disordered ferromagnets, degenerate quantum states like two-level systems (TLS) with a pseudo-half spin can couple with the continuum to mimic Kondo physics, creating the orbital two-channel Kondo (2CK) effect below the characteristic Kondo temperature (TK). By employing vacuum-annealing to inject ∼12 at.% nitrogen vacancies (VN) in TiN1-x films, we generated room-temperature ferromagnetic ordering with 13.6 emu g−1 saturation magnetization. The transport characteristics exhibited non-Fermi-liquid (NFL) behavior below TK of 20.2 K. The orbital 2CK effect is signified by a clear transition from logarithmic (T < T0∼40 K), to square-root dependence (T < TK) and subsequent deviation from it (T < TD∼10 K) in resistivity upturn behavior in three distinct low-temperature regimes. By controlling VN, we establish the necessity of ferromagnetism and ultrafast tunneling centers for generating orbital 2CK effect and NFL behavior in disordered metallic systems, extending their scope in non-magnetic nanomaterials.

Spectroscopic evidence for the direct involvement of local moments in the pairing process of the heavy-fermion superconductor CeCoIn5

The microscopic mechanism for electron pairing in heavy-fermion superconductors remains a major challenge in quantum materials. Some form of magnetic mediation is widely accepted with spin fluctuations as a prime candidate. A novel mechanism, 'composite pairing' based on the cooperative two-channel Kondo effect directly involving the f-electron moments has also been proposed for some heavy fermion compounds including CeCoIn$_5$. The origin of the spin resonance peak observed in neutron scattering measurements on CeCoIn$_5$ is still controversial and the corresponding hump-dip structure in the tunneling conductance is missing. This is in contrast to the cuprate and Fe-based high-temperature superconductors, where both characteristic signatures are observed, indicating spin fluctuations are likely involved in the pairing process. Here, we report results from planar tunneling spectroscopy along three major crystallographic orientations of CeCoIn5 over wide ranges of temperature and magnetic field. The pairing gap opens at T$_p$ ~ 5 K, well above the bulk T$_c$ = 2.3 K, and its directional dependence is consistent with d$_{x^2-y^2}$ symmetry. With increasing magnetic field, this pairing gap is suppressed as expected but, intriguingly, a gaplike structure emerges smoothly, increasing linearly up to the highest field applied. This field-induced gaplike feature is only observed below T$_p$. The concomitant appearance of the pairing gap and the field-induced gaplike feature, along with its linear increase with field, indicates that the f-electron local moments are directly involved in the pairing process in CeCoIn$_5$.

Quantum Critical Point between Two-Channel Kondo and Fermi-Liquid Phases

We investigate the emergence of quantum critical points near a two-channel Kondo phase by evaluating an $f$-electron entropy of a seven-orbital impurity Anderson model hybridized with three ($\Gamma_7$ and $\Gamma_8$) conduction bands with the use of a numerical renormalization group method First we consider the case of Pr$^{3+}$ ion, in which quadrupole two-channel Kondo effect is known to occur for the local $\Gamma_3$ doublet state. When we control crystalline electric field (CEF) potentials so as to change the local CEF ground state from $\Gamma_3$ doublet to $\Gamma_1$ singlet or $\Gamma_5$ triplet, we commonly observe a residual entropy of $\log \phi$ with the golden ratio $\phi=(1+\sqrt{5})/2$, which is equal to that for three-channel Kondo effect. This peculiar residual entropy is also observed for the case of Nd$^{3+}$ ion, in which magnetic two-channel Kondo phase is found to occur for the local $\Gamma_6$ doublet state. We envisage a scenario that the quantum critical point characterized by $\log \phi$ generally appears between two-channel Kondo and Fermi-liquid phases.

Oxygen vacancy-driven orbital multichannel Kondo effect in Dirac nodal line metals IrO2 and RuO2

Strong electron correlations have long been recognized as driving the emergence of novel phases of matter. A well recognized example is high-temperature superconductivity which cannot be understood in terms of the standard weak-coupling theory. The exotic properties that accompany the formation of the two-channel Kondo (2CK) effect, including the emergence of an unconventional metallic state in the low-energy limit, also originate from strong electron interactions. Despite its paradigmatic role for the formation of non-standard metal behavior, the stringent conditions required for its emergence have made the observation of the nonmagnetic, orbital 2CK effect in real quantum materials difficult, if not impossible. We report the observation of orbital one- and two-channel Kondo physics in the symmetry-enforced Dirac nodal line (DNL) metals IrO2 and RuO2 nanowires and show that the symmetries that enforce the existence of DNLs also promote the formation of nonmagnetic Kondo correlations. Rutile oxide nanostructures thus form a versatile quantum matter platform to engineer and explore intrinsic, interacting topological states of matter.

Low-temperature resistivity anomaly and weak spin disorder in Co2MnGa epitaxial thin films

The topological material of $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnGa}$ with potentially high spin polarization has attracted more and more attention, in the fields of fundamental science and spintronic applications. Here we report the electrical- and magnetotransport behaviors in epitaxial $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnGa}$ thin films. An angle-independent negative linear magnetoresistance and a negative anisotropy magnetoresistance are observed in the whole temperature range from 3 to 300 K, indicating the existence of weak spin disorder and a high spin polarization. Intriguingly, with decreasing temperature an anomalous resistivity upturn that exhibits $\ensuremath{-}{T}^{1/2}$ dependence is observed, and this phenomenon is robust under magnetic fields. Further analysis demonstrates that the three-dimensional enhanced electron-electron interaction effect is responsible for these phenomena rather than the orbital two-channel Kondo effect or other quantum interference effects, which provides deeper insight into the transport behavior of the $\mathrm{C}{\mathrm{o}}_{2}\mathrm{MnGa}$ materials.

Neutron Scattering Studies on 4f2-Electron Multipoles in Pr-based Systems

The degrees of freedom of electron multipoles in various rare-earth alloy compounds have been investigated over the last four decades. Recently, it has been found that the multipole orderings accompany exotic transport properties, metal–insulator transitions, superconductivity, heavy fermions, a two-channel Kondo effect, etc. In the present article, neutron scattering studies on the ordering phenomena of the degrees of freedom of multipoles in several Pr-based cubic compounds are reviewed, which are associated with the relevant magnetic or nonmagnetic wave functions of the crystal-electric-field levels of the 4f2 configuration and their hybridization with conduction electrons.

Influence of orbital two-channel Kondo effect on anomalous Hall effect in ferrimagnetic composites of LaNiO3 and CoFe2O4

In this report, we have investigated the magnetoresistance (MR) and Hall effect of the ferrimagnetic composites containing LaNiO3 and CoFe2O4 (CFO) (with CFO content 15% and 20%) which exhibit orbital two-channel Kondo (2CK) effect and therefore pronounced resistivity upturn at low temperature. Both composites manifest a negative to positive crossover in MR with increasing temperature. The MR is described by the Khosla and Fisher model of spin fluctuations scattering of conduction electrons and the two-band theory based on hybridized p-d sub-bands. The Hall resistivity of the composites consists of both ordinary and anomalous part. The negative sign of the ordinary Hall coefficient suggests electrons as the dominating charge carriers. The coefficient of anomalous Hall resistivity () follows the scaling relation () with longitudinal resistivity () at high temperature above the resistivity upturn. However, at low temperature shows non-monotonous behaviour and deviates from the scaling relation where orbital 2CK effect takes place. More detailed study below the resistivity upturn of the composite with 20% CFO reveals that this deviation occurs around the Kondo temperature. This breakdown of scaling relation around the Kondo temperature indicates the possible influence of orbital 2CK on the anomalous Hall effect.

Cubic hastatic order in the two-channel Kondo-Heisenberg model

Materials with non-Kramers doublet ground states naturally manifest the two-channel Kondo effect, as the valence fluctuations are from a non-Kramers doublet ground state to an excited Kramers doublet. Here, the development of a heavy Fermi liquid requires a channel symmetry breaking spinorial hybridization that breaks both single and double time-reversal symmetry, and is known as hastatic order. Motivated by cubic Pr-based materials with $\Gamma_3$ non-Kramers ground state doublets, this paper provides a survey of cubic hastatic order using the simple two-channel Kondo-Heisenberg model. Hastatic order necessarily breaks time-reversal symmetry, but the spatial arrangement of the hybridization spinor can be either uniform (ferrohastatic) or break additional lattice symmetries (antiferrohastatic). The experimental signatures of both orders are presented in detail, and include tiny conduction electron magnetic moments. Interestingly, there can be several distinct antiferrohastatic orders with the same moment pattern that break different lattice symmetries, revealing a potential experimental route to detect the spinorial nature of the hybridization. We employ an SU(N) fermionic mean-field treatment on square and simple cubic lattices, and examine how the nature and stability of hastatic order varies as we vary the Heisenberg coupling, conduction electron density, band degeneracies, and apply both channel and spin symmetry breaking fields. We find that both ferrohastatic and several types of antiferrohastatic orders are stabilized in different regions of the mean-field phase diagram, and evolve differently in strain and magnetic fields.

Tuning spin one channel to exotic orbital two-channel Kondo effect in ferrimagnetic composites of LaNiO3 and CoFe2O4

We report the tuning from spin one channel to orbital two-channel Kondo (2CK) effect by varying CoFe2O4 (CFO) content in the composites with LaNiO3 (LNO) along with the presence of ferrimagnetism. Although there is no signature of resistivity upturn in the case of pure LNO, all the composites exhibit a distinct upturn in the temperature range of 30–80 K. For composites with lower percentage of CFO (10%), the electron spin plays the key role in the emergence of resistivity upturn which is affected by external magnetic field. On the other hand, when the CFO content is increased (⩾15%), the upturn shows strong robustness against high magnetic field (⩽14 T) and a crossover in temperature variation from to T1/2 at the Kondo temperature, indicating the appearance of orbital 2CK effect. The orbital 2CK effect originates due to the scattering of conduction electrons from the structural two-level systems which is created at the interfaces between the two phases (LNO and CFO) of different crystal structures as well as inside the crystal planes. The specific heat data at low temperature (⩽40 K), deviates from the usual linear temperature variation of the electronic contribution. With higher CFO content it shows more deviation which also indicates the increasing amount of two-level system. A negative magnetoresistance (MR) is observed at low temperature (<30 K) for composites containing both lower (10%) and higher percentage (15%) of CFO. We have analyzed the negative MR using Khosla and Fisher semi-empirical model based on spin dependent scattering of conduction electrons from localized spins.

Charge Fractionalization in the Two-Channel Kondo Effect.

The phenomenon of charge fractionalization describes the emergence of novel excitations with fractional quantum numbers, as predicted in strongly correlated systems such as spin liquids. We elucidate that precisely such an unusual effect may occur in the simplest possible non-Fermi liquid, the two-channel Kondo effect. To bring this concept down to experimental test, we study nonequilibrium transport through a device realizing the charge two-channel Kondo critical point in a recent experiment by Iftikhar etal. [Nature (London) 526, 233 (2015)NATUAS0028-083610.1038/nature15384]. The shot noise at low voltages is predicted to result in a universal Fano factor e^{*}/e=1/2. This allows us to experimentally identify elementary transport processes of emergent fermions carrying half-integer charge.

Origin of the −|A|T1/2 term in the resistivity of disordered ZrAs1.58Se0.39

Recently, Cichorek et al. have analyzed the magnetic-field-independent $\ensuremath{-}|A|{T}^{1/2}$ term in the resistivity of disordered ${\mathrm{ZrAs}}_{1.58}{\mathrm{Se}}_{0.39}$ within the Altshuler-Arononv model of electron-electron interaction in the presence of disorder [Phys. Rev. Lett. 117, 106601 (2016)]. Making the assumption that diffusion of conduction electrons in this compound is isotropic, they could not get quantitative agreement between the considered model and the experimental results. This led the authors to conclude that the singular ${T}^{1/2}$ contribution to the resistivity of ${\mathrm{ZrAs}}_{1.58}{\mathrm{Se}}_{0.39}$ could not be caused by electron-electron interaction but could only be explained by a two-channel Kondo effect. Here, we perform a detailed analysis of the $\ensuremath{-}|A|{T}^{1/2}$ correction to the resistivity of disordered ${\mathrm{ZrAs}}_{1.58}{\mathrm{Se}}_{0.39}$ using analogous Altshuler-Aronov relation but taking into account that the diffusion coefficient in the tetragonal ${\mathrm{ZrAs}}_{1.58}{\mathrm{Se}}_{0.39}$ is anisotropic. For the considered resistivity anisotropy, we found that the calculated values of the $A$ coefficient are in very good agreement with those derived from the resistivity measurements. Moreover, analysis indicates that the values of the screening parameter ${\ensuremath{\lambda}}^{(j=1)}$ are close to zero, which satisfies the condition that the $A$ coefficient does not depend on magnetic field. This shows that the magnetic-field-independent $\ensuremath{-}|A|{T}^{1/2}$ correction to the resistivity of disordered ${\mathrm{ZrAs}}_{1.58}{\mathrm{Se}}_{0.39}$ can be explained within the electron-electron interaction scenario in disordered metallic systems.

Topological Majorana Two-Channel Kondo Effect.

A one-dimensional time-reversal-invariant topological superconductor hosts a Majorana Kramers pair at each end, where time-reversal symmetry acts as a supersymmetry that flips local fermion parity. We examine the transport anomaly of such a superconductor, floating and tunnel-coupled to normal leads at its two ends. We demonstrate the realization of a topologically protected, channel-symmetric, two-channel Kondo effect without fine-tuning. Whereas the nonlocal teleportation vanishes, a lead present at one end telecontrols the universal transport through the other end.

Electrical Transport of Perpendicularly Magnetized L10-MnGa and MnAl Films

Ferromagnetic films of [Formula: see text]-ordered MnGa and MnAl that exhibit giant perpendicular magnetic anisotropy and great controllability in the magnetism and structural disorders show promising applications not only in magnetic recording, permanent magnets and spintronics, but also in controllable studies of disorder-relevant electrical transport phenomena. In this paper, we review the intriguing experimental observations of the orbital two-channel Kondo effect and anomalous Hall effect in [Formula: see text]-ordered MnGa and MnAl thin films with perpendicular magnetic anisotropy. We also give a perspective with regards to the future technological and fundamental applications of these perpendicularly magnetized Mn-based binary alloy films.

Comparative studies of the cage systems ThFe2Al10 and UFe2Al10

We have grown single crystals of ThFe2Al10 and used them for the refinement of its crystal structure. From the specific heat data, we determined the phonon components, that is, the Debye and Einstein modes, for Th- and U-based isostructural aluminides. To approximate the Sommerfeld coefficients, we had to include the T3lnT term characteristic of spin-fluctuations originating from the Fe-sublattice. The roughly estimated spin-fluctuation temperature is about 11 K. ThFe2Al10 is a weakly temperature-dependent Pauli-paramagnet. However, at lower temperatures the ferromagnetic correlations are observed, which signals that the system drives to quantum criticality. The distinct minimum in electrical resistivity observed at about 20 K suggests a realization of a nonmagnetic two-channel Kondo-effect in ThFe2Al10, as discussed for ThAsSe [Phys. Rev. Lett. 94, 236603 (2005)], for example. The [ρ(T) – ρmin] versus T curves of ThFe2Al10, determined along the a- and c-axes, were used to subtract the phonon contributions from the corresponding ρ(T)a,c of UFe2Al10. The resulting magnetic part of the average ρm(T)av curve was then analysed in terms of the influence of the crystal field effect on the transport properties. However, to obtain agreement with the experiment, we had to take into account another effect, namely the Kondo-like one. This kind of probe has been applied for the first time in the case of uranium compounds. Based on the magnetoresistivity, we have revealed the anisotropic low-frequency vibrations of the Th atom (located in its [Al16Fe4] cage) interacting with the conduction band, the phenomenon revealed previously in the metallic UB12 [Phil. Mag. B 95, 2343 (2015)]. Furthermore, fully relativistic band structure calculations performed for ThFe2Al10 revealed its metallic-like character with a similarly large contribution of the Fe 3d electrons at the Fermi level as predicted previously for its 5f-electron analogue UFe2Al10. In addition, there are substantial differences between their Fermi surfaces.

Two-Channel Kondo Effect Emerging from Nd Ions

We discuss Kondo phenomena in a seven-orbital impurity Anderson model hybridized with $\Gamma_8$ conduction electrons by employing a numerical renormalization group method. In particular, we focus on the case with three local $f$ electrons, corresponding to a Nd$^{3+}$ ion. For realistic values of Coulomb interactions, spin-orbit coupling, cubic crystalline electric field potentials, and hybridization, we find a residual entropy of $0.5\log 2$, a characteristic of two-channel Kondo phenomena, for the wide range of parameters of the local $\Gamma_6$ ground state. This is considered to be the magnetic two-channel Kondo effect, consistent with the result from an extended $s$-$d$ model constructed on the basis of the $j$-$j$ coupling scheme. Finally, we briefly discuss candidates of Nd compounds to observe the two-channel Kondo effect.