Kondo-correlated Quantum Dots Research Articles

Magnetic-Field Universality of the Kondo Effect Revealed by Thermocurrent Spectroscopy.

Probing the universal low-temperature magnetic-field scaling of Kondo-correlated quantum dots via electrical conductance has proved to be experimentally challenging. Here, we show how to probe this in nonlinear thermocurrent spectroscopy applied to a molecular quantum dot in the Kondo regime. Our results demonstrate that the bias-dependent thermocurrent is a sensitive probe of universal Kondo physics, directly measures the splitting of the Kondo resonance in a magnetic field, and opens up possibilities for investigating nanosystems far from thermal and electrical equilibrium.

Erratum: Magnetic field dependence of the thermopower of Kondo-correlated quantum dots: Comparison with experiment [Phys. Rev. B 100 , 155126 (2019)

Erratum: Magnetic field dependence of the thermopower of Kondo-correlated quantum dots: Comparison with experiment [Phys. Rev. B <b>100</b> , 155126 (2019)

Three-body correlations in nonlinear response of correlated quantum liquid

Behavior of quantum liquids is a fascinating topic in physics. Even in a strongly correlated case, the linear response of a given system to an external field is described by the fluctuation-dissipation relations based on the two-body correlations in the equilibrium. However, to explore nonlinear non-equilibrium behaviors of the system beyond this well-established regime, the role of higher order correlations starting from the three-body correlations must be revealed. In this work, we experimentally investigate a controllable quantum liquid realized in a Kondo-correlated quantum dot and prove the relevance of the three-body correlations in the nonlinear conductance at finite magnetic field, which validates the recent Fermi liquid theory extended to the non-equilibrium regime.

Magnetic field dependence of the thermopower of Kondo-correlated quantum dots: Comparison with experiment

Signatures of the Kondo effect in the electrical conductance of strongly correlated quantum dots are well understood both experimentally and theoretically, while those in the thermopower have been the subject of recent interest. Here, we extend theoretical work [T. A. Costi, Phys. Rev. B {\bf 100}, 161106(R) (2019)] on the field-dependent thermopower of such systems, and carry out calculations in order to address a recent experiment on the field dependent thermoelectric response of Kondo-correlated quantum dots [A. Svilans {\em et al.,} Phys. Rev. Lett. {\bf 121}, 206801 (2018)]. In addition to the sign changes in the thermopower at temperatures $T_1(B)$ and $T_2(B)$ (present also for $B=0$) in the Kondo regime, an additional sign change was found [T. A. Costi, Phys. Rev. B {\bf 100}, 161106(R) (2019)] at a temperature $T_0(B)<T_1(B)<T_2(B)$ for fields exceeding a gate-voltage dependent value $B_0$, where $B_0$ is comparable to, but larger, than the field $B_c$ at which the Kondo resonance splits. We describe the evolution of the Kondo-induced sign changes in the thermopower at temperatures $T_0(B),T_1(B)$ and $T_2(B)$ with magnetic field and gate voltage from the Kondo regime to the mixed valence and empty orbital regimes. By carrying out detailed NRG calculations for the above quantities we address the recent experiment by A. Svilans {\em et al.,} Phys. Rev. Lett. {\bf 121}, 206801 (2018), which measures the field-dependent thermoelectric response of InAs quantum dots exhibiting the Kondo effect, finding good agreement for the overall trends in the measured field- and temperature-dependent thermoelectric response as a function of gate voltage.

Magnetic field dependence of the thermopower of Kondo-correlated quantum dots

Recent experiments have measured the signatures of the Kondo effect in the zero-field thermopower of strongly correlated quantum dots [Svilans {\em et al.,} Phys. Rev. Lett. {\bf 121}, 206801 (2018); Dutta {\em et al.,} Nano Lett. {\bf 19}, 506 (2019)]. They confirm the predicted Kondo-induced sign change in the thermopower, upon increasing the temperature through a gate-voltage dependent value $T_{1}\gtrsim T_{\rm K}$, where $T_{\rm K}$ is the Kondo temperature. Here, we use the numerical renormalization group (NRG) method to investigate the effect of a finite magnetic field $B$ on the thermopower of such quantum dots. We show that, for fields $B$ exceeding a gate-voltage dependent value $B_{0}$, an additional sign change takes place in the Kondo regime at a temperature $T_{0}(B\geq B_{0})>0$ with $T_0<T_1$. The field $B_{0}$ is comparable to, but larger than, the field $B_{c}$ at which the zero-temperature spectral function splits in a magnetic field. The validity of the NRG results for $B_{0}$ are checked by comparison with asymptotically exact higher-order Fermi-liquid calculations [Oguri {\em et al.,} Phys. Rev. B {\bf 97}, 035435 (2018)]. Our calculations clarify the field-dependent signatures of the Kondo effect in the thermopower of Kondo-correlated quantum dots and explain the recently measured trends in the $B$-field dependence of the thermoelectric response of such systems [Svilans {\em et al.,} Phys. Rev. Lett. {\bf 121}, 206801 (2018)].

Thermoelectric Characterization of the Kondo Resonance in Nanowire Quantum Dots.

We experimentally verify hitherto untested theoretical predictions about the thermoelectric properties of Kondo correlated quantum dots (QDs). The specific conditions required for this study are obtained by using QDs epitaxially grown in nanowires, combined with a recently developed method for controlling and measuring temperature differences at the nanoscale. This makes it possible to obtain data of very high quality both below and above the Kondo temperature, and allows a quantitative comparison with theoretical predictions. Specifically, we verify that Kondo correlations can induce a polarity change of the thermoelectric current, which can be reversed either by increasing the temperature or by applying a magnetic field.

Nanomechanical Characterization of the Kondo Charge Dynamics in a Carbon Nanotube

Using the transversal vibration resonance of a suspended carbon nanotube as a charge detector for its embedded quantum dot, we investigate the case of strong Kondo correlations between a quantum dot and its leads. We demonstrate that even when large Kondo conductance is carried at odd electron number, the charging behavior remains similar between odd and even quantum dot occupations. While the Kondo conductance is caused by higher order processes, a sequential tunneling only model can describe the time-averaged charge. The gate potentials of the maximum current and fastest charge increase display a characteristic relative shift, which is suppressed at increased temperature. These observations agree very well with models for Kondo-correlated quantum dots.

Leading temperature dependence of the conductance in Kondo-correlated quantum dots

Using renormalized perturbation theory in the Coulomb repulsion, we derive an analytical expression for the leading term in the temperature dependence of the conductance through a quantum dot described by the impurity Anderson model, in terms of the renormalized parameters of the model. Taking these parameters from the literature, we compare the results with published ones calculated using the numerical renormalization group obtaining a very good agreement. The approach is superior to alternative perturbative treatments. We compare in particular to the results of a simple interpolative perturbation approach.

Quantum Fluctuations along Symmetry Crossover in a Kondo-Correlated Quantum Dot.

Universal properties of entangled many-body states are controlled by their symmetry and quantum fluctuations. By the magnetic-field tuning of the spin-orbital degeneracy in a Kondo-correlated quantum dot, we have modified quantum fluctuations to directly measure their influence on the many-body properties along the crossover from SU(4) to SU(2) symmetry of the ground state. High-sensitive current noise measurements combined with the nonequilibrium Fermi liquid theory clarify that the Kondo resonance and electron correlations are enhanced as the fluctuations, measured by the Wilson ratio, increase along the symmetry crossover. Our achievement demonstrates that nonlinear noise constitutes a measure of quantum fluctuations that can be used to tackle quantum phase transitions.

Low-temperature behavior of transmission phase shift across a Kondo correlated quantum dot

We study the transmission phase shift across a Kondo correlated quantum dot in a GaAs heterostructure at temperatures below the Kondo temperature ($T < T_{\rm K}$), where the phase shift is expected to show a plateau at $\pi/2$ for an ideal Kondo singlet ground state. Our device is tuned such that the ratio $\Gamma/U$ of level width $\Gamma$ to charging energy $U$ is quite large ($\lesssim 0.5$ rather than $\ll 1$). This situation is commonly used in GaAs quantum dots to ensure Kondo temperatures large enough ($\simeq 100$ mK here) to be experimentally accessible; however it also implies that charge fluctuations are more pronounced than typically assumed in theoretical studies focusing on the regime $\Gamma/U \ll 1$ needed to ensure a well-defined local moment. Our measured phase evolves monotonically by $\pi$ across the two Coulomb peaks, but without being locked at $\pi/2$ in the Kondo valley for $T \ll T_{\rm K}$, due to a significant influence of large $\Gamma/U$. Only when $\Gamma/U$ is reduced sufficiently does the phase start to be locked around $\pi/2$ and develops into a plateau at $\pi/2$. Our observations are consistent with numerical renormalization group calculations, and can be understood as a direct consequence of the Friedel sum rule that relates the transmission phase shift to the local occupancy of the dot, and thermal average of a transmission coefficient through a resonance level near the Fermi energy.

Competition between Kondo Screening and Quantum Hall Edge Reconstruction.

We report on a Kondo correlated quantum dot connected to two-dimensional leads where we demonstrate the renormalization of the g factor in the pure Zeeman case. i.e., for magnetic fields parallel to the plane of the quantum dot. For the same system, we study the influence of orbital effects by investigating the quantum Hall regime; i.e., a perpendicular magnetic field is applied. In this case an unusual behavior of the suppression of the Kondo effect and of the split zero-bias anomaly is observed. The splitting decreases with magnetic field and shows discontinuous changes that are attributed to the intricate interplay between Kondo screening and the quantum Hall edge structure originating from electrostatic screening. This edge structure, made up of compressible and incompressible stripes, strongly affects the Kondo temperature of the quantum dot and thereby influences the renormalized g factor.

Robust electron pairing in the integer quantum hall effect regime.

Electron pairing is a rare phenomenon appearing only in a few unique physical systems; for example, superconductors and Kondo-correlated quantum dots. Here, we report on an unexpected electron pairing in the integer quantum Hall effect regime. The pairing takes place within an interfering edge channel in an electronic Fabry-Perot interferometer at a wide range of bulk filling factors, between 2 and 5. We report on three main observations: high-visibility Aharonov-Bohm conductance oscillations with magnetic flux periodicity equal to half the magnetic flux quantum; an interfering quasiparticle charge equal to twice the elementary electron charge as revealed by quantum shot noise measurements, and full dephasing of the pairs' interference by induced dephasing of the adjacent inner edge channel-a manifestation of inter-channel entanglement. Although this pairing phenomenon clearly results from inter-channel interaction, the exact mechanism that leads to electron-electron attraction within a single edge channel is not clear. We believe that substantial efforts are needed in order to clarify these intriguing and unexpected findings.

Transmission phase in the Kondo regime revealed in a two-path interferometer.

We report on the direct observation of the transmission phase shift through a Kondo correlated quantum dot by employing a new type of two-path interferometer. We observed a clear π/2-phase shift, which persists up to the Kondo temperature TK. Above this temperature, the phase shifts by more than π/2 at each Coulomb peak, approaching the behavior observed for the standard Coulomb blockade regime. These observations are in remarkable agreement with two-level numerical renormalization group calculations. The unique combination of experimental and theoretical results presented here fully elucidates the phase evolution in the Kondo regime.

Reply to “Comment on ‘Conductance scaling in Kondo-correlated quantum dots: Role of level asymmetry and charging energy’”

The Comment of A. A. Aligia claims that the superperturbation theory (SPT) approach [E. Mu\~noz, C. J. Bolech, and S. Kirchner, Phys. Rev. Lett. 110, 016601 (2013)] formulated using dual fermions [A. N. Rubtsov, M. I. Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 77, 033101 (2008)] and used by us to compare with numerical renormalization group (NRG) results for the conductance [L. Merker, S. Kirchner, E. Mu\~noz, and T. A. Costi, Phys. Rev. B 87, 165132 (2013)], fails to correctly extend the results of the symmetric Anderson impurity model (SIAM) for general values of the local level ${E}_{d}$ in the Kondo regime. We answer this criticism. We also compare new NRG results for ${c}_{B}$, with ${c}_{B}$ calculated directly from the low-field conductance, with new higher-order SPT calculations for this quantity, finding excellent agreement for all ${E}_{d}$ and for $U/\ensuremath{\pi}\ensuremath{\Delta}$ extending into the strong coupling regime.

Comment on “Conductance scaling in Kondo-correlated quantum dots: Role of level asymmetry and charging energy”

In a recent work [L. Merker, S. Kirchner, E. Munoz, and T. A. Costi, Phys. Rev. B 87, 165132 (2013)], the authors compared results of numerical renormalization group and a perturbative approach for the dependence on temperature T and magnetic field B of the conductance through a quantum dot described by the impurity Anderson model, for small T and B. We show that the equation used to extract the dependence on B from NRG results is incorrect out of the particle-hole symmetric case. As a consequence, in the Kondo regime, the correct NRG results have a weaker dependence on B and the disagreement between both approaches increase.

Mesoscopic features in the transport properties of a Kondo-correlated quantum dot in a magnetic field

We study the transport behavior induced by a small bias voltage through a quantum dot connected to one-channel finite-size wires. We describe the quantum dot using the Hubbard–Anderson impurity model and we obtain solutions by means of a quantum Monte Carlo method. We investigate the effect of a magnetic field applied at the quantum dot in the Kondo regime. We identify mesoscopic oscillations in the conductance, which are introduced by the magnetic field. This behavior is analogous to that observed as a function of the temperature.

Spin-dependent thermoelectric properties of a Kondo-correlated quantum dot with Rashba spin–orbit coupling

Thermoelectric transport phenomena in a single-level quantum dot coupled to ferromagnetic leads are considered theoretically in the Kondo regime. The dot is described by the Anderson model with Rashba type spin–orbit interactions. The finite-U mean field slave boson technique is used to describe transport characteristics, such as the heat conductance, thermopower and thermoelectric efficiency (figure of merit). The role of quantum interference effects in the thermoelectric parameters is also analyzed.

Thermoelectric and Interference Effects in a Kondo-Correlated Quantum Dot with Rashba Spin-Orbit Coupling

Thermoelectric e ects in spin-polarized transport through a strongly correlated quantum dot coupled to two ferromagnetic leads is investigated theoretically by means of the nite-U slave boson technique. The dot is coupled to the leads both symmetrically via the spin-conserving tunneling processes and asymmetrically via spin-nonconserving Rashba-induced tunneling terms. The asymmetric coupling leads to various interference e ects which modify transport properties. We have analyzed such thermoelectric coe cients like the electronic contribution to heat conductance κ, thermopower S, and thermoelectric e ciency ZT .

Comment on “Universal Out-of-Equilibrium Transport in Kondo-Correlated Quantum Dots: Renormalized Dual Fermions on the Keldysh Contour”

It is shown that the lesser and greater self energies and Green functions calculated in a recent work on universal noequilibrium transport in interacting quantum dots [E. Mu\~noz, C. J. Bolech, and S. Kirchner, Phys. Rev. Lett. 110, 016601 (2013)] are incorrect. The authors start from renormalized second-order perturbation theory in the Coulomb repulsion in the particle-hole symmetric impurity Anderson model. The reported lesser self-energy is compared with the correct one, and with an analytic result valid for small frequency and applied voltage. As a consequence of the mistakes, the conservation of the current is not established and the results are unreliable.

Conductance scaling in Kondo-correlated quantum dots: Role of level asymmetry and charging energy

The low temperature electrical conductance through correlated quantum dots provides a sensitive probe of the physics (e.g., of Fermi-liquid vs non-Fermi-liquid behavior) of such systems. Here, we investigate the role of level asymmetry (gate voltage) and local Coulomb repulsion (charging energy) on the low temperature and low field scaling properties of the linear conductance of a quantum dot described by the single level Anderson impurity model. We use the numerical renormalization group to quantify the regime of gate voltages and charging energies where universal Kondo scaling may be observed and also quantify the deviations from this universal behavior with increasing gate voltage away from the Kondo regime and with decreasing charging energy. We also compare our results with those from a recently developed method for linear and non-linear transport, which is based on renormalized perturbation theory using dual fermions, finding excellent agreement at particle-hole symmetry and for all charging energies and reasonable agreement at small finite level asymmetry. Our results could be a useful guide for detailed experiments on conductance scaling in semiconductor and molecular quantum dots exhibiting the Kondo effect.