SU(2) and SU(4) Kondo effect in double quantum dots (original) (raw)
Analysis of low energy response and possible emergent SU(4) Kondo state in a double quantum dot
2013
We examine the low energy behavior of a double quantum dot in a regime where spin and pseudospin excitations are degenerate. The individual quantum dots are described by Anderson impurity models with an on-site interaction U which are capacitively coupled by an interdot interaction U12 < U . The low energy response functions are expressed in terms of renormalized parameters, which can be deduced from an analysis of the fixed point in a numerical renormalization group calculation. At the point where the spin and pseudospin degrees of freedom become degenerate, the free quasiparticle excitations have a phase shift of π/4 and a 4-fold degeneracy. We find, however, when the quasiparticle interactions are included, that the low energy effective model has SU(4) symmetry only in the special case U12 = U , contrary to the claims in previous studies. We show that the gate voltage dependence of the temperature dependent differential conductance observed in recent experiments can be described by a quasiparticle density of states with temperature dependent renormalized parameters.
Kondo effect in double quantum dots with interdot repulsion
Physical Review B, 2006
We investigate a symmetrical double quantum dot system serially attached to the leads. The emphasis is on the numerical analysis of finite inter-dot tunneling in the presence of inter-dot repulsive capacitive coupling. The results reveal the competition between extended Kondo phases and local singlet phases in spin and charge degrees of freedom. The corresponding phase diagram is determined quantitatively.
From spin and orbital SU(4) to spin SU(2) Kondo effect in double quantum dot
arXiv: Mesoscale and Nanoscale Physics, 2007
We consider spin and orbital Kondo effect in a parallel arrangement of two strongly electrostatically coupled quantum dots. Increasing the exchange of electrons between the dots through the attached leads induces a smooth crossover between SU(4) spin- and orbital Kondo effect and SU(2) spin Kondo effect. Being the same for the SU(4) and SU(2) symmetry points, the Kondo temperature drops slightly in the intermediate regime. Experimentally, two kinds of Kondo effect can be discriminated by the sensitivity to the suppression of the spin Kondo effect by Zeeman field. The dependence of the Kondo temperature and of the differential conductance on the strength of electronic exchange through the leads and Zeeman fi eld is analyzed in detail. PACS: 73.23.-b, 73.63.Kv, 72.15.Qm
Orbital and spin Kondo effects in a double quantum dot
Europhysics Letters (EPL), 2001
Motivated by recent experiments, in which the Kondo effect has been observed for the first time in a double quantum-dot structure, we study electron transport through a system consisting of two ultrasmall, capacitively-coupled dots with large level spacing and charging energy. Due to strong interdot Coulomb correlations, the Kondo effect has two possible sources, the spin and orbital degeneracies, and it is maximized when both occur simultaneously. The large number of tunable parameters allows a range of manipulations of the Kondo physics-in particular, the Kondo effect in each dot is sensitive to changes in the state of the other dot. For a thorough account of the system dynamics, the linear and nonlinear conductance is calculated in perturbative and non-perturbative approaches. In addition, the temperature dependence of the resonant peak heights is evaluated in the framework of a renormalization group analysis.
O ct 2 00 7 From spin and orbital SU ( 4 ) to spin SU ( 2 ) Kondo effect in double quantum dot
2021
We consider spin and orbital Kondo effect in a parallel arrangement of two strongly electrostatically coupled quantum dots. Increasing the exchange of electrons between the dots through the attached leads induces a smooth crossover between SU(4) spinand orbital Kondo effect and SU(2) spin Kondo effect. Being the same for the SU(4) and SU(2) symmetry points, the Kondo temperature drops slightly in the intermediate regime. Experimentally, two kinds of Kondo effect can be discriminated by the sensitivity to the suppression of the spin Kondo effect by Zeeman field. The dependence of the Kondo temperature and of the differential conductance on the strength of electronic exchange through the leads and Zeeman field is analyzed in detail.
SU(4) Kondo effect in double quantum dots with ferromagnetic leads
Physical Review B, 2018
We investigate the spin-resolved transport properties, such as the linear conductance and the tunnel magnetoresistance, of a double quantum dot device attached to ferromagnetic leads and look for signatures of SU (4) symmetry in the Kondo regime. We show that the transport behavior greatly depends on the magnetic configuration of the device, and the spin-SU (2) as well as the orbital and spin-SU (4) Kondo effects become generally suppressed when the magnetic configuration of the leads varies from the antiparallel to the parallel one. Furthermore, a finite spin polarization of the leads lifts the spin degeneracy and drives the system from the SU (4) to an orbital-SU (2) Kondo state. We analyze in detail the crossover and show that the Kondo temperature between the two fixed points has a non-monotonic dependence on the degree of spin polarization of the leads. In terms of methods used, we characterize transport by using a combination of analytical and numerical renormalization group approaches.
Observation of the SU(4) Kondo state in a double quantum dot
2013
A. J. Keller, S. Amasha1,†, I. Weymann, C. P. Moca, I. G. Rau1,‡, J. A. Katine, Hadas Shtrikman, G. Zaránd, and D. Goldhaber-Gordon Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA 94305, USA Faculty of Physics, Adam Mickiewicz University, Poznań, Poland BME-MTA Exotic Quantum Phases “Lendület” Group, Institute of Physics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary Department of Physics, University of Oradea, 410087, Romania HGST, San Jose, CA 95135, USA Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 96100, Israel †Present address: MIT Lincoln Laboratory, Lexington, MA 02420, USA ‡Present address: IBM Research – Almaden, San Jose, CA 95120, USA Corresponding author; goldhaber-gordon@stanford.edu
Emergent SU(4) Kondo physics in a spin–charge-entangled double quantum dot
Nature Physics, 2013
Central to condensed matter physics are quantum impurity models, which describe how a local degree of freedom interacts with a continuum. Surprisingly, these models are often universal in that they can quantitatively describe many outwardly unrelated physical systems. Here we develop a double quantum dot-based experimental realization of the SU(4) Kondo model, which describes the maximally symmetric screening of a local fourfold degeneracy. As demonstrated through transport measurements and detailed numerical renormalization group calculations, our device affords exquisite control over orbital and spin physics. Because the two quantum dots are coupled only capacitively, we can achieve orbital state-or "pseudospin"-resolved bias spectroscopy, providing intimate access to the interplay of spin and orbital Kondo effects. This cannot be achieved in the few other systems realizing the SU(4) Kondo state.
Towards two-channel Kondo effect in triple quantum dot
Europhysics Letters (EPL), 2003
The effective spin Hamiltonian of a triple quantum dot with odd electron occupation weakly connected in series with left (l) and right (r) metal leads is composed of two-channel exchange and co-tunneling terms. Renormalization group equations for the corresponding three exchange constants J l , Jr and J lr are solved (to third order). Since J lr is relevant, the system is mapped on an anisotropic two-channel Kondo problem. The structure of the conductance as function of temperature and gate voltage implies that in the weak and intermediate coupling regimes, twochannel Kondo physics persists at temperatures as low as several TK. At even electron occupation, the number of channels equals twice the spin of the triple dot (hence it is a fully screened impurity).
SU(4) Kondo entanglement in double quantum dot devices
Physical Review B, 2017
We analyze, from a quantum information theory perspective, the possibility of realizing an SU(4) entangled Kondo regime in semiconductor double quantum dot devices. We focus our analysis on the ground state properties and consider the general experimental situation where the coupling parameters of the two quantum dots differ. We model each quantum dot with an Anderson type Hamiltonian including an interdot Coulomb repulsion and tunnel couplings for each quantum dot to independent fermionic baths. We find that the spin and pseudospin entanglements can be made equal, and the SU(4) symmetry recovered, if the gate voltages are chosen in such a way that the average charge occupancies of the two quantum dots are equal, and the double occupancy on the double quantum dot is suppressed. We present density matrix renormalization group numerical results for the spin and pseudospin entanglement entropies, and analytical results for a simplified model that captures the main physics of the problem.
Kondo effect in triple quantum dots
Physical Review B, 2006
Numerical analysis of the simplest odd-numbered system of coupled quantum dots reveals an interplay between magnetic ordering, charge fluctuations and the tendency of itinerant electrons in the leads to screen magnetic moments. The transition from local-moment to molecular-orbital behavior is visible in the evolution of correlation functions as the inter-dot coupling is increased. Resulting novel Kondo phases are presented in a phase diagram which can be sampled by measuring the zero-bias conductance. We discuss the origin of the even-odd effects by comparing with the double quantum dot.
Pseudo-spin Kondo effect versus hybridized molecular states in parallel Double Quantum Dots
2003
A two quantum-dot device is coupled in parallel for studying the competition between the pseudo-spin Kondo effect and strongly hybridized molecular states. Cryogenic measurements are performed in the regime of weak coupling of the two dots to lead states under linear transport conditions. Detailed simulations verify the finding of the transition between the two different regimes.
Two-channel Kondo physics in tunnel-coupled double quantum dots
Physical Review B, 2011
We investigate theoretically the possibility of observing two-channel Kondo (2CK) physics in tunnel-coupled double quantum dots (TCDQDs), at both zero and finite magnetic fields; taking the two-impurity Anderson model (2AIM) as the basic TCDQD model, together with effective low-energy models arising from it by Schrieffer-Wolff transformations to second and third order in the tunnel couplings. The models are studied primarily using Wilson's numerical renormalization group. At zero-field our basic conclusion is that while 2CK physics arises in principle provided the system is sufficiently strongly-correlated, the temperature window over which it could be observed is much lower than is experimentally feasible. This finding disagrees with recent work on the problem, and we explain why. At finite field, we show that the quantum phase transition known to arise at zero-field in the two-impurity Kondo model (2IKM), with an essentially 2CK quantum critical point, persists at finite fields. This raises the prospect of access to 2CK physics by tuning a magnetic field, although preliminary investigation suggests this to be even less feasible than at zero field.
Quantum phase transition in a two-channel-Kondo quantum dot device
Physical Review B, 2004
We develop a theory of electron transport in a double quantum dot device recently proposed in Ref. 1 for the observation of the two-channel Kondo effect. Our theory provides a strategy for tuning the device to the non-Fermi-liquid fixed point, which is a quantum critical point in the space of device parameters. We explore the corresponding quantum phase transition, and make explicit predictions for behavior of the differential conductance in the vicinity of the quantum critical point.
Transport in coupled quantum dots: Kondo effect versus antiferromagnetic correlation
Physical Review B, 2000
The interplay between the Kondo effect and the inter-dot magnetic interaction in a coupled-dot system is studied. An exact result for the transport properties at zero temperature is obtained by diagonalizing a cluster, composed by the double-dot and its vicinity, which is connected to leads. It is shown that the system goes continuously from the Kondo regime to an anti-ferromagnetic state as the inter-dot interaction is increased. The conductance, the charge at the dots and the spin-spin correlation are obtained as a function of the gate potential.
Spintronic transport and Kondo effect in quantum dots
2005
We investigate the spin-dependent transport properties of quantum-dot based structures where Kondo correlations dominate the electronic dynamics. The coupling to ferromagnetic leads with parallel magnetizations is known to give rise to nontrivial effects in the local density of states of a single quantum dot. We show that this influence strongly depends on whether charge fluctuations are present or absent in the dot. This result is confirmed with numerical renormalization group calculations and perturbation theory in the on-site interaction. In the Fermi-liquid fixed point, we determine the correlations of the electric current at zero temperature (shot noise) and demonstrate that the Fano factor is suppressed below the Poissonian limit for the symmetric point of the Anderson Hamiltonian even for nonzero lead magnetizations. We discuss possible avenues of future research in this field: coupling to the low energy excitations of the ferromagnets (magnons), extension to double quantum dot systems with interdot antiferromagnetic interaction and effect of spin-polarized currents on higher symmetry Kondo states such as SU(4).
Kondo effect in a double quantum-dot molecule under the effect of an electric and magnetic field
Solid State Communications, 2003
Electron tunneling through a double quantum dot molecule, in the Kondo regime, under the effect of a magnetic field and an applied voltage, is studied. This system possesses a complex response to the applied fields characterized by a tristable solution for the conductance. The different nature of the solutions are studied in and out thermodynamical equilibrium. It is shown that the interdot coupling and the fields can be used to control the region of multistability. The mean-field slave-boson formalism is used to obtain the solution of the problem. PACS numbers: PACS number(s): 73.21.La; 73.63.Kv; 85.35.Be
Kondo effect in side coupled double quantum-dot molecule
Solid State Communications, 2005
Electron tunneling through a double quantum dot molecule side attached to a quantum wire, in the Kondo regime, is studied. The mean-field finite-U slave-boson formalism is used to obtain the solution of the problem. We found conductance cancelations when the molecular energies of the side attached double quantum-dot cross the Fermi energy. We investigate the many body molecular Kondo states as a function of the parameters of the system.
Conductance signatures of Kondo interference and quantum criticality in double quantum dots
arXiv (Cornell University), 2008
We study the linear conductance through a double-quantum-dot system consisting of an interacting dot in its Kondo regime and an effectively noninteracting dot, connected in parallel to metallic leads. Signatures in the zero-bias conductance at temperatures T > 0 mark a pair of quantum (T = 0) phase transitions between a Kondo-screened many-body ground state and non-Kondo ground states. Notably, the conductance features become more prominent with increasing T , which enhances the experimental prospects for accessing the quantum-critical region through tuning of gate voltages in a single device.
Physical Review B, 2005
We investigate the nonequilibrium transport properties of a three-terminal quantum dot in the strongly interacting limit. At low temperatures, a Kondo resonance arises from the antiferromagnetic coupling between the localized electron in the quantum dot and the conduction electrons in source and drain leads. It is known that the local density of states is accessible through the differential conductance measured at the (weakly coupled) third lead. Here, we consider the multiterminal current-current correlations (shot noise and cross correlations measured at two different terminals). We discuss the dependence of the current correlations on a number of external parameters: bias voltage, magnetic field and magnetization of the leads. When the Kondo resonance is split by fixing the voltage bias between two leads, the shot noise shows a nontrivial dependence on the voltage applied to the third lead. We show that the cross correlations of the current are more sensitive than the conductance to the appearance of an external magnetic field. When the leads are ferromagnetic and their magnetizations point along opposite directions, we find a reduction of the cross correlations. Moreover, we report on the effect of dephasing in the Kondo state for a two-terminal geometry when the third lead plays the role of a fictitious voltage probe.