### Analysis of low energy response and possible emergent SU(4) Kondo state in a double quantum dot

**Authors:**Y. Nishikawa, A.C. Hewson, D.J. G. Crow and J. Bauer

**submitted to**Physical Review B (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 pi/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 unless both U and U12 are greater than D, the half-bandwidth of the conduction electron bath. 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.

arXiv:1309.1715 Available on Cond-Mat Archive### Hund’s rule coupling in models of magnetic impurities and quantum dots

**Authors:**Y. Nishikawa and A.C. Hewson

**published in**Physical Review B**86**245131 (2012)

different models have led to quite different predictions for the Kondo temperature TK as a function of JH. We show that the differences depend on whether or not the models conserve orbital angular momentum about the impurity site. Using numerical renormalization-group calculations, we deduce the renormalized parameters for the Fermi liquid regime and show that, despite the differences between the models, the low-energy fixed point in the strong-correlation regime is universal, with a single energy scale TK and just two renormalized interaction parameters, a renormalized single orbital term, ˜U = 4TK, and a renormalized Hund’s rule term, J˜H = 8TK/3.

arXiv:1211.0363 Available on Cond-Mat Archive### Phase diagram and critical points of a double quantum dot

**Authors:**Y. Nishikawa, D.J.G. Crow and A.C. Hewson

**published in**Physical Review B**86**125134 (2012)

We apply a combination of numerical renormalization group (NRG) and renormalized perturbation theory (RPT) to a model of two quantum dots (impurities) described by two Anderson impurity models hybridized to their respective baths. The dots are coupled via a direct Coulomb interaction $U_{12}$ and a spin exchange interaction $J$. The model has two types of quantum critical points, one at $J=J_c$ to a local singlet state and one at $U_{12}=U_{12}^c$ to a locally charge ordered state. The renormalized parameters which determine the low energy behavior are calculated from the NRG. The results confirm the values predicted from the RPT on the approach to the critical points, which can be expressed in terms of a single energy scale $T^*$ in all cases. This includes cases without particle-hole symmetry, and cases with asymmetry between the dots, where there is also a transition at $J=J_c$. The results give a comprehensive quantitative picture of the behavior of the model in the low energy Fermi liquid regimes, and some of the conclusions regarding the emergence of a single energy scale may apply to a more general class of quantum critical points, such as those observed in some heavy fermion systems.

Available on Cond-Mat Archive### Full counting statistics for orbital-degenerate impurity Anderson model with Hund's rule exchange coupling

**Authors:**Rui Sakano, Yunori Nishikawa, Akira Oguri, Alex C. Hewson, and Seigo Tarucha

**published in:**Physical Review Letters**108**266401 (2012)

We study non-equilibrium current fluctuations through a quantum dot, which includes a ferromagnetic Hund’s rule coupling J, in the low-energy Fermi liquid regime using the renormalized perturbation theory. The resulting cumulant for the current distribution in the particle-hole symmetric case, shows that spin-triplet and Kondo-spin-singlet pairs of quasiparticles are formed in the current due to the Hund’s rule coupling and these pairs enhance the current fluctuations. In the fully screened higher-spin Kondo limit, the Fano factor takes a value Fb = (9M + 6)=(5M + 4) determined by the orbital degeneracy M. We also investigate the crossover between the small and large J limits in the two-orbital case M = 2, using the numerical renormalization group approach.

Available on Cond-Mat Archive### Kondo effects in a triangular triple quantum dot: Numerical renormalization group study in the whole region of the electron filling

**Authors:**A. Oguri, S. Amaha, Y. Nishikawa, T. Numata, M. Shimamoto, A.C. Hewson and S. Tarucha

**published in**Physical Review B**83**205304 (2011)

We study the low-energy properties and characteristic Kondo energy scale of a triangular triple quantum dot, connected to two non-interacting leads, in a wide parameter range of a gate voltage and distortions which lower the symmetry of an equilateral structure, using the numerical renormalization group approach. For large Coulomb interactions, the ground states with different characters can be classified according to the plateaus of Theta = (delta(e) - delta(o))(2/pi), where delta(e) and delta(o) are the phase shifts for the even and odd partial waves. At these plateaus of Theta, both Theta and the occupation number Ntot = (delta(e) + delta(o))(2/pi) take values close to integers, and thus the ground states can be characterized by these two integers. The Kondo effect with a local moment with total spin S = 1 due to a Nagaoka mechanism appears on the plateau, which can be identified by Theta approximately equals 2.0 and Ntot approximately equals 4.0. For large distortions, however, the high-spin moment disappears through a singlet-triplet transition occurring within the four-electron region. It happens at a crossover to the adjacent plateaus for Theta approximately equals 0.0 and Theta approximately equals 4.0, and the two-terminal conductance has a peak in the transient regions. For weak distortions, the SU(4) Kondo effect also takes place for Ntot approximately equals 3.0. It appears as a sharp conductance valley between the S = 1/2 Kondo ridges on both sides. We also find that the characteristic energy scale Tstar reflect these varieties of the Kondo effect. Particularly, Tstar is sensitive to the distribution of the charge and spin in the triangular triple dot.

Available on Cond-Mat Archive### Gate-voltage dependence of the Kondo effect in a triangular quantum dot

**Authors:**T. Numata, Y. Nisikawa, A. Oguri, A. C. Hewson

**published in:**J. Phys.: Conference Series**150**022067 (2009)

This ia a study the conductance through a triangular triple quantum dot, which are connected to two noninteracting leads. The calculations are performed using the numerical renormalization group (NRG). It is found that the system shows a variety of Kondo effects depending on the filling of the triangle. The SU(4) Kondo effect occurs at half-filling, and a sharp conductance dip due to a phase lapse appears in the gate-voltage dependence. Furthermore, when four electrons occupy the three sites on average, a local S=1 moment, which is caused by the Nagaoka mechanism, is induced along the triangle. The temperature dependence of the entropy and spin susceptibility of the triangle shows that this moment is screened by the conduction electrons via two separate stages at different temperatures. The two-terminal and four-terminal conductances show a clear difference at the gate voltages, where the SU(4) or the S=1 Kondo effects occurring.

Available on Cond-Mat Archive### Renormalized Perturbation Approach to Electron Transport through Quantum Dots

**Authors:**A.C. Hewson, A. Oguri and J. Bauer

**published in:**Proceedings of the workshop on 'Physical Properties of Nanosystems', Yalta (Ed. J. Bonca and S. Kruchinin)

We review the basic ideas of a renormalized perturbation theory which works directly in terms of fully dressed quasiparticles, and its application to the calculation of the current through a quantum dot both in equilibrium and non-equilibrium steady state conditions. The method is illustrated for the impurity Anderson model. We show how the relevant renormalized parameters can be deduced from a numerical renormalization group calculation, and also how they can be generalized to include an arbitrary magnetic field. In applying the method to electron transmission through quantum dots, we show how the zero field conductance can be expressed in terms of the renormalized parameters, and how asymptotically exact results at low bias voltages can be derived from the expansion to second order. The potential for the further application of this approach to this class of problems is assessed.

Pdf Version### Spectral properties of locally correlated electrons in a BCS superconductor

**Authors:**J. Bauer, Akira Oguri, A. C. Hewson

**Submitted to**Journal of Physics: cond-mat

This is a detailed study of the spectral properties of a locally correlated site embedded in a BCS superconducting medium. The one and two-particle dynamic response functions are calculated to elucidate the spectral excitations and the nature of the ground state for different parameter regimes with and without particle-hole symmetry. The position and weight of the Andreev bound states is given for all relevant parameter regimes.

Available on Cond-Mat Archive### Kondo effect in asymmetric Josephson couplings through a quantum dot

**Authors:**Yoshihide Tanaka, Akira Oguri, A. C. Hewson

**published in:**New Journal of Physics**9**115 (2007)

A study is made of how the asymmetry of the coupling of a quantum dot to two superconductors affects the singlet to doublet transition which occurs when the on-site interaction U reaches a critical value.

Available on Cond-Mat Archive### Non-equilibrium Differential Conductance through a Quantum Dot in a Magnetic Field

**Authors:**A.C. Hewson, J. Bauer and A. Oguri

**published in:**J. Phys.: Condens. Matter**17**5413 (2005)

We show how the leading non-linear correction to the differential conductance through a quantum dot in a magnetic field can be calculated exactly in the Kondo regime using renormalised perturbtion theory. We deduce the critical value of the field for a two peak structure to be seen in the differential conductivity as a function of bias voltage.

Available on Cond-Mat Archive### Determination of the phase shifts for interacting electrons connected to reservoirs

**Authors:**A. Oguri, Y. Nisikawa and A. C. Hewson

**published in:**Journal of the Physical Society of Japan**74**2554 (2005)

We show how one can deduce the phase shifts, and hence the T=0 conductance, for a general model from an analysis of the NRG fixed point. The method is applied to a dot corresponding to a three site Hubbard chain coupled to two non-interacting leads.

Available on Cond-Mat Archive### NRG approach to transport through a finite Hubbard chain connected to resevoirs

**Authors:**A. Oguri and A.C. Hewson

**published in:**Journal of the Physical Society of Japan**74**988 (2005)

We use the NRG to study the low energy properties of a finite Hubbard chain connected to two non-interacting reservoirs. We show how the conductance can be deduced from the approach of the NRG energy levels to the fixed point.

Available on Cond-Mat Archive### Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction

**Authors:**A. Oguri, Y. Tanaka and A.C. Hewson

**published in:**Journal of the Physical Society of Japan**73**2494 (2004)

We show that the model for a quantum dot connected to two superconductors, simplifies when the superconducting gap for one of the superconductors is very large, such that it corresponds to a model connected to a single superconductor plus an additional boundary condition. The numerical renormalisation group (NRG) is used to study the Josephson current through the dot in this limit, and the singlet to doublet transition, which occurs when the interaction on the dot U reaches a critical value.

Available on Cond-Mat Archive