We study the two-impurity Kondo model (TIKM) in two dimensions with spin-orbit coupled conduction electrons. In the first part of the paper we analyze how spin-orbit interactions of Rashba as well as Dresselhaus type influence the Kondo and Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions in the TIKM, generalizing results obtained by H. Imamura et al. [Phys. Rev. B 69, 121303(R) (2004)] and J. Malecki [J. Stat. Phys. 129, 741 (2007)]. Using our findings we then explore the effect from spin-orbit interactions on the non-Fermi-liquid quantum critical transition between the RKKY-singlet and Kondo-screened RKKY-triplet states. We argue that spin-orbit interactions under certain conditions produce a line of critical points exhibiting the same leading scaling behavior as that of the ordinary TIKM. In the second part of the paper we shift focus and turn to the question of how spin-orbit interactions affect the entanglement between two localized RKKY-coupled spins in the parameter regime where the competition from the direct Kondo interaction can be neglected. Using data for a device with two spinful quantum dots patterned in a gated InAs heterostructure we show that a gate-controlled spin-orbit interaction may drive a maximally entangled state to one with vanishing entanglement or vice versa (as measured by the concurrence). This has important implications for proposals using RKKY interactions for nonlocal control of qubit entanglement in semiconductor heterostructures.
Motivated by proposals to employ RKKY-coupled spins as building blocks in a solid-state quantum computer, we analyze how the RKKY interaction in a 2D electron gas is influenced by spin-orbit interactions. Using a two-impurity Kondo model with added Dresselhaus and Rashba spin-orbit interactions we find that spin-rotational invariance of the RKKY interaction — essential for a well-controllable two-qubit gate — is restored when tuning the Rashba coupling to have the same strength as the Dresselhaus coupling. We also discuss the critical properties of the two-impurity Kondo model in the presence of spin-orbit interactions, and extract the leading correction to the block entanglement scaling due to these interactions.
Using the framework of the density-matrix renormalization group (DMRG), we study a quantum dot coupled to a superconducting nanowire with strong Rashba spin-orbit coupling. Regarding the singlet-to-doublet ``0-$\ensuremath{\pi}$'' transition that takes place when the Kondo effect is overcome by the superconducting gap, we show that the Rashba coupling modifies the critical values at which the transition occurs, favoring the doublet phase. In addition, using a generalized Haldane's formula for the Kondo temperature
TK, we show that it is lowered by the Rashba coupling. We benchmark our DMRG results, comparing them with previous numerical renormalization group results. The good agreement obtained opens the possibility of studying chains or clusters of impurities coupled to superconductors by means of DMRG.
We study the interplay between Kondo correlations and the singlet-triplet exchange splitting K between the two spins in a double quantum dot. We calculate the cotunneling current with elastic and inelastic contributions and its renormalization due to Kondo correlations, away and at the degeneracy point K = 0. We show that these Kondo correlations induce pronounced peaks in the conductance G as a function of magnetic field B , inter-dot coupling t H , and temperature. The long-range part of the Coulomb interaction becomes visible due to Kondo correlations resulting in an additional peak in G vs. t H with a strong B -field dependence. These conductance peaks thus provide direct experimental access to K , and thus to a crucial control parameter for spin-based qubits and entanglement.
Semiconductor double‐quantum dots represent an ideal system for studying the novel spin physics of localized spins. On each quantum dot when the number of electrons is odd and the net spin is 1/2, a strong coupling of this localized spin to conducting electrons in the leads gives rise to Kondo correlation. On the other hand, in the coupled double‐quantum‐dot if the inter‐dot antiferromagnetic interaction is strong, the two spins can form a correlated spin‐singlet state, quenching the Kondo effect. This competition between Kondo and antiferromagnetic correlation is studied in a controlled manner by tuning the inter‐dot tunnel coupling. Increasing the inter‐dot tunneling, we observe a continuous transition from a single‐peaked to a double‐peaked Kondo resonance in the differential conductance. On the double‐peaked side, the differential conductance becomes suppressed at zero source‐drain bias. The observed strong suppression of the differential conductance at zero bias provides direct evidence signaling the formation of an entangled spin‐singlet state. This evidence for entanglement and the tunability of our devices bode well for quantum computation applications.
The system of several
(N) quantum dots coupled in parallel to the same single-mode conduction channel can be modeled as a single-channel
N-impurity Anderson model. Using the generalized Schrieffer-Wolff transformation we show that near the particle-hole symmetric point, the effective Hamiltonian in the local moment regime is the
N-impurity
S=1∕2 Kondo model. The conduction-band-mediated RKKY exchange interaction between the dots is ferromagnetic and at intermediate temperatures locks the moments into a maximal spin
S=N∕2 ground state. We provide an analytical estimate for the RKKY interaction. At low temperatures the spin is partially screened by the conduction electrons to $N∕2\ensuremath{-}1∕2$ due to the Kondo effect. By comparing accurate numerical renormalization group results for magnetic susceptibility of the
N-impurity Anderson model to the exact Bethe ansatz results of a
S=N∕2 SU(2) Kondo system we show that at low-temperature the quantum dots can be described by the effective
S=N∕2 Kondo model. Moreover, the Kondo temperature is independent of the number of impurities
N. We demonstrate the robustness of the spin
N∕2 ground state as well as of the associated
S=N∕2 Kondo effect by studying the stability of the system with respect to various experimentally relevant perturbations. We finally explore various quantum phase transitions driven by these perturbations.