Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0109155 · Europhysics Letters (EPL)

Kondo effect and singlet-triplet splitting in coupled quantum dots in a magnetic field

Vitaly N. Golovach, Daniel Loss

Published Apr 1, 2003• 19 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1209/epl/i2003-00365-x

Related papers

The Kondo Effect and Controlled Spin Entanglement in Coupled Double-Quantum-Dots

A. M. Chang

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.

AIP conference proceedings•Jan 1, 2005•1 citation

Pauli spin blockade in cotunneling transport through a double quantum dot

Hongwu Liu, T. Fujisawa, T. Hayashi +1 more

We study spin correlation in a double quantum dot containing a few electrons in each dot (around 10). Clear current rectification with negative differential conductance is observed in the cotunneling regime, which is well explained by a Pauli spin blockade. The current feature is discussed in connection with exchange singlet-triplet splitting based on two simple models, one of which takes coherent interdot coupling and the other incoherent interdot coupling into account.

arXiv:cond-mat/0509232•Physical Review B•Oct 18, 2005•41 citations

Long-range exchange interaction in triple quantum dots in the Kondo regime

YongXi Cheng, Yuandong Wang, Jianhua Wei +2 more

Long-range interactions in triple quantum dots in the Kondo regime are investigated by accurately solving the three-impurity Anderson model. For the occupation configuration of $({N}_{1},{N}_{2},{N}_{3})=(1,0,1)$, a long-range antiferromagnetic exchange interaction (${J}_{\mathrm{AF}}$) is demonstrated and induces a crossover from the separated Kondo singlet to the long-range spin singlet state between edge dots. In the long-range spin singlet phase, a long-range overlapping or entanglement of Kondo clouds is discovered, which induces a transition peak in the spectral function of the middle dot under equilibrium conditions. Under nonequilibrium conditions, the long-range entanglement of the Kondo clouds is characterized by the conductance peak at zero bias, which can be observed in experiments.

arXiv:1701.06369•Physical review. B./Physical review. B•Apr 12, 2017•25 citations

Kondo effect and continuous quantum phase transitions in double quantum dots with on-site and interdot repulsion and magnetic field

Wei-zhong Wang

By means of the numerical renormalization group method, I study the Kondo effect and quantum phase transitions in a double quantum dot system with on-site repulsion $U$, interdot repulsion $V,$ and magnetic field $B$. At zero temperature and $B=0$, there is a local spin triplet-singlet transition of the Kosterlitz-Thouless type when $V$ increases to a critical value ${V}_{c}\ensuremath{\approx}U$. With increasing $B$, a singlet-triplet transition of the second order occurs at a critical magnetic field ${B}_{c}\ensuremath{\approx}V\ensuremath{-}U$. The magnetic susceptibility and the first derivatives of the spin correlation and double occupation are expected to diverge at ${B}_{c}$ and to have different critical exponents, which are universal for different parameters. An appropriate magnetic field can restore the Kondo effect.

Physical Review B•Feb 23, 2011•24 citations

Transition between Quantum States in a Parallel-Coupled Double Quantum Dot

J. C. Chen, A. M. Chang, M. R. Melloch

Strong electron and spin correlations in a double quantum dot (DQD) can give rise to different quantum states. We observe a continuous transition from a Kondo state exhibiting a single-peak Kondo resonance to another exhibiting a double peak by increasing the interdot coupling (t) in a parallel-coupled DQD. The transition into the double-peak state provides evidence for spin entanglement between the excess electrons on each dot. Toward the transition, the peak splitting merges and becomes substantially smaller than t because of strong Coulomb effects. Our device tunability bodes well for future quantum computation applications.

arXiv:cond-mat/0305289•Physical Review Letters•Apr 27, 2004•209 citations

Spin interactions and switching in vertically tunnel-coupled quantum dots

Guido Burkard, Georg Seelig, Daniel Loss

We determine the spin-exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few T, and perpendicular fields of the order of 10 T for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken techniques, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states, and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch the spin coupling on and off with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.

arXiv:cond-mat/9910105•Physical review. B, Condensed matter•Jul 15, 2000•141 citations
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.
Long-range interactions in triple quantum dots in the Kondo regime are investigated by accurately solving the three-impurity Anderson model. For the occupation configuration of (N1,N2,N3)=(1,0,1)({N}_{1},{N}_{2},{N}_{3})=(1,0,1)(N1​,N2​,N3​)=(1,0,1), a long-range antiferromagnetic exchange interaction (JAF{J}_{\mathrm{AF}}JAF​) is demonstrated and induces a crossover from the separated Kondo singlet to the long-range spin singlet state between edge dots. In the long-range spin singlet phase, a long-range overlapping or entanglement of Kondo clouds is discovered, which induces a transition peak in the spectral function of the middle dot under equilibrium conditions. Under nonequilibrium conditions, the long-range entanglement of the Kondo clouds is characterized by the conductance peak at zero bias, which can be observed in experiments.
By means of the numerical renormalization group method, I study the Kondo effect and quantum phase transitions in a double quantum dot system with on-site repulsion UUU, interdot repulsion V,V,V, and magnetic field BBB. At zero temperature and B=0B=0B=0, there is a local spin triplet-singlet transition of the Kosterlitz-Thouless type when VVV increases to a critical value ${V}_{c}\ensuremath{\approx}U$. With increasing BBB, a singlet-triplet transition of the second order occurs at a critical magnetic field ${B}_{c}\ensuremath{\approx}V\ensuremath{-}U$. The magnetic susceptibility and the first derivatives of the spin correlation and double occupation are expected to diverge at Bc{B}_{c}Bc​ and to have different critical exponents, which are universal for different parameters. An appropriate magnetic field can restore the Kondo effect.
Strong electron and spin correlations in a double quantum dot (DQD) can give rise to different quantum states. We observe a continuous transition from a Kondo state exhibiting a single-peak Kondo resonance to another exhibiting a double peak by increasing the interdot coupling (t) in a parallel-coupled DQD. The transition into the double-peak state provides evidence for spin entanglement between the excess electrons on each dot. Toward the transition, the peak splitting merges and becomes substantially smaller than t because of strong Coulomb effects. Our device tunability bodes well for future quantum computation applications.
We determine the spin-exchange coupling J between two electrons located in two vertically tunnel-coupled quantum dots, and its variation when magnetic (B) and electric (E) fields (both in-plane and perpendicular) are applied. We predict a strong decrease of J as the in-plane B field is increased, mainly due to orbital compression. Combined with the Zeeman splitting, this leads to a singlet-triplet crossing, which can be observed as a pronounced jump in the magnetization at in-plane fields of a few T, and perpendicular fields of the order of 10 T for typical self-assembled dots. We use harmonic potentials to model the confining of electrons, and calculate the exchange J using the Heitler-London and Hund-Mulliken techniques, including the long-range Coulomb interaction. With our results we provide experimental criteria for the distinction of singlet and triplet states, and therefore for microscopic spin measurements. In the case where dots of different sizes are coupled, we present a simple method to switch the spin coupling on and off with exponential sensitivity using an in-plane electric field. Switching the spin coupling is essential for quantum computation using electronic spins as qubits.