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Chinese Physics Letters

Quantum Phase Transition and Ferromagnetic Spin Correlation in Parallel Double Quantum Dots

Guo-Hui Ding, Ye Fei

Published Sep 28, 2007• 3 citations
Publisher

Abstract

We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2 e 2 / h ) due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.

DOI
10.1088/0256-307x/24/10/059

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We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction, as well as the interdot tunnelling. By applying numerical renormalization group method, the ground state of the system and the transmission probability at zero temperature are obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic, and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2 e 2 / h ) due to the Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to anti-ferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
We investigate electronic transport through a parallel double quantum dot (DQD) system with strong on-site Coulomb interaction and capacitive interdot coupling. By applying the numerical renormalization group (NRG) method, the ground state of the system and the transmission probability at zero temperature have been obtained. For a system of quantum dots with degenerate energy levels and small interdot tunnel coupling, the spin correlations between the DQDs is ferromagnetic and the ground state of the system is a spin-1 triplet state. The linear conductance will reach the unitary limit (2e(2)/h) due to the underscreened Kondo effect at low temperature. As the interdot tunnel coupling increases, there is a quantum phase transition from ferromagnetic to antiferromagnetic spin correlation in DQDs and the linear conductance is strongly suppressed.
The quantum phase transition and the electronic transport in a triangular quantum dot system are investigated using the numerical renormalization group method. We concentrate on the interplay between the interdot capacitive coupling V and the interdot tunnel coupling t . For small t , three dots form a local spin doublet. As t increases, due to the competition between V and t , there exist two first-order transitions with phase sequence spin-doublet-magnetic frustration phase-orbital spin singlet. When t is absent, the evolutions of the total charge on the dots and the linear conductance are of the typical Coulomb-blockade features with increasing gate voltage. While for sufficient t , the antiferromagnetic spin correlation between dots is enhanced, and the conductance is strongly suppressed for the bonding state is almost doubly occupied.
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.
Exact eigenstates of the parallel coupled double quantum dots attached to the non-interacting leads taken in zero-bandwidth limit are analytically obtained in each particle and spin sector. The ground state of the half-filled system is identified from a four dimensional subspace of the twenty dimensional Hilbert space for different values of tunable parameters of the system viz. the energy levels of the quantum dots, the interdot tunneling matrix-element, the ondot and interdot Coulomb interactions and quantities like spin-spin correlation between the dots, occupancies of the dots are calculated. In the parameter space of the interdot tunneling matrix-element and ondot Coulomb interaction, the dots exhibit both ferromagnetic and antiferromagnetic correlation. There is a critical dependency of the interdot tunneling matrix-element on the ondot Coulomb interaction which leads to transition from the ferromagnetic correlation to the antiferromagnetic correlation as the interdot tunneling matrix-element is increased. The ferromagnetic and antiferromagnetic correlations also exist in the absence of interdot tunneling matrix-element through indirect exchange via the leads. The interdot Coulomb interaction is found to affect this dependency considerably.
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 study the low-temperature transport properties of systems of parallel quantum dots described by the NNN-impurity Anderson model. We calculate the quasiparticle scattering phase shifts, spectral functions, and correlations as a function of the gate voltage for NNN up to 5. For any NNN, the conductance at the particle-hole symmetric point is unitary. For $N\ensuremath{\ge}2$, a transition from ferromagnetic to antiferromagnetic impurity spin correlations occurs at some gate voltage. For $N\ensuremath{\ge}3$, there is an additional transition due to an abrupt change in average impurity occupancy. For odd NNN, the conductance is discontinuous through both quantum phase transitions, while for even NNN only the magnetic transition affects the conductance. Similar effects should be experimentally observable in systems of quantum dots with ferromagnetic conduction-band-mediated interdot exchange interactions.