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Journal of Atomic Molecular Condensate and Nano Physics

Exact Diagonalization Study of Double Quantum Dot System in Zero-bandwidth Limit

Haroon, M. A. H. Ahsan

Published Dec 29, 2015• 0 citations
Publisher

Abstract

Using exact diagonalization, we study double quantum dot system with one of the dots attached to the ideal leads acting as source and drain in T-shaped geometry. The leads are incorporated in zero-bandwidth limit by replacing their band structures with one level coinciding with Fermi levels in the respective leads. For the half-filled case, the spin-spin correlation for the dots are calculated numerically at zero as well as finite temperatures. At zero temperature, an antiferromagnetic correlation between the dots is observed for finite values of interdot tunneling matrix-element. The antiferromagnetic correlation between the dots changes remarkably for large values of ondot Coulomb interaction both at zero as well as finite temperatures. The spin-spin correlation between the dots is significantly reduced even for small values of the inderdot Coulomb interaction compared to the ondot Coulomb interaction. At a small value of temperature, the spin-spin correlation between the dots exhibits a (negative) maximum due to contributions coming from thermal excitations to low-lying states.

DOI
10.26713/jamcnp.v2i3.339

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Using exact diagonalization, we study double quantum dot system with one of the dots attached to the ideal leads acting as source and drain in T-shaped geometry. The leads are incorporated in zero-bandwidth limit by replacing their band structures with one level coinciding with Fermi levels in the respective leads. For the half-filled case, the spin-spin correlation for the dots are calculated numerically at zero as well as finite temperatures. At zero temperature, an antiferromagnetic correlation between the dots is observed for finite values of interdot tunneling matrix-element. The antiferromagnetic correlation between the dots changes remarkably for large values of ondot Coulomb interaction both at zero as well as finite temperatures. The spin-spin correlation between the dots is significantly reduced even for small values of the inderdot Coulomb interaction compared to the ondot Coulomb interaction. At a small value of temperature, the spin-spin correlation between the dots exhibits a (negative) maximum due to contributions coming from thermal excitations to low-lying states.
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.
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.
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.
Energy spectra, spin configurations, and entanglement characteristics of a system of four electrons in lateral double quantum dots are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field, and strength of interelectron repulsion. A distinctly different quantum behavior is found compared to that of circular single quantum dots. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin of the four electrons and the ensuing spin degeneracies. These six states appear to cross at a single value of the magnetic field, with the crossing point becoming sharper for larger interdot distances. As the strength of the Coulomb repulsion increases, the six states tend to become degenerate and a well defined energy gap separates them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule, with the four electrons (two in each dot) being localized at the vertices of a rectangular parallelogram. Using the spin-resolved pair-correlation functions, one can map the EXD many-body wave functions onto the spin functions associated with the four localized electrons. Analogies with nanomagnets, such as finite Heisenberg clusters, are discussed. The ability to determine associated spin functions enables investigations concerning entanglement properties of the system of four electrons. In particular, the formation of Wigner supermolecules generates EXD solutions belonging to the class of strongly entangled states referred to as N-qubit Dicke states in the quantum-information literature.
The ground-state persistent current and electron addition spectrum in two-dimensional quantum dot arrays and one-dimensional quantum dot rings, pierced by an external magnetic flux, are investigated using the extended Hubbard model. The collective multidot problem is shown to map exactly into the strong-field noninteracting finite-size Hofstadter butterfly problem at the spin polarization transition. The finite-size Hofstadter problem is discussed, and an analytical solution for limiting values of flux is obtained. In weak fields we predict interesting flux periodic oscillations in the spin component along the quantization axis with a periodicity given by $\ensuremath{\nu}h/e$ $(\ensuremath{\nu}<~1)$. The sensitivity of the calculated persistent current to interaction and disorder is shown to reflect the intricacies of various Mott-Hubbard quantum phase transitions in two-dimensional systems: the persistent current is suppressed in the antiferromagnetic Mott-insulating phase governed by intradot Coulomb interactions; the persistent current is maximized at the spin density wave--charge density wave transition driven by the nearest-neighbor interdot interaction; the Mott-insulating phase persistent current is enhanced by the long-range interdot interactions to its noninteracting value; the strong suppression of the noninteracting current in the presence of random disorder is seen only at large disorder strengths; at half-filling even a relatively weak intradot Coulomb interaction enhances the disordered noninteracting system persistent current; in general, the suppression of the persistent current by disorder is less significant in the presence of the long-range interdot Coulomb interaction.
Energy spectra and spin configurations of a system of N=4N=4N=4 electrons in lateral double quantum dots (quantum dot helium molecules) are investigated using exact diagonalization (EXD), as a function of interdot separation, applied magnetic field (B)(B)(B), and strength of interelectron repulsion. As a function of the magnetic field, the energy spectra exhibit a low-energy band consisting of a group of six states, with the number six being a consequence of the conservation of the total spin and the ensuing spin degeneracies for four electrons. The energies of the six states appear to cross at a single value of the magnetic field, and with increasing Coulomb repulsion they tend to become degenerate, with a well-defined energy gap separating them from the higher-in-energy excited states. The appearance of the low-energy band is a consequence of the formation of a Wigner supermolecule, with the four electrons (two in each dot) being localized at the vertices of a rectangle. Using spin-resolved pair-correlation distributions, a method for mapping the complicated EXD many-body wave functions onto simpler spin functions associated with a system of four localized spins is introduced. Detailed interpretation of the EXD spin functions and EXD spectra associated with the low-energy band via a four-site Heisenberg cluster (with BBB-dependent exchange integrals) is demonstrated. Aspects of spin entanglement, referring to the well-known NNN-qubit Dicke states, are also discussed.