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Physical review. B, Condensed matter

Enlarged symmetry and coherence in arrays of quantum dots

Alexey V. Onufriev, John Bradley Marston

Published May 15, 1999• 35 citations
Publisher

Abstract

Enlarged symmetry characterized by the group SU(4) can be realized in isolated semiconducting quantum dots. A Hubbard model then describes a pillar array of coupled dots, and at half-filling the system can be mapped onto an SU(4) spin chain. The physics of these structures is rich as novel phases are attainable. The spins spontaneously dimerize, and this state is robust to perturbations that break SU(4) symmetry. We propose ways to experimentally verify the existence of the dimerized phase.

DOI
10.1103/physrevb.59.12573

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Enlarged symmetry characterized by the group SU(4) can be realized in isolated semiconducting quantum dots. A Hubbard model then describes a pillar array of coupled dots, and at half-filling the system can be mapped onto an SU(4) spin chain. The physics of these structures is rich as novel phases are attainable. The spins spontaneously dimerize, and this state is robust to perturbations that break SU(4) symmetry. We propose ways to experimentally verify the existence of the dimerized phase.
Enlarged symmetry characterized by the group SU(4) can be realized in isolated semiconducting quantum dots. A Hubbard model then describes a pillar array of coupled dots and at half-filling the system can be mapped onto an SU(4) spin chain. The physics of these new structures is rich as novel phases are attainable. The spins spontaneously dimerize and, by using the Density Matrix Renormalization Group (DMRG), we show that the dimer state is robust to perturbations which break SU(4) symmetry. We propose ways to experimentally verify the existence of the dimerized phase.
We analyze, from a quantum information theory perspective, the possibility of realizing an SU(4) entangled Kondo regime in semiconductor double quantum dot devices. We focus our analysis on the ground-state properties and consider the general experimental situation where the coupling parameters of the two quantum dots differ. We model each quantum dot with an Anderson-type Hamiltonian including an interdot Coulomb repulsion and tunnel couplings for each quantum dot to independent fermionic baths. We find that the spin and pseudospin entanglements can be made equal, and the SU(4) symmetry recovered, if the gate voltages are chosen in such a way that the average charge occupancies of the two quantum dots are equal, and the double occupancy on the double quantum dot is suppressed. We present density matrix renormalization group numerical results for the spin and pseudospin entanglement entropies, and analytical results for a simplified model that captures the main physics of the problem.
Abstract : The authors use electrostatically defined quantum dot arrays to study quantum simulation, examining both large arrays to explore the ground state and excitations of the Fermi-Hubbard model, and to examine very small arrays of 3-4 quantum dots as the basis for simulating superexchange, frustration, magnetism, etc. The large arrays were created by defining a grid-shaped gate on a semiconductor, forcing the electrons to see a periodic potential and be confined in a lattice of sites, where the low temperature reachable by the system in a dilution refrigerator allows examining the phase diagram of the model in a regime where spin correlations have an important influence. Initial plans to perform transport measurement were unsuccessful as the clean room realization of contacts to the two layers of the bilayered heterostructure had very low yield, so the authors performed capacitance spectroscopy measurement instead. This provides direct measurement of density of states, and the lithography process involved allowed grids with 150-200nm periods to be successfully written. The small array examination analyzed how a system of four quantum dots on a square and filled with three electrons allowed the authors to study magnetism of few-body systems, examining whether the Nagaoka theorem could be realizable with quantum dots (conclusion: the ferromagnetic-paramagnetic state is in reach experimentally) and examining the experimental techniques to test the spin-structure of the ground state and induce the transition (finding: application of magnetic field can break the ferromagnetic ground state, in contrast to the usual). The authors also studied a linear array of three dots, resulting in publications in Nature Nanotechnology, Applied Physics Letters, and Annalen Der Physik.
The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization-group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of coherent spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become incoherent. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.