Following the recent claimed obsevation of Nagaoka ferromagnetism in finite size quantum dot plaquettes, a general theoretical analysis is warranted in order to ascertain in rather generic terms which arrangements of a small number of quantum dots can produce saturated ferromagnetic ground states and under which constraints on interaction and inter-dot tunneling in the plaquette. This is particularly necessary since Nagaoka ferromagnetism is fragile and arises only under rather special conditions. We test the robustness of ground state ferromagnetism in the presence of a long-range Coulomb interaction and long-range as well as short-range interdot hopping by modeling a wide range of different plaquette geometries accessible by arranging a few (~4) quantum dots in a controlled manner. We find that ferromagnetism is robust to the presence of long range Coulomb interactions, and we develop conditions constraining the tunneling strength such that the ground state is ferromagnetic. Additionally, we predict the presence of a partially spin-polarized ferromagnetic state for 4 electrons in a Y-shaped 4-quantum dot plaquette. Finally, we consider 4 electrons in a ring of 5 dots. This does not satisfy the Nagaoka condition, however, we show that the ground state is spin one for strong, but not infinite, onsite interaction. Thus, even though Nagaoka's theorem does not apply, the ground state for the finite system with one hole in a ring of 5 dots is partially ferromagnetic. We provide detailed fully analytical results for the existence or not of ferromagnetic ground states in several quantum dot geometries which can be studied in currently available coupled quantum dot systems.
Engineered, highly-controllable quantum systems hold promise as simulators of emergent physics beyond the capabilities of classical computers. An important problem in many-body physics is itinerant magnetism, which originates purely from long-range interactions of free electrons and whose existence in real systems has been subject to debate for decades. Here we use a quantum simulator consisting of a four-site square plaquette of quantum dots to demonstrate Nagaoka ferromagnetism. This form of itinerant magnetism has been rigorously studied theoretically but has remained unattainable in experi…
A (II,Mn)VI diluted magnetic semiconductor quantum dot with an integer number of electrons controlled with a gate voltage is considered. We show that a single conduction band electron is able to induce a spontaneous collective magnetization of the Mn spins, overcoming the short range antiferromagnetic interactions. The carrier mediated ferromagnetism in the dot survives at temperatures above 1 Kelvin, two orders of magnitude larger than the Curie temperature for the same material in bulk. The magnetic behavior of the dot depends dramatically on the parity of the number of injected electrons.
We present an Anderson-type model Hamiltonian with exchange coupling between the localized spins and the confined holes in the quantum dots to study the ferromagnetism in diluted magnetic semiconductor (DMS) quantum dot arrays embedded in semiconductors. The hybridization between the quantum-confined holes in the DMS quantum dots and the itinerant holes in the semiconductor valence band makes hole transfer between quantum dots, which can induce the long range ferromagnetic order of the localized spins. In addition, it makes the carrier spins both in the DMS quantum dots and in the semiconducto…
Magnetic semiconductor quantum dots with a few carriers represent an interesting model system where ferromagnetic interactions can be tuned by voltage. By designing the geometry of a doped quantum dot, one can tailor the anisotropic quantum states of magnetic polarons. The strong anisotropy of magnetic polaron states in disk-like quantum dots with holes comes from the spin splitting in the valence band. The binding energy and spontaneous magnetization of quantum dots oscillate with the number of particles and reflect the shell structure. Due to the Coulomb interaction, the maximum binding ener…
We study the ground state of $N$ weakly interacting electrons (with $N\le 10$) in a two-dimensional parabolic quantum dot with strong Rashba spin-orbit coupling. Using dimensionless parameters for the Coulomb interaction, $λ\lesssim 1$, and the Rashba coupling, $α\gg 1$, the low-energy physics is characterized by an almost flat single-particle dispersion. From an analytical approach for $α\to \infty$ and $N=2$, and from numerical exact diagonalization and Hartree-Fock calculations, we find a transition from a conventional unmagnetized ground state (for $λ<λ_c$) to an orbital ferromagnet (for $…
Possibility of flat-band ferromagnetism in quantum dot arrays is theoretically discussed. By using a quantum dot as a building block, quantum dot superlattices are possible. We consider dot arrays on Lieb and kagome lattices known to exhibit flat band ferromagnetism. By performing an exact diagonalization of the Hubbard Hamiltonian, we calculate the energy difference between the ferromagnetic ground state and the paramagnetic excited state, and discuss the stability of the ferromagnetism against the second nearest neighbor transfer. We calculate the dot-size dependence of the energy difference…
We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite $U$ Hubbard model. We find that for one dimensional systems disorder has no influence, while for two dimensional systems disorder enhances the spin polarization of the system. The tendency of disorder to enhance magnetism in the ground state may be relevant to recent experimental observations of spin polarized ground states in quantum dots and small metallic grains.
Based on calculations using the local density approximation, we propose quantum wire networks with square and plaquette type lattice structures that form quantum dot superlattices. These artificial structures are well described by the Hubbard model. Numerical analysis reveals a superconducting ground state with transition temperatures $T_c$ of up to 90 mK for the plaquette, which is more than double the value of 40 mK for the square lattice type and is sufficiently high to allow for the experimental observation of superconductivity.
We present several interesting phenomena related to flatband ferromagnetism in the Hubbard model. The first is a mathematical theorem stating certain conditions under which a flatband ferromagnetic must necessarily be degenerate with a nonferromagnetic state. This theorem is generally applicable and geometry-independent, but holds only for a small number of holes in an otherwise filled band. The second phenomenon is a peculiar example where the intuition fails that particles prefer to doubly occupy low-energy states before filling higher-energy states. Lastly, we show a pattern of ferromagneti…
Spin-polarized transport through a double quantum dot system attached to a common superconducting lead and two ferromagnetic electrodes (fork geometry) is investigated theoretically. The key objective of the analysis is to describe the influence of electrodes' ferromagnetism on the Andreev tunneling. Both direct and crossed Andreev tunneling processes are considered, in general. The other objective is a detailed analysis of the role of Coulomb interaction and its impact on the Andreev tunneling processes.
Many-particle electron states in semiconductor quantum dots with carrier-mediated ferromagnetism are studied theoretically within the self-consistent Boltzmann equation formalism. Depending on the conditions, a quantum dot may contain there phases: partially spin-polarized ferromagnetic, fully spin-polarized ferromagnetic, and paramagnetic phases. The physical properties of many-body ferromagnetic confined systems come from the competing carrier-mediated ferromagnetic and Coulomb interactions. The magnetic phases in gated quantum dots with holes can be controlled by the voltage or via optical …
We propose a new approximation scheme within equation of motion approach (EOM) to spin polarized transport through a quantum dot coupled to ferromagnetic leads. It has some advantages over a widely used in the literature standard EOM technique, in particular when we are interested in spin polarized quantities. Namely, it gives the values of the dot spin polarization which are closer to the ones obtained within numerical renormalization group (NRG), than the standard EOM approach. While restoring the Kondo effect, the spin polarization vanishes and the transport becomes unpolarized, in agreemen…
We consider a quantum dot coupled to both superconducting and spin-polarized electrodes, and study the triad interplay of the Kondo effect, superconductivity, and ferromagnetism, any pair of which compete with and suppress each other. We find that the interplay leads to a mixed-valence quantum phase transition, which for other typical sysmstems is merely a crossover rather than a true transition. At the transition, the system changes from the spin doublet to singlet state. The singlet phase is adiabatically connected (through crossovers) to the so-called 'charge Kondo state' and to the superco…
The Kondo effect in quantum dots (QDs) - artificial magnetic impurities - attached to ferromagnetic leads is studied with the numerical renormalization group (NRG) method. It is shown that the QD level is spin-split due to presence of ferromagnetic electrodes, leading to a suppression of the Kondo effect. We find that the Kondo effect can be restored by compensating this splitting with a magnetic field. Although the resulting Kondo resonance then has an unusual spin asymmetry with a reduced Kondo temperature, the ground state is still a locally-screened state, describable by Fermi liquid theor…
Performing an exact diagonalization of the effective spin problem, a ferromagnetic ground state of kinetic origin is shown to emerge in a system of $N$ strongly correlated electrons on a $L$-site ring ($L > N$). This phenomenon is brought about by the quantum necklace statistics originated from the no double occupancy constraint leading to a fractional shifted electron momentum quantization. As a consequence of such special energy level distribution, the kinetic ferromagnetism is stable only for $N=3$. For odd $N>3$ the fully polarized FM state energy is only a local minimum but it is protecte…
We study transport through a triangle triple quantum dot connected to two noninteracting leads using the numerical renormalization group (NRG). The triangle has a high-spin ground state of S=1 caused by a Nagaoka ferromagnetism, when it is isolated and has one extra electron introduced into a half-filling. The results show that the conduction electrons screen the local moment via two separate stages with different energy scales. The half of the S=1 is screened first by one of the channel degrees, and then at very low temperature the remaining half is fully screened to form a Kondo singlet. The…
