arXiv subjects

M. Koskinen

Publications and source records attributed to M. Koskinen.

At least 19 recordsLinked to original sources

arXiv2008

Magnetism of quantum dot clusters: A Hubbard model study

Magnetic properties of two and three-dimensional clusters of quantum dots are studied with exact diagonalization of a generalized Hubbard model. We study the weak coupling limit, where the electrons interact only within a quantum dot and consider cases where the second or third harmonic oscillator shell is partially filled. The results show that in the case of half-filled shell the magnetism is determined by the antiferromagnetic Heisenberg model with spin 1/2, 1 or 3/2, depending on the number of electrons in the open shell. For other fillings the system in most cases favors a large total spin, indicating a ferromagnetic coupling between the dots.

cond-mat.str-el↗

arXiv2008

Magnetic phases of one-dimensional lattices with 2 to 4 fermions per site

We study the spectral and magnetic properties of one-dimensional lattices filled with 2 to 4 fermions (with spin 1/2) per lattice site. We use a generalized Hubbard model that takes account all interactions on a lattice site, and solve the many-particle problem by exact diagonalization. We find an intriguing magnetic phase diagram which includes ferromagnetism, spin-one Heisenberg antiferromagnetism, and orbital antiferromagnetism.

cond-mat.str-el↗

arXiv2008

Universality of Many-Body States in Rotating Bose and Fermi Systems

We propose a universal transformation from a many-boson state to a corresponding many-fermion state in the lowest Landau level approximation of rotating many-body systems, inspired by the Laughlin wave function and by the Jain composite-fermion construction. We employ the exact-diagonalization technique for finding the many-body states. The overlap between the transformed boson ground state and the true fermion ground state is calculated in order to measure the quality of the transformation. For very small and high angular momenta, the overlap is typically above 90%. For intermediate angular momenta, mixing between states complicates the picture and leads to small ground-state overlaps at some angular momenta.

cond-mat.mes-hall↗

arXiv2006

Spectral properties of rotating electrons in quantum dots and their relation to quantum Hall liquids

The exact diagonalization technique is used to study many-particle properties of interacting electrons with spin, confined in a two-dimensional harmonic potential. The single-particle basis is limited to the lowest Landau level. The results are analyzed as a function of the total angular momentum of the system. Only at angular momenta corresponding to the filling factors 1, 1/3, 1/5 etc. the system is fully polarized. The lowest energy states exhibit spin-waves, domains, and localization, depending on the angular momentum. Vortices exist only at excited polarized states. The high angular momentum limit shows localization of electrons and separation of the charge and spin excitations.

cond-mat.mes-hall↗

arXiv2006

Vortex localization in rotating clouds of bosons and fermions

Finite quantal systems at high angular momenta may exhibit vortex formation and localization. These phenomena occur independent of the statistics of the repulsively interacting particles, which may be of bosonic or fermionic nature. We analyze the relation between vortex localization and formation of stable Wigner molecules at high angular momenta in the view of particle-hole duality.Trial wave functions for the vortex states and the corresponding fermion-boson relations are discussed.

cond-mat.mes-hall↗

arXiv2006

Rotating quantum liquids crystallize

Small crystallites form when finite quantal systems are set highly rotating. This crystallization is independent of the statistics of the particles, and occurs for both trapped bosons and fermions. The spin degree of freedom does not change the tendency for localization. In a highly rotating state, the strongly correlated bosonic and fermionic systems approach to that of classical particles.

cond-mat.mes-hall↗

arXiv2005

Magnetism in one-dimensional quantum dot arrays

We employ the density functional Kohn-Sham method in the local spin-density approximation to study the electronic structure and magnetism of quasi one-dimensional periodic arrays of few-electron quantum dots. At small values of the lattice constant, the single dots overlap, forming a non-magnetic quantum wire with nearly homogenous density. As the confinement perpendicular to the wire is increased, i.e. as the wire is squeezed to become more one-dimensional, it undergoes a spin-Peierls transition. Magnetism sets in as the quantum dots are placed further apart. It is determined by the electronic shell filling of the individual quantum dots. At larger values of the lattice constant, the band structure for odd numbers of electrons per dot indicates that the array could support spin-polarized transport and therefore act as a spin filter.

cond-mat.mes-hall↗

arXiv2004

Vortices and Edge Reconstruction in Small Quantal Systems at High Angular Momenta

Vortices can form when finite quantal systems are set to rotate. In the limit of small particle numbers the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. We show that for a larger number of fermions, $N\gtrsim15$, the fermion vortices compete and co-exist with (Chamon-Wen) edge-reconstructed ground states, forcing some ground states, for instance the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could for instance be a semiconductor heterostructure, a quantum dot, and the corresponding boson system a magneto optical trap (MOT).

cond-mat.mes-hall↗

arXiv2004

Electron-hole duality and vortex rings in quantum dots

In a quantum-mechanical system, particle-hole duality implies that instead of studying particles, we can get equivalent information by studying the missing particles, the so-called holes. Using this duality picture for rotating fermion condensates the vortices appear as holes in the Fermi see. Here we predict that the formation of vortices in quantum dots at high magnetic fields causes oscillations in the energy spectrum which can be experimentally observed using accurate tunnelling spectroscopy. We use the duality picture to show that these oscillations are caused by the localisation of vortices in rings.

cond-mat.mes-hall↗

arXiv2004

Universal vortex formation in rotating traps with bosons and fermions

When a system consisting of many interacting particles is set rotating, it may form vortices. This is familiar to us from every-day life: you can observe vortices while stirring your coffee or watching a hurricane. In the world of quantum mechanics, famous examples of vortices are superconducting films and rotating bosonic $^4$He or fermionic $^3$He liquids. Vortices are also observed in rotating Bose-Einstein condensates in atomic traps and are predicted to exist for paired fermionic atoms. Here we show that the rotation of trapped particles with a repulsive interaction leads to a similar vortex formation, regardless of whether the particles are bosons or (unpaired) fermions. The exact, quantum mechanical many-particle wave function provides evidence that in fact, the mechanism of this vortex formation is the same for boson and fermion systems.

cond-mat.mes-hall↗

arXiv2003

Energy spectrum, persistent current and electron localization in quantum rings

Energy spectra of quasi-one-dimensional quantum rings with a few electrons are studied using several different theoretical methods. Discrete Hubbard models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body system can be described with a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the periodicity of the oscillations is always the flux quantum Phi_0. For nonpolarized electrons the periodicity depends on the strength of the effective Heisenberg coupling and changes from Φ_0 first to Phi_0/2 and eventually to Phi_0/N when the ring gets narrower.

cond-mat.mes-hall↗

arXiv2003

Electron-hole bilayer quantum dots: Phase diagram and exciton localization

We studied a vertical ``quantum dot molecule'', where one of the dots is occupied with electrons and the other with holes. We find that different phases occur in the ground state, depending on the carrier density and the interdot distance. When the system is dominated by shell structure, orbital degeneracies can be removed either by Hund's rule, or by Jahn-Teller deformation. Both mechanisms can lead to a maximum of the addition energy at mid-shell. At low densities and large interdot distances, bound electron-hole pairs are formed.

cond-mat.mes-hall↗

arXiv2003

Exchange-correlation energy of a multicomponent two-dimensional electron gas

We discuss the exchange-correlation energy of a multicomponent (multi-valley) two-dimensional electron gas and show that an extension of the recent parametrisation of the exchange-correlation energy by Attacalite et al (Phys. Rev. Lett. 88, 256601 (2002)) describes well also the multicomponent system. We suggest a simple mass dependence of the correlation energy and apply it to study the phase diagram of the multicomponent 2D electron (or hole) gas. The results show that even a small mass difference of the components (e.g. heavy and light holes) decreases the concentration of the lighter components already at relatively high densities.

cond-mat.mes-hall↗

arXiv2003

Fractional Periodicity of Persistent Currents: A Signature of Broken Internal Symmetry

We show from the symmetries of the many body Hamiltonian, cast into the form of the Heisenberg (spin) Hamiltonian, that the fractional periodicities of persistent currents are due to the breakdown of internal symmetry and the spin Hamiltonian holds the explanation to this transition. Numerical diagonalizations are performed to show this explicitely. Persistent currents therefore, provide an easy way to experimentally verify broken internal symmetry in electronic systems.

cond-mat.mes-hall↗

arXiv2001

Many-body spectrum and particle localization in quantum dots and finite rotating Bose condensates

The yrast spectra (i.e. the lowest states for a given total angular momentum) of quantum dots in strong magnetic fields, are studied in terms of exact numerical diagonalization and analytic trial wave functions. We argue that certain features (cusps) in the many-body spectrum can be understood in terms of particle localization due to the strong field. A new class of trial wavefunctions supports the picture of the electrons being localized in Wigner molecule-like states consisting of consecutive rings of electrons, with low-lying excitations corresponding to rigid rotation of the outer ring of electrons. The geometry of the Wigner molecule is independent of interparticle interactions and the statistics of the particles.

cond-mat.mes-hall↗

arXiv2000

Current-spin-density functional study of persistent currents in quantum rings

We present a numerical study of persistent currents in quantum rings using current spin density functional theory (CSDFT). This formalism allows for a systematic study of the joint effects of both spin, interactions and impurities for realistic systems. It is illustrated that CSDFT is suitable for describing the physical effects related to Aharonov-Bohm phases by comparing energy spectra of impurity-free rings to existing exact diagonalization and experimental results. Further, we examine the effects of a symmetry-breaking impurity potential on the density and current characteristics of the system and propose that narrowing the confining potential at fixed impurity potential will suppress the persistent current in a characteristic way.

cond-mat.mes-hall↗

arXiv2000

On the formation of Wigner molecules in small quantum dots

It was recently argued that in small quantum dots the electrons could crystallize at much higher densities than in the infinite two-dimensional electron gas. We compare predictions that the onset of spin polarization and the formation of Wigner molecules occurs at a density parameter $r_s\approx 4 a_B^*$ to the results of a straight-forward diagonalization of the Hamiltonian matrix.

cond-mat.mes-hall↗

arXiv2000

Rotational and vibrational spectra of quantum rings

One can confine the two-dimensional electron gas in semiconductor heterostructures electrostatically or by etching techniques such that a small electron island is formed. These man-made ``artificial atoms'' provide the experimental realization of a text-book example of many-particle physics: a finite number of quantum particles in a trap. Much effort was spent on making such "quantum dots" smaller and going from the mesoscopic to the quantum regime. Far-reaching analogies to the physics of atoms, nuclei or metal clusters were obvious from the very beginning: The concepts of shell structure and Hund's rules were found to apply -- just as in real atoms! In this Letter, we report the discovery that electrons confined in ring-shaped quantum dots form rather rigid molecules with antiferromagnetic order in the ground state. This can be seen best from an analysis of the rotational and vibrational excitations.

cond-mat.mes-hall↗