arXiv subjects
Publications and source records attributed to Constantine Yannouleas.
This paper (concerning the infinite-mass boundary condition) has been withdrawn by the author. Another, independent study regarding the zigzag boundary condition has appeared in Phys. Rev. B 82, 125419 (2010).
A description of neutral and multiply charged fullerenes is proposed based on a stabilized jellium (structureless pseudopotential) approximation for the ionic background and the local density approximation for the sigma and pi valence electrons. A recently developed shell-correction method is used to calculate total energies and properties of both the neutral and multiply charged anionic and cationic fullerenes. The effect of the icosahedral symmetry is included perturbatively. The calculated single-particle energy level spectrum of C_60 is in good correspondence with experimentally measured ones and previous self-consistent local-density-approximation calculations. For the multiply charged fullerenes, we calculate microscopically the charging energies for up to 12 excess charges. A semiclassical interpretation of these results is developed, which views the fullerenes as Coulomb islands possessing a classical capacitance. The calculated values for the first ionization potential and the first electron affinity agree well with the experimental ones. Our calculations support the results from charge transfer bracketing experiments and from direct ionization experiments through electron impact. The doubly charged negative ion is found to be a very long-lived metastable species, in agreement with observations.
Energy spectra and spin configurations of a system of N=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), 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 4-site Heisenberg cluster (with B-dependent exchange integrals) is demonstrated. Aspects of spin entanglement, referring to the well known N-qubit Dicke states, are also discussed.
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.
We investigate the way that the degenerate manifold of midgap edge states in quasicircular graphene quantum dots with zig-zag boundaries supports, under free-magnetic-field conditions, strongly correlated many-body behavior analogous to the fractional quantum Hall effect (FQHE), familiar from the case of semiconductor heterostructures in high magnetic fields. Systematic exact-diagonalization (EXD) numerical studies are presented for the first time for 5 <= N <= 8 fully spin-polarized electrons and for total angular momenta in the range of N(N-1)/2 <= L <= 150. We present a derivation of a rotating-electron-molecule (REM) type wave function based on the methodology introduced earlier [C. Yannouleas and U. Landman, Phys. Rev. B 66, 115315 (2002)] in the context of the FQHE in two-dimensional semiconductor quantum dots. The EXD wave functions are compared with FQHE trial functions of the Laughlin and the derived REM types. It is found that a variational extension of the REM offers a better description for all fractional fillings compared with that of the Laughlin functions (including total energies and overlaps), a fact that reflects the strong azimuthal localization of the edge electrons. In contrast with the multiring arrangements of electrons in circular semiconductor quantum dots, the graphene REMs exhibit in all instances a single (0,N) polygonal-ring molecular (crystalline) structure, with all the electrons localized on the edge. Disruptions in the zig-zag boundary condition along the circular edge act effectively as impurities that pin the electron molecule, yielding single-particle densities with broken rotational symmetry that portray directly the azimuthal localization of the edge electrons.
Through the introduction of a class of appropriate translationally invariant trial wave functions, we show that the strong correlations in the lowest Landau level (LLL) reflect in finite systems the emergence of intrinsic point-group symmetries associated with rotations and vibrations of molecules formed through particle localization. This molecular description is universal, being valid for both bosons and fermions, for both the yrast and excited states of the LLL spectra, and for both low and high angular momenta. This physical picture is fundamentally different from the "quantum-fluid" one associated with Jastrow-type trial functions.
Systematic trends of nonuniversal behavior of electron transmission phases through a quantum dot, with no phase lapse for the transition N=1 -> N=2 and a lapse of pi for the N=2 -> N=3 transition, are predicted, in agreement with experiments, from many-body transport calculations involving exact diagonalization of the dot Hamiltonian. The results favor shape anisotropy of the dot and strong e-e repulsion with consequent electron localization, showing dependence on spin configurations and the participation of excited doorway transmission channels.
The properties of a special class of correlated many-body wave functions, named rotating vortex clusters (RVCs), that preserve the total angular momentum of a small cloud of trapped rotating bosons are investigated. They have lower energy and provide a superior description for the formation of vortices compared to the mean-field Gross-Pitaevskii (GP) states that break the rotational symmetry. The GP vortex states are shown to be wave packets composed of such RVC states. Our results suggest that, for a small number of bosons, the physics is different from that of ideal Bose-Einstein condensates which characterize larger assemblies
Exact-diagonalization calculations for N=3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection S_z=1/2 are similar to the representative class of strongly entangled states referred to as W-states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy.
The Hamiltonian for a small number, N <= 11, of bosons in a rapidly rotating harmonic trap, interacting via a short range (contact potential) or a long range (Coulomb) interaction, is studied via an exact diagonalization in the lowest Landau level. Our analysis shows that, for both low and high fractional fillings, the bosons localize and form rotating boson molecules (RBMs) consisting of concentric polygonal rings. Focusing on systems with the number of trapped atoms sufficiently large to form multi-ring bosonic molecules, we find that, as a function of the rotational frequency and regardless of the type of repulsive interaction, the ground-state angular momenta grow in specific steps that coincide with the number of localized bosons on each concentric ring. Comparison of the conditional probability distributions (CPDs) for both interactions suggests that the degree of crystalline correlations appears to depend more on the fractional filling nu than on the range of the interaction. The RBMs behave as nonrigid rotors, i.e., the concentric rings rotate independently of each other. At filling fractions nu < 1/2, we observe well developed crystallinity in the CPDs (two-point correlation functions). For larger filling fractions nu > 1/2, observation of similar molecular patterns requires consideration of even higher-order correlation functions.
We present a variational many-body wave function for repelling bosons in rotating traps, focusing on rotational frequencies that do not lead to restriction to the lowest Landau level. This wave function incorporates correlations beyond the Gross-Pitaevskii (GP) mean field approximation, and it describes rotating boson molecules (RBMs) made of localized bosons that form polygonal-ring-like crystalline patterns in their intrinsic frame of reference. The RBMs exhibit characteristic periodic dependencies of the ground-state angular momenta on the number of bosons in the polygonal rings. For small numbers of neutral bosons, the RBM ground-state energies are found to be always lower than those of the corresponding GP solutions, in particular in the regime of GP vortex formation.
We discuss the formation of crystalline electron clusters in semiconductor quantum dots and of crystalline patterns of neutral bosons in harmonic traps. In a first example, we use calculations for two electrons in an elliptic quantum dot to show that the electrons can localize and form a molecular dimer. The calculated singlet-triplet splitting (J) as a function of the magnetic field (B) agrees with cotunneling measurements, with its behavior reflecting the effective dissociation of the dimer for large B. Knowledge of the dot shape and of J(B) allows determination of the degree of entanglement. In a second example, we study strongly repelling neutral bosons in two-dimensional harmonic traps. Going beyond the Gross-Pitaevskii (GP) mean-field approximation, we show that bosons can localize and form polygonal-ring-like crystalline patterns. The total energy of the crystalline phase saturates in contrast to the GP solution, and its spatial extent becomes smaller than that of the GP condensate.
We discuss symmetry breaking in two-dimensional quantum dots resulting from strong interelectron repulsion relative to the zero-point kinetic energy associated with the confining potential. Such symmetry breaking leads to the emergence of crystalline arrangements of electrons in the dot. The so-called Wigner molecules form already at field-free conditions. The appearance of rotating Wigner molecules in circular dots under high magnetic field, and their relation to magic angular momenta and quantum-Hall-effect fractional fillings, is also discussed. Recent calculations for two electrons in an elliptic quantum dot, using exact diagonalization and an approximate generalized-Heitler-London treatment, show that the electrons can localize and form a molecular dimer for screened interelectron repulsion. The calculated singlet-triplet splitting (J) as a function of the magnetic field (B) agrees with cotunneling measurements; its behavior reflects the effective dissociation of the dimer for large B. Knowledge of the dot shape and of J(B) allows determination of two measures of entanglement (concurrence and von Neumann entropy for indistinguishable fermions), whose behavior correlates also with the dissociation of the dimer. The theoretical value for the concurrence at B=0 agrees with the experimental estimates.
Using the method of breaking of circular symmetry and of subsequent symmetry restoration via projection techiques, we present calculations for the ground-state energies and excitation spectra of N-electron parabolic quantum dots in strong magnetic fields in the medium-size range 10 <= N <= 30. The physical picture suggested by our calculations is that of finite rotating electron molecules (REMs) comprising multiple rings, with the rings rotating independently of each other. An analytic expression for the energetics of such non-rigid multi-ring REMs is derived; it is applicable to arbitrary sizes given the corresponding equilibrium configuration of classical point charges. We show that the rotating electron molecules have a non-rigid (non-classical) rotational inertia exhibiting simultaneous crystalline correlations and liquid-like (non-rigidity) characteristics. This mixed phase appears in high magnetic fields and contrasts with the picture of a classical rigid Wigner crystal in the lowest Landau level.
We show that a supersolid phase, exhibiting simultaneously solid and superfluid behavior, properly describes the finite electron crystallites that form in two-dimensional quantum dots under high magnetic fields. These crystallites rotate already in their ground state and exhibit a nonclassical rotational inertia. They are precursors to a supersolid crystal in the lowest Landau level. We use exact numerical diagonalization, calculations employing analytic many-body wave functions, and a newly derived analytic expression for the total energies that permits calculations for arbitrary number of electrons.
Calculations for two electrons in an elliptic quantum dot, using symmetry breaking at the unrestricted Hartree-Fock level and subsequent restoration of the broken parity via projection techniques, show that the electrons can localize and form a molecular dimer, described by a Heitler-London-type wave function. The calculated singlet-triplet splitting (J) as a function of the magnetic field (B) agrees with cotunneling measurements. Knowledge of the dot shape and of J(B) allows determination of the degree of entanglement in the ground state of the dot, which is of interest for the implementation of quantum logic gates. The theoretical value agrees with the experimental estimates.
The crystalline or liquid character of the downward cusp states in N-electron parabolic quantum dots (QD's) at high magnetic fields is investigated using conditional probability distributions obtained from exact diagonalization. These states are of crystalline character for fractional fillings covering both low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in remarkable agreement with the rotating-Wigner-molecule ones [Phys. Rev. B 66, 115315 (2002)]. The crystalline arrangement consists of concentric polygonal rings that rotate independently of each other, with the electrons on each ring rotating coherently. We show that the rotation stabilizes the Wigner molecule relative to the static one defined by the broken-symmetry unrestricted-Hartree-Fock solution. We discuss the non-rigid behavior of the rotating Wigner molecule and pertinent features of the excitation spectrum, including the occurrence of a gap between the ground and first excited states that underlies the incompressibility of the system. This leads us to conjecture that the rotating crystal (and not the static one) remains the relevant ground state for low fractional fillings even at the thermodynamic limit.
Strongly repelling bosons in two-dimensional harmonic traps are described through breaking of rotational symmetry at the Hartree-Fock level and subsequent symmetry restoration via projection techniques, thus incorporating correlations beyond the Gross-Pitaevskii (GP) solution. The bosons localize and form polygonal-ring-like crystalline patterns, both for a repulsive contact potential and a Coulomb interaction, as revealed via conditional-probability-distribution analysis. For neutral bosons, the total energy of the crystalline phase saturates in contrast to the GP solution, and its spatial extent becomes smaller than that of the GP condensate. For charged bosons, the total energy and dimensions approach the values of classical point-like charges in their equilibrium configuration.