Single-particle Level Spacing Research Articles

Level densities inFe56,57andMo96,97

Level densities up close to the neutron binding energy have been extracted from primary $\ensuremath{\gamma}$ spectra for $^{56,57}\mathrm{Fe}$ and $^{96,97}\mathrm{Mo}$ nuclei using $(^{3}\mathrm{He},\ensuremath{\alpha}\ensuremath{\gamma})$ and $(^{3}\mathrm{He},^{3}\mathrm{He}\ensuremath{'}\ensuremath{\gamma})$ reactions on $^{57}\mathrm{Fe}$ and $^{97}\mathrm{Mo}$ targets. It is shown that statistical spectroscopy provides a useful tool in this mass region. Apparent step structures in the level-density curves are tentatively explained by a schematic microscopic model comprising single-particle level spacings and seniority-conserving and seniority-nonconserving interactions.

Elementary excitations of ferromagnetic metal nanoparticles

We present a theory of the elementary spin excitations in transition metal ferromagnet nanoparticles which achieves a unified and consistent quantum description of both collective and quasiparticle physics. The theory starts by recognizing the essential role played by spin-orbit interactions in determining the energies of ferromagnetic resonances in the collective excitation spectrum and the strength of their coupling to low-energy particle-hole excitations. We argue that a crossover between Landau-damped ferromagnetic resonance and pure-state collective magnetic excitations occurs as the number of atoms in typical transition metal ferromagnet nanoparticles drops below approximately $10^4$, approximately where the single-particle level spacing, $\delta$, becomes larger than, $\sqrt{\alpha} E_{\rm res}$, where $E_{\rm res}$ is the ferromagnetic resonance frequency and $\alpha$ is the Gilbert damping parameter. We illustrate our ideas by studying the properties of semi-realistic model Hamiltonians, which we solve numerically for nanoparticles containing several hundred atoms. For small nanoparticles, we find one isolated ferromagnetic resonance collective mode below the lowest particle-hole excitation energy, at $E_{\rm res} \approx 0.1$ meV. The spectral weight of this pure excitation nearly exhausts the transverse dynamical susceptibility spectral weight. As $\delta$ approaches $\sqrt{\alpha} E_{\rm res}$, the ferromagnetic collective excitation is more likely to couple strongly with discrete particle-hole excitations. In this regime the distinction between the two types of excitations blurs. We discuss the significance of this picture for the interpretation of recent single-electron tunneling experiments.

Adiabatic quantum pump of spin-polarized current.

We propose a mechanism by which an open quantum dot driven by two ac (radio frequency) gate voltages in the presence of a moderate in-plane magnetic field generates a spin-polarized, phase-coherent dc current. The idea combines adiabatic, nonquantized (but coherent) pumping through periodically modulated external parameters and the strong fluctuations of the electron wave function existent in chaotic cavities. We estimate that the spin polarization of the current can be observed for temperatures and Zeeman splitting energies of the order of the single-particle mean level spacing.

Model for pairing phase transition in atomic nuclei

A model is developed which allows the investigation and classification of the pairing phase transition in atomic nuclei. The regions of the parameter space are discussed for which a pairing phase transition can be observed. The model parameters include: number of particles, attenuation of pairing correlations with increasing seniority, single particle level spacing, and pairing gap parameter. It is argued that for nuclear models, the pairing phase transition has to be separated in temperature from the signal of the exhaustion of the finite model space.

Statistical distribution of Coulomb blockade peak heights in adiabatically pumped quantum dots

We study adiabatic quantum pumping in the resonant tunneling regime of a nearly-closed quantum dot, which is coupled to two leads via tunneling barriers. Using small cyclic variations of the tunneling rates of the barriers as the pumping mechanism, a current is obtained which depends sensitively on the system parameters and exhibits peaks due to Coulomb blockade. The distribution of the peak heights is found for temperatures $\Gam \ll k_{B} T \ll \Delta$, with $\Gam$ the total decay width into the leads and $\Delta$ the single-particle level spacing of the dot, and their average height is predicted to increase by a factor of $\frac{5\sqrt{2}}{18} \pi \approx 1.2$ upon breaking time-reversal symmetry. This is the pumping analog of the statistical theory of Coulomb blockade conductance peaks.

Coulomb-blockade peak-spacing distribution: Interplay of temperature and spin

We calculate the Coulomb Blockade peak spacing distribution at finite temperature using the recently introduced ``universal Hamiltonian'' to describe the e-e interactions. We show that the temperature effect is important even at kT~0.1\Delta (\Delta is the single-particle mean level spacing). This sensitivity arises because: (1) exchange reduces the minimum energy of excitation from the ground state and (2) the entropic contribution depends on the change of the spin of the quantum dot. Including the leading corrections to the universal Hamiltonian yields results in quantitative agreement with the experiments. Surprisingly, temperature appears to be the most important effect.

Decoherence in nearly isolated quantum dots.

Decoherence in nearly isolated GaAs quantum dots is investigated using the change in the average Coulomb blockade peak height when time-reversal symmetry is broken. The normalized change in the average peak height approaches the predicted universal value of 1/4 at temperatures well below the single-particle level spacing, T < Delta, but is greatly suppressed for T > Delta, suggesting that inelastic scattering or other dephasing mechanisms dominate in this regime.

Interaction-Induced Restoration of Phase Coherence

We study the conductance of a quantum T-junction coupled to two electron reservoirs and a quantum dot. In the absence of electron-electron interactions, the conductance $g$ is sensitive to interference between trajectories which enter the dot and those which bypass it. We show that including an intra-dot charging interaction has a marked influence-- it can enforce a coherent response from the dot at temperatures much larger than the single particle level spacing $\Delta$. The result is large oscillations of $g$ as a function of the voltage applied to a gate capacitively coupled to the dot. Without interactions, the conductance has only a weak interference signature when $T>\Delta$.

Statistical theory of finite Fermi systems with chaotic excited eigenstates

Abstract A theory of strongly interacting Fermi systems of a few particles is developed. At high excitation energies (a few times the single-particle level spacing) these systems are characterized by an extreme degree of complexity due to strong mixing of the shell-model-based many-particle basis states by the residual two-body interaction. This regime can be described as many-body quantum chaos. Practically, it occurs when the excitation energy of the system is greater than a few single-particle level spacings near the Fermi energy. Physical examples of such systems are compound nuclei, heavy open shell atoms (e.g. rare earths) and multicharged ions, molecules, clusters and quantum dots in solids. The main quantity of the theory is the strength function which describes spreading of the eigenstates over many-particle basis states (determinants) constructed using the shell-model orbital basis. A nonlinear equation for the strength function is derived, which enables one to describe the eigenstates without d...

The different effect of electron-electron interaction on the spectrum of atoms and quantum dots

The electron-electron scattering rate of single particle excitations in atoms is estimated and compared with the corresponding rate in quantum dots. It is found that in alkali atoms single particle excitations do not acquire a width due to electron-electron interaction, while in complex atoms they may. This width is typically smaller than the single particle level spacing, and hence does not affect the number of discrete single particle excitations resolved below the ionization threshold. This situation is contrasted with that of quantum dots where electron-electron interaction severely limits the number of resolved excitations. Unlike the case of quantum dots, the scattering rate in atoms is found to decrease with increasing excitation energy. The different effect of electron-electron interaction on the spectrum of quantum dots and atoms is traced to the different confining potentials in the two systems.

Quantum dots with even number of electrons: kondo effect in a finite magnetic field

We show that the Kondo effect can be induced by an external magnetic field in quantum dots with an even number of electrons. If the Zeeman energy B is close to the single-particle level spacing Delta in the dot, the scattering of the conduction electrons from the dot is dominated by an anisotropic exchange interaction. A Kondo resonance then occurs despite the fact that B exceeds by far the Kondo temperature T(K). As a result, at low temperatures T<<T(K) the differential conductance approaches a unitary limit G(K) approximately e(2)/piPlanck's over 2pi. A possible experimental realization of this effect is discussed.

Spacing and width of Coulomb blockade peaks in a silicon quantum dot

We present an experimental study of the fluctuations of Coulomb blockade peak positions of a quantum dot. The dot is defined by patterning the two-dimensional electron gas of a silicon MOSFET structure using stacked gates. The ratio of charging energy to single-particle energy is considerably larger than in comparable GaAs/AlGaAs quantum dots. The statistical distribution of the conductance peak spacings in the Coulomb blockade regime was found to be unimodal and does not follow the Wigner surmise. The fluctuations of the spacings are much larger than the typical single-particle level spacing and thus clearly contradict the expectation of random matrix theory. Measurements of the natural line width of a set of several adjacent conductance peaks suggest that all of the peaks in the set are dominated by electrons being transported through a single-broad energy level.

Pauli-limited superconductivity in small grains

We report on an exploration of the mean-field phase diagram for Pauli-limited superconductivity in small metallic grains. Emphasis is placed on the crossover from the ultra-small grain limit where superconductivity disappears to the bulk thin-film limit as the single-particle level spacing in the grain decreases. We find that the maximum Zeeman coupling strength compatible with superconductivity increases with decreasing grain size, in spite of a monotonically decreasing condensation energy per unit volume.

Addition spectrum and Koopmans’ theorem for disordered quantum dots

We investigate the addition spectrum of disordered quantum dots containing spinless interacting fermions using the self-consistent Hartree-Fock approximation. We concentrate on the regime ${r}_{s}\ensuremath{\gtrsim}1,$ with finite dimensionless conductance $g.$ We find that in this approximation the peak spacing fluctuations do not scale with the mean single-particle level spacing for either Coulomb or nearest-neighbor interactions when ${r}_{s}\ensuremath{\gtrsim}1.$ We also show that Koopmans' approximation to the addition spectrum can lead to errors that are of order the mean level spacing or larger, both in the mean addition spectrum peak spacings, and in the peak spacing fluctuations.

Resonant Raman scattering of quantum dots

We theoretically investigate the resonant Raman scattering of GaAs quantum dots. The electron system is treated within the time-dependent local-density approximation and the cross section is calculated by including valence-band states as intermediate states in the scattering process. We show that, besides the strongly collective charge-density excitations and spin-density excitations, which dominate the spectra in the nonresonant case, additional modes close to the single-particle level spacings become resonant for certain laser energies in polarized and depolarized geometry. However, these modes are also subjected to a small collective shift and occur at slightly different energies in the two polarization geometries.

Statistics of the Coulomb-blockade peak spacings of a silicon quantum dot

We present an experimental study of the fluctuations of Coulomb-blockade peak positions of a quantum dot. The dot is defined by patterning the two-dimensional electron gas of a silicon metal-oxide-semiconductor field-effect transistor structure using stacked gates. This permits variation of the number of electrons on the quantum dot without significant shape distortion. The ratio of charging energy to single-particle energy is considerably larger than in comparable $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum dots. The statistical distribution of the conductance peak spacings in the Coulomb-blockade regime was found to be unimodal and does not follow the Wigner surmise. The fluctuations of the spacings are much larger than the typical single-particle level spacing and thus clearly contradict the expectation of constant interaction--random matrix theory.

Superfluid, Superconducting, and Magnetic Ordering in Mesoscopic Quantum Dots

The nature of superfluid, superconducting, and magnetic ordering is elucidated for mesoscopic systems in which the single-particle level spacing is much larger than both the temperature and the critical temperature of ordering. Ordering is defined as a spontaneous breaking of symmetry, the gauge invariance and time reversal being by definition symmetries broken in superfluidity (superconductivity) and magnetism contexts, respectively. Superfluidity and superconductivity are realized in thermodynamic equilibrium states with a nonintegral average number of particles and are accompanied by the spontaneous breaking of time homogeneity. In Fermi systems, two types of superfluidity and superconductivity are possible which are characterized by the presence of pair or single-particle “condensates.” The latter is remarkable in that spontaneous breaking of fundamental symmetries such as spatial 2π rotation and double time reversal takes place. Possible experiments on metallic nanoparticles and ultracold atomic gases in magnetic traps are discussed.

Edge spin-density modes in quantum dots in a magnetic field

We investigate electronic excitations in GaAs–AlGaAs quantum dots by means of resonant inelastic light scattering in the presence of an external magnetic field B. At magnetic field B=0, we observe a series of discrete electronic excitations, namely, charge-density excitations (CDE i ) and spin-density excitations (SDE i ), in one and the same quantum dot sample. We find at finite magnetic field, additionally to the well-known splitting of the CDE i modes (plasmons), a quite similar splitting of the lowest SDE mode whose energy is very close to the single-particle level spacing in the quantum dot. In analogy to the edge magnetoplasmon, we call this excitation an edge spin-density mode.

Superfluidity, superconductivity and magnetism in mesoscopics

The nature of superfluid, superconducting, and magnetic ordering is elucidated for mesoscopic systems in which the single-particle level spacing is much larger than both the temperature and the critical temperature of ordering. Ordering is defined as a spontaneous violation of symmetry, the gauge invariance and time reversal being by definition symmetries violated in superfluidity (superconductivity) and magnetism contexts, respectively. Superfluidity and superconductivity are realized in thermodynamic equilibrium states with a non-integral average number of particles and are accompanied by the spontaneous violation of time homogeneity. In Fermi systems two types of superfluidity and superconductivity are possible which are characterized by the presence of pair or single-particle 'condensates'. The latter is remarkable in that spontaneous violation of fundamental symmetries such as spatial 2π rotation and double time reversal takes place. Possible experiments on metallic nanoparticles and ultracold atomic gases in magnetic traps are discussed.

Statistics of peak spacings and widths in the quantum coulomb blockade regime

Measurements of Coulomb blockade conductance peak spacings and widths measured over large ensembles (∼10 4 peaks) of peaks in ballistic GaAs quantum dots are reported. Distributions of spacings for both broken ( B≠0) and unbroken ( B=0) time-reversal symmetry are roughly Gaussian with broad non-Gaussian tails and a standard deviation of 2–6% of the average spacing, comparable to the single-particle level spacing. Spacing distributions for B=0 are wider by a factor of ∼1.2±0.1 compared to B≠0, consistent with random matrix theory. Surprisingly, spacing distributions are unimodal, suggesting an absence of spin-degeneracy. Peak width distributions reflect fluctuations in the “lever arm,” or capacitance ratio η= C gate/ C dot. Field-averaged peak width and spacing both change smoothly as electrons are added to the dot, but fluctuations in peak width appear uncorrelated with spacing fluctuations.