Absorption and Emission in quantum dots: Fermi surface effects of Anderson excitons

Recent experiments measuring the emission of exciton recombination in a self-organized single quantum dot (QD) have revealed that novel effects occur when the wetting layer surrounding the QD becomes filled with electrons, because the resulting Fermi sea can hybridize with the local electron levels on the dot. Motivated by these experiments, we study an extended Anderson model, which describes a local conduction band level coupled to a Fermi sea, but also includes a local valence band level. We are interested, in particular, on how many-body correlations resulting from the presence of the Fermi sea affect the absorption and emission spectra. Using Wilson's numerical renormalization group method, we calculate the zero-temperature absorption (emission) spectrum of a QD which starts from (ends up in) a strongly correlated Kondo ground state. We predict two features: Firstly, we find that the spectrum shows a power law divergence close to the threshold, with an exponent that can be understood by analogy to the well-known X-ray edge absorption problem. Secondly, the threshold energy $\omega_0$ - below which no photon is absorbed (above which no photon is emitted) - shows a marked, monotonic shift as a function of the exciton binding energy $U_{\rm exc}$Comment: 10 pages, 9 figure

Frequency-dependent transport through a quantum dot in the Kondo regime

We study the AC conductance and equilibrium current fluctuations of a Coulomb blockaded quantum dot. A relation between the equilibrium spectral function and the linear AC conductance is derived which is valid for frequencies well below the charging energy of the quantum dot. Frequency-dependent transport measurements can thus give experimental access to the Kondo peak in the equilibrium spectral function of a quantum dot. We illustrate this in detail for typical experimental parameters using the numerical renormalization group method in combination with the Kubo formalism.Comment: 4 pages, 4 figure

Vanadium oxide clusters in substellar atmospheres: A quantum chemical study

We aim to understand the formation of cloud condensation nuclei in oxygen-rich substellar atmospheres by calculating fundamental properties of the energetically most favorable vanadium oxide molecules and clusters. A hierarchical optimization approach is applied in order to find the most favorable structures for clusters of (VO)$_{N}$ and (VO$_2$)$_{N}$ for N=1-10, and (V$_2$O$_5$)$_{N}$ for N=1-4 and to calculate their thermodynamical potentials. The candidate geometries are initially optimized applying classical interatomic potentials and then refined at the B3LYP/cc-pVTZ level of theory to obtain accurate zero-point energies and thermochemical quantities. We present previously unreported vanadium oxide cluster structures as lowest-energy isomers. We report revised cluster energies and their thermochemical properties. Chemical equilibrium calculations are used to asses the impact of the updated and newly derived thermodynamic potentials on the gas-phase abundances of vanadium-bearing species. In chemical equilibrium, larger clusters from different stoichiometric families are found to be the most abundant vanadium-bearing species for temperatures below ~1000 K, while molecular VO is the most abundant between ~1000 K and ~2000 K. We determine the nucleation rates of each stoichiometric family for a given (T$_{gas}$, p$_{gas}$) profile of a brown dwarf using classical and non-classical nucleation theory. Small differences in the revised Gibbs free energies of the clusters have a large impact on the abundances of vanadium bearing species in chemical equilibrium at temperatures below ~1000 K, which subsequently has an impact on the nucleation rates of each stoichiometric family. We find that with the revised and more accurate cluster data non-classical nucleation rates are up to 15 orders of magnitude higher than classical nucleation rates.Comment: accepted to A&A, 16 pages, 10 figure

Infrared spectra of TiO2 clusters for hot Jupiter atmospheres

Context. Clouds seem unavoidable in cool and dense environments, and hence, are necessary to explain observations of exoplanet atmospheres, most recently of WASP 96b with JWST. Understanding the formation of cloud condensation nuclei in non-terrestrial environments is therefore crucial to develop accurate models to interpret present and future observations. Aims. The goal of the paper is to support observations with infrared spectra for (TiO2)N clusters in order to study cloud formation in exoplanet atmospheres. Methods. Vibrational frequencies are derived from quantum-chemical calculations for 123 (TiO2)-clusters and their isomers, and line-broadening mechanisms are evaluated. Cluster spectra are calculated for several atmospheric levels for two example exoplanet atmospheres (WASP 121b-like and WASP 96b-like) to identify possible spectral fingerprints for cloud formation. Results. Rotational motion of and transitions in the clusters cause significant line broadening, so that individual vibrational lines are broadened beyond the spectral resolution of the medium resolution mode of the JWST mid-infrared instrument MIRI at R = 3000. However, each individual cluster isomer exhibits a "fingerprint" IR spectrum. In particular, larger (TiO2)-clusters have distinctly different spectra from smaller clusters. Morning and evening terminator for the same planet can exhibit different total absorbances due to different cluster sizes being more abundant. Conclusions. The largest (TiO2)-clusters are not necessarily the most abundant (TiO2)-clusters in the high-altitude regions of ultra-hot Jupiters, and the different cluster isomers will contribute to the local absorbance. Planets with a considerable day-night asymmetry will be most suitable to search for (TiO2)-cluster isomers in order to improve cloud formation modelling.Comment: 8 pages, 8 figures, 1 table, accepted for publication in A&

Kondo quantum dot coupled to ferromagnetic leads: Numerical renormalization group study

We systematically study the influence of ferromagnetic leads on the Kondo resonance in a quantum dot tuned to the local moment regime. We employ Wilson's numerical renormalization group method, extended to handle leads with a spin asymmetric density of states, to identify the effects of (i) a finite spin polarization in the leads (at the Fermi-surface), (ii) a Stoner splitting in the bands (governed by the band edges) and (iii) an arbitrary shape of the leads density of states. For a generic lead density of states the quantum dot favors being occupied by a particular spin-species due to exchange interaction with ferromagnetic leads leading to a suppression and splitting of the Kondo resonance. The application of a magnetic field can compensate this asymmetry restoring the Kondo effect. We study both the gate-voltage dependence (for a fixed band structure in the leads) and the spin polarization dependence (for fixed gate voltage) of this compensation field for various types of bands. Interestingly, we find that the full recovery of the Kondo resonance of a quantum dot in presence of leads with an energy dependent density of states is not only possible by an appropriately tuned external magnetic field but also via an appropriately tuned gate voltage. For flat bands simple formulas for the splitting of the local level as a function of the spin polarization and gate voltage are given.Comment: 18 pages, 18 figures, accepted for publication in PR

Gate-controlled spin splitting in quantum dots with ferromagnetic leads in the Kondo regime

科研費報告書収録論文(課題番号:16340097/研究代表者:前川禎通/スピン及び軌道による量子伝導の制御理論)47

NRG study of the Kondo effect in the presence of itinerant-electron ferromagnetism

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 theory and a generalized Friedel sum rule, and transport in the unitary limit is not spin dependent.Comment: 4 pages, 4 figure

Electric-field controlled spin reversal in a quantum dot with ferromagnetic contacts

Manipulation of the spin-states of a quantum dot by purely electrical means is a highly desirable property of fundamental importance for the development of spintronic devices such as spin-filters, spin-transistors and single-spin memory as well as for solid-state qubits. An electrically gated quantum dot in the Coulomb blockade regime can be tuned to hold a single unpaired spin-1/2, which is routinely spin-polarized by an applied magnetic field. Using ferromagnetic electrodes, however, the properties of the quantum dot become directly spin-dependent and it has been demonstrated that the ferromagnetic electrodes induce a local exchange-field which polarizes the localized spin in the absence of any external fields. Here we report on the experimental realization of this tunneling-induced spin-splitting in a carbon nanotube quantum dot coupled to ferromagnetic nickel-electrodes. We study the intermediate coupling regime in which single-electron states remain well defined, but with sufficiently good tunnel-contacts to give rise to a sizable exchange-field. Since charge transport in this regime is dominated by the Kondo-effect, we can utilize this sharp many-body resonance to read off the local spin-polarization from the measured bias-spectroscopy. We show that the exchange-field can be compensated by an external magnetic field, thus restoring a zero-bias Kondo-resonance, and we demonstrate that the exchange-field itself, and hence the local spin-polarization, can be tuned and reversed merely by tuning the gate-voltage. This demonstrates a very direct electrical control over the spin-state of a quantum dot which, in contrast to an applied magnetic field, allows for rapid spin-reversal with a very localized addressing.Comment: 19 pages, 11 figure

Residual Kondo effect in quantum dot coupled to half-metallic ferromagnets

We study the Kondo effect in a quantum dot coupled to half-metallic ferromagnetic electrodes in the regime of strong on-dot correlations. Using the equation of motion technique for nonequilibrium Green functions in the slave boson representation we show that the Kondo effect is not completely suppressed for anti-parallel leads magnetization. In the parallel configuration there is no Kondo effect but there is an effect associated with elastic cotunneling which in turn leads to similar behavior of the local (on-dot) density of states (LDOS) as the usual Kondo effect. Namely, the LDOS shows the temperature dependent resonance at the Fermi energy which splits with the bias voltage and the magnetic field. Moreover, unlike for non-magnetic or not fully polarized ferromagnetic leads the only minority spin electrons can form such resonance in the density of states. However, this resonance cannot be observed directly in the transport measurements and we give some clues how to identify the effect in such systems.Comment: 15 pages, 8 figures, accepted for publication in J. Phys.: Condens. Mat