Detection and measurement of the Dzyaloshinskii-Moriya interaction in double quantum dot systems

Spins in quantum dots can act as the qubit for quantum computation. In this context we point out that spins on neighboring dots will experience an anisotropic form of the exchange coupling, called the Dzyaloshinskii-Moriya (DM) interaction, which mixes the spin singlet and triplet states. This will have an important effect on both qubit interactions and spin-dependent tunneling. We show that the interaction depends strongly on the direction of the external field, which gives an unambiguous signature of this effect. We further propose a new experiment using coupled quantum dots to detect and characterize the DM interaction.Comment: Updated version. Submitted to Physical Review

Spin-Valley Kondo Effect in Multi-electron Silicon Quantum Dots

We study the spin-valley Kondo effect of a silicon quantum dot occupied by $\mathcal{N}$ electrons, with $\mathcal{N}$ up to four. We show that the Kondo resonance appears in the $\mathcal{N}=1,2,3$ Coulomb blockade regimes, but not in the $\mathcal{N}=4$ one, in contrast to the spin-1/2 Kondo effect, which only occurs at $\mathcal{N}=$ odd. Assuming large orbital level spacings, the energy states of the dot can be simply characterized by fourfold spin-valley degrees of freedom. The density of states (DOS) is obtained as a function of temperature and applied magnetic field using a finite-U equation-of-motion approach. The structure in the DOS can be detected in transport experiments. The Kondo resonance is split by the Zeeman splitting and valley splitting for double- and triple-electron Si dots, in a similar fashion to single-electron ones. The peak structure and splitting patterns are much richer for the spin-valley Kondo effect than for the pure spin Kondo effect.Comment: 8 pages, 4 figures, in PRB format. This paper is a sequel to the paper published in Phys. Rev. B 75, 195345 (2007

Valley Splitting Theory of SiGe/Si/SiGe Quantum Wells

We present an effective mass theory for SiGe/Si/SiGe quantum wells, with an emphasis on calculating the valley splitting. The theory introduces a valley coupling parameter, $v_v$, which encapsulates the physics of the quantum well interface. The new effective mass parameter is computed by means of a tight binding theory. The resulting formalism provides rather simple analytical results for several geometries of interest, including a finite square well, a quantum well in an electric field, and a modulation doped two-dimensional electron gas. Of particular importance is the problem of a quantum well in a magnetic field, grown on a miscut substrate. The latter may pose a numerical challenge for atomistic techniques like tight-binding, because of its two-dimensional nature. In the effective mass theory, however, the results are straightforward and analytical. We compare our effective mass results with those of the tight binding theory, obtaining excellent agreement.Comment: 13 pages, 7 figures. Version submitted to PR

Water Adsorption at Two Unsolvated Peptides with a Protonated Lysine Residue: From Self-Solvation to Solvation

We study the initial steps of the interaction of water molecules with two unsolvated peptides: Ac-Ala₅-LysH⁺ and Ac-Ala₈-LysH⁺. Each peptide has two primary candidate sites for water adsorption near the C-terminus: a protonated carboxyl group and the protonated ammonium group of LysH⁺, which is fully hydrogen-bonded (self-solvated) in the absence of water. Earlier experimental studies have shown that H₂O adsorbs readily at Ac-Ala₅-LysH⁺ (a non-helical peptide) but with a much lower propensity at Ac-Ala₈-LysH⁺ (a helix) under the same conditions. The helical conformation of Ac-Ala₈-LysH⁺ has been suggested as the origin of the different behavior. We here use first-principles conformational searches (all-electron density functional theory based on a van der Waals corrected version of the PBE functional, PBE+vdW) to study the microsolvation of Ac-Ala₅-LysH⁺ with one to five water molecules and the monohydration of Ac-Ala₈-LysH⁺. In both cases, the most favorable water adsorption sites break intramolecular hydrogen bonds associated with the ammonium group, in contrast to earlier suggestions in the literature. A simple thermodynamic model yields Gibbs free energies Δ<i>G</i>⁰(<i>T</i>) and equilibrium constants in agreement with experiments. A qualitative change of the first adsorption site does not occur. For few water molecules, we do not consider carboxyl deprotonation or finite-temperature dynamics, but in a liquid solvent, both effects would be important. Exploratory <i>ab initio</i> molecular dynamics simulations illustrate the short-time effects of a droplet of 152 water molecules on the initial unsolvated conformation, including the deprotonation of the carboxyl group. The self-solvation of the ammonium group by intramolecular hydrogen bonds is lifted in favor of a solvation by water

Water Adsorption at Two Unsolvated Peptides with a Protonated Lysine Residue: From Self-Solvation to Solvation

We study the initial steps of the interaction of water molecules with two unsolvated peptides: Ac-Ala₅-LysH⁺ and Ac-Ala₈-LysH⁺. Each peptide has two primary candidate sites for water adsorption near the C-terminus: a protonated carboxyl group and the protonated ammonium group of LysH⁺, which is fully hydrogen-bonded (self-solvated) in the absence of water. Earlier experimental studies have shown that H₂O adsorbs readily at Ac-Ala₅-LysH⁺ (a non-helical peptide) but with a much lower propensity at Ac-Ala₈-LysH⁺ (a helix) under the same conditions. The helical conformation of Ac-Ala₈-LysH⁺ has been suggested as the origin of the different behavior. We here use first-principles conformational searches (all-electron density functional theory based on a van der Waals corrected version of the PBE functional, PBE+vdW) to study the microsolvation of Ac-Ala₅-LysH⁺ with one to five water molecules and the monohydration of Ac-Ala₈-LysH⁺. In both cases, the most favorable water adsorption sites break intramolecular hydrogen bonds associated with the ammonium group, in contrast to earlier suggestions in the literature. A simple thermodynamic model yields Gibbs free energies Δ<i>G</i>⁰(<i>T</i>) and equilibrium constants in agreement with experiments. A qualitative change of the first adsorption site does not occur. For few water molecules, we do not consider carboxyl deprotonation or finite-temperature dynamics, but in a liquid solvent, both effects would be important. Exploratory <i>ab initio</i> molecular dynamics simulations illustrate the short-time effects of a droplet of 152 water molecules on the initial unsolvated conformation, including the deprotonation of the carboxyl group. The self-solvation of the ammonium group by intramolecular hydrogen bonds is lifted in favor of a solvation by water

Validation Challenge of Density-Functional Theory for PeptidesExample of Ac-Phe-Ala₅‑LysH⁺

We assess the performance of a group of exchange-correlation functionals for predicting the secondary structure of peptide chains, up to a new many-body dispersion corrected hybrid density functional, dubbed PBE0+MBD* by its original authors. For the purpose of validation, we first compare to published, high-level benchmark conformational energy hierarchies (coupled cluster at the singles, doubles, and perturbative triples level, CCSD­(T)) for 73 conformers of small three-residue peptides, establishing that the van der Waals corrected PBE0 functional yields an average error of only ∼20 meV (∼0.5 kcal/mol). This compares to ∼40–50 meV for nondispersion corrected PBE0 and 40–100 meV for different empirical force fields (estimated for the alanine tetrapeptide). For longer peptide chains that form a secondary structure, CCSD­(T) level benchmark data are currently unaffordable. We thus turn to the <i>experimentally</i> well studied Ac-Phe-Ala₅-LysH⁺ peptide, for which four closely competing conformers were established by infrared spectroscopy. For comparison, an exhaustive theoretical conformational space exploration yields at least 11 competing low energy minima. We show that (i) the many-body dispersion correction, (ii) the hybrid functional nature of PBE0+MBD*, and (iii) zero-point corrections are needed to reveal the four experimentally observed structures as the minima that would be populated at low temperature