We study the Kondo effect in a quantum dot which is coupled to ferromagnetic leads and analyse its properties as a function of the spin polarization of the leads. Based on a scaling approach we predict that for parallel alignment of the magnetizations in the leads the strong-coupling limit of the Kondo effect is reached at a finite value of the magnetic field. Using an equation-of-motion technique we study nonlinear transport through the dot. For parallel alignment the zero-bias anomaly may be split even in the absence of an external magnetic field. For antiparallel spin alignment and symmetric coupling, the peak is split only in the presence of a magnetic field, but shows a characteristic asymmetry in amplitude and position.PACS numbers: PACS numbers: 75.20.Hr, 72.15.Qm, 73.23.Hk The Kondo effect [1] in electron transport through a quantum dot (QD) with an odd number of electrons is experimentally well established [2, 3]. Screening of the dot spin due to the exchange coupling with lead electrons yields, at low temperatures, a Kondo resonance. The main goal of the present work is to investigate how ferromagnetic leads influence the Kondo effect. In the extreme case of half-metallic leads, minority-spin electrons are completely absent, i.e., the screening of the dot spin is not possible, and no Kondo-correlated state can form. What happens, however, for the generic case of partially spin polarized leads? How does the spin-asymmetry affect the Kondo effect? Is there still a strong coupling limit, and how are transport properties modified?Based on a poor man's scaling analysis we first show that the strong-coupling limit can still be reached in this case if an external magnetic field is applied. This is familiar from the Kondo effect in QDs with an even number of electrons [4, 5, 6, 7], which occurs at finite magnetic fields, although the physical mechanism is different in the present case. In the second part of the paper we analyze within an equation-of-motion (EOM) approach the nonlinear transport through the QD. We find that for parallel alignment of the lead magnetizations the zerobias anomaly is split. This splitting can be removed by appropriately tuning the strength of an external magnetic field B. In the antiparallel configuration of the lead magnetizations no splitting occurs at zero field.The Anderson Hamiltonian for a QD with a single level at energy ǫ 0 coupled to ferromagnetic leads iswhere c rkσ and d σ are the Fermi operators for electrons with wavevector k and spin σ in the leads, r = L, R, and in the QD, V rk is the tunneling amplitude,, and the last term is the Zeeman energy of the dot. (Stray fields from the leads are neglected.) We assume identical leads and symmetric coupling, V Lk = V Rk . The ferromagnetism of the leads is accounted for by different densities of states (DOS) ν r↑ (ω) and ν r↓ (ω) for up and down-spin electrons.In the following we study the two cases of parallel (P) and antiparallel (AP) alignment of the leads' magnetic moments. For the AP configuration and zero magnetic f...

We study the full counting statistics of electron transport through multiterminal interacting quantum dots under a finite magnetic field. Microscopic reversibility leads to a symmetry of the cumulant generating function, which generalizes the fluctuation theorem in the context of the quantum transport. Using the symmetry, we derive the Onsager-Casimir relations in the linear transport regime and universal relations among nonlinear transport coefficients. One of the measurable relations is that the nonlinear conductance, the second-order coefficient with respect to the bias voltage, is connected to the third current cumulant in equilibrium, which can be a finite and uneven function of the magnetic field for two-terminal noncentrosymmetric system.

Through litter decomposition enormous amounts of carbon is emitted to the atmosphere. Numerous large-scale decomposition experiments have been conducted focusing on this fundamental soil process in order to understand the controls on the terrestrial carbon transfer to the atmosphere. However, previous studies were mostly based on site-specific litter and methodologies, adding major uncertainty to syntheses, comparisons and meta-analyses across different experiments and sites. In the TeaComposition initiative, the potential litter decomposition is investigated by using standardized substrates (Rooibos and Green tea) for comparison of litter mass loss at 336 sites (ranging from -9 to +26 °C MAT and from 60 to 3113 mm MAP) across different ecosystems. In this study we tested the effect of climate (temperature and moisture), litter type and land-use on early stage decomposition (3 months) across nine biomes. We show that litter quality was the predominant controlling factor in early stage litter decomposition, which explained about 65% of the variability in litter decomposition at a global scale. The effect of climate, on the other hand, was not litter specific and explained <0.5% of the variation for Green tea and 5% for Rooibos tea, and was of significance only under unfavorable decomposition conditions (i.e. xeric versus mesic environments). When the data were aggregated at the biome scale, climate played a significant role on decomposition of both litter types (explaining 64% of the variation for Green tea and 72% for Rooibos tea). No significant effect of land-use on early stage litter decomposition was noted within the temperate biome. Our results indicate that multiple drivers are affecting early stage litter mass loss with litter quality being dominant. In order to be able to quantify the relative importance of the different drivers over time, long-term studies combined with experimental trials are needed.