Universal scaling in transport out of equilibrium through a single quantum dot using the noncrossing approximation

The universal scaling behavior is studied for nonequilibrium transport through a quantum dot. To describe the dot we use the standard Anderson impurity model and use the non-equilibrium non-crossing approximation in the limit of infinite Coulomb repulsion. After solving de hamiltonian, we calculate the conductance through the system as a function of temperature $T$ and bias voltage $V$ in the Kondo and in the mixed valent regime. We obtain a good scaling function in both regimes. In particular, in the mixed valent regime, we find excellent agreement with recent experiments and previous theoretical works.Comment: 6 pages, 5 figures, Accepted Physical Review

Quantum Transport Through a Stretched Spin--1 Molecule

We analyze the electronic transport through a model spin-1 molecule as a function of temperature, magnetic field and bias voltage. We consider the effect of magnetic anisotropy, which can be generated experimentally by stretching the molecule. In the experimentally relevant regime the conductance of the unstretched molecule reaches the unitary limit of the underscreened spin- 1 Kondo effect at low temperatures. The magnetic anisotropy generates an antiferromagnetic coupling between the remaining spin 1/2 and a singular density of quasiparticles, producing a second Kondo effect and a reduced conductance. The results explain recent measurements in spin-1 molecules [Science 328 1370 (2010)].Comment: 5 pages, 3 figures, minor changes, accepted for publication in EP

Bohrification

New foundations for quantum logic and quantum spaces are constructed by merging algebraic quantum theory and topos theory. Interpreting Bohr's "doctrine of classical concepts" mathematically, given a quantum theory described by a noncommutative C*-algebra A, we construct a topos T(A), which contains the "Bohrification" B of A as an internal commutative C*-algebra. Then B has a spectrum, a locale internal to T(A), the external description S(A) of which we interpret as the "Bohrified" phase space of the physical system. As in classical physics, the open subsets of S(A) correspond to (atomic) propositions, so that the "Bohrified" quantum logic of A is given by the Heyting algebra structure of S(A). The key difference between this logic and its classical counterpart is that the former does not satisfy the law of the excluded middle, and hence is intuitionistic. When A contains sufficiently many projections (e.g. when A is a von Neumann algebra, or, more generally, a Rickart C*-algebra), the intuitionistic quantum logic S(A) of A may also be compared with the traditional quantum logic, i.e. the orthomodular lattice of projections in A. This time, the main difference is that the former is distributive (even when A is noncommutative), while the latter is not. This chapter is a streamlined synthesis of 0709.4364, 0902.3201, 0905.2275.Comment: 44 pages; a chapter of the first author's PhD thesis, to appear in "Deep Beauty" (ed. H. Halvorson

Nonequilibrium transport through magnetic vibrating molecules

We calculate the nonequilibrium conductance through a molecule or a quantum dot in which the occupation of the relevant electronic level is coupled with intensity $\lambda$ to a phonon mode, and also to two conducting leads. The system is described by the Anderson-Holstein Hamiltonian. We solve the problem using the Keldysh formalism and the non-crossing approximation (NCA) for both, the electron-electron and the electron-phonon interactions. We obtain a moderate decrease of the Kondo temperature $T_K$ with $\lambda$ for fixed renormalized energy of the localized level $\tilde{E_d}$. The meaning and value of $\tilde{E_d}$ are discussed. The spectral density of localized electrons shows in addition to the Kondo peak of width $2 T_K$, satellites of this peak shifted by multiples of the phonon frequency $\omega_0$. The nonequilibrium conductance as a function of bias voltage $V_b$ at small temperatures, also displays peaks at multiples of $\omega_0$ in addition to the central dominant Kondo peak near $V_b=0$.Comment: 11 pages, 13 figures, accepted in Phys. Rev.

Impact of capacitance and tunneling asymmetries on Coulomb blockade edges and Kondo peaks in non-equilibrium transport through molecular quantum dots

We investigate theorerically the non-equilibrium transport through a molecular quantum dot as a function of gate and bias voltage, taking into account the typical situation in molecular electronics. In this respect, our study includes asymmetries both in the capacitances and tunneling rates to the source and drain electrodes, as well as an infinitely large charging energy on the molecule. Our calculations are based on the out-of-equilibrium Non-Crossing-Approximation (NCA), which is a reliable technique in the regime under consideration. We find that Coulomb blockade edges and Kondo peaks display strong renormalization in their width and intensity as a function of these asymmetries, and that basic expectations from Coulomb blockade theory must be taken with care in general, expecially when Kondo physics is at play. In order to help comparison of theory to experiments, we also propose a simple phenomenological model which reproduces semi-quantitatively the Coulomb blockade edges that were numerically computed from the NCA in all regimes of parameters.Comment: 9 pages, 8 figure

Replicas of the Kondo peak due to electron-vibration interaction in molecular transport properties

The low temperature properties of single level molecular quantum dots including both, electron-electron and electron-vibration interactions, are theoretically investigated. The calculated differential conductance in the Kondo regime exhibits not only the zero bias anomaly but also side peaks located at bias voltages which coincide with multiples of the energy of vibronic mode $V \sim \hbar\Omega/e$. We obtain that the evolution with temperature of the two main satellite conductance peaks follows the corresponding one of the Kondo peak when $\hbar\Omega \gg k_B T_K$, being $T_K$ the Kondo temperature, in agreement with recent transport measurements in molecular junctions. However, we find that this is no longer valid when $\hbar\Omega$ is of the order of a few times $k_B T_K$.Comment: 6 pages, 4 figures. Accepted for publication in Physical Review

Restoring the SU(4) Kondo regime in a double quantum dot system

We calculate the spectral density and occupations of a system of two capacitively coupled quantum dots, each one connected to its own pair of conducting leads, in a regime of parameters in which the total coupling to the leads for each dot $\Gamma_i$ are different. The system has been used recently to perform pseudospin spectroscopy by controlling independently the voltages of the four leads. For an odd number of electrons in the system, $\Gamma_1=\Gamma_2$, equal dot levels $E_1=E_2$ and sufficiently large interdot repulsion $U_{12}$ the system lies in the SU(4) symmetric point of spin and pseudospin degeneracy in the Kondo regime. In the more realistic case $\Gamma_1 \neq \Gamma_2$, pseudospin degeneracy is broken and the symmetry is reduced to SU(2). Nevertheless we find that the essential features of the SU(4) symmetric case are recovered by appropriately tuning the level difference $\delta=E_2-E_1$. The system behaves as an SU(4) Kondo one at low energies. Our results are relevant for experiments which look for signatures of SU(4) symmetry in the Kondo regime of similar systems.Comment: 9 pages, 10 figure