Five approaches to exact open-system dynamics: Complete positivity, divisibility, and time-dependent observables

To extend the classical concept of Markovianity to an open quantum system, different notions of the divisibility of its dynamics have been introduced. Here, we analyze this issue by five complementary approaches: equations of motion, real-time diagrammatics, Kraus-operator sums, as well as time-local and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study featuring several types of divisible dynamics, we examine in detail an exactly solvable noninteracting fermionic resonant level coupled arbitrarily strongly to a fermionic bath at an arbitrary temperature in the wideband limit. In particular, the impact of divisibility on the time-dependence of the observable level occupation is investigated and compared with typical Markovian approximations. We find that the loss of semigroup-divisibility is accompanied by a prominent reentrant behavior: Counter to intuition, the level occupation may temporarily increase significantly in order to reach a stationary state with smaller occupation, implying a reversal of the measurable transport current. In contrast, the loss of the so-called completely positive divisibility is more subtly signaled by the prohibition of such current reversals in specific time-intervals. Experimentally, it can be detected in the family of transient currents obtained by varying the initial occupation. To quantify the nonzero footprint left by the system in its effective environment, we determine the exact time-dependent state of the latter as well as related information measures such as entropy, exchange entropy, and coherent information.

Switchable Coupling of Vibrations to Two-Electron Carbon-Nanotube Quantum Dot States

We report transport measurements on a quantum dot in a partly suspended carbon nanotube. Electrostatic tuning allows us to modify and even switch "on" and "off" the coupling to the quantized stretching vibration across several charge states. The magnetic-field dependence indicates that only the two-electron spin-triplet excited state couples to the mechanical motion, indicating mechanical coupling to both the valley degree of freedom and the exchange interaction, in contrast to standard models.

Interaction of spin and vibrations in transport through single-molecule magnets

We study electron transport through a single-molecule magnet (SMM) and the interplay of its anisotropic spin with quantized vibrational distortions of the molecule. Based on numerical renormalization group calculations we show that, despite the longitudinal anisotropy barrier and small transverse anisotropy, vibrational fluctuations can induce quantum spin-tunneling (QST) and a QST-Kondo effect. The interplay of spin scattering, QST and molecular vibrations can strongly enhance the Kondo effect and induce an anomalous magnetic field dependence of vibrational Kondo side-bands.

Transport and accumulation of spin anisotropy

We show that spin anisotropy can be transferred to an isotropic system by transport of a spin-quadrupole moment. We derive the quadrupole moment current and continuity equation and study a spin-valve structure consisting of two ferromagnets coupled to a quantum dot probing an impurity spin. The quadrupole backaction on their coupled spin results in spin torques and anisotropic spin relaxation which do not follow from standard spin-current considerations. We demonstrate the detection of the impurity spin by charge transport and its manipulation by electric fields.

Electric field controlled magnetic anisotropy in a single molecule

We have measured quantum transport through an individual Fe(4) single-molecule magnet embedded in a three-terminal device geometry. The characteristic zero-field splittings of adjacent charge states and their magnetic field evolution are observed in inelastic tunneling spectroscopy. We demonstrate that the molecule retains its magnetic properties and, moreover, that the magnetic anisotropy is significantly enhanced by reversible electron addition/subtraction controlled with the gate voltage. Single-molecule magnetism can thus be electrically controlled.

Charge transport through single molecules, quantum dots and quantum wires

We review recent progress in the theoretical description of correlation and quantum fluctuation phenomena in charge transport through single molecules, quantum dots and quantum wires. Various physical phenomena are addressed, relating to cotunneling, pair-tunneling, adiabatic quantum pumping, charge and spin fluctuations, and inhomogeneous Luttinger liquids. We review theoretical many-body methods to treat correlation effects, quantum fluctuations, non-equilibrium physics, and the time evolution into the stationary state of complex nanoelectronic systems.

Dzyaloshinskii-Moriya interaction in transport through single-molecule transistors

The Dzyaloshinskii-Moriya interaction is shown to result in a canting of spins in a single-molecule transistor. We predict nonlinear transport signatures of this effect induced by spin-orbit coupling for the generic case of a molecular dimer. The conductance is calculated using a master equation and is found to exhibit a non-trivial dependence on the magnitude and direction of an external magnetic field. We show how three-terminal transport measurements allow for a determination of the coupling vector characterizing the Dzyaloshinskii-Moriya interaction. In particular, we show how its orientation, defining the intramolecular spin chirality, can be probed with ferromagnetic electrodes.

Interaction-induced adiabatic nonlinear transport

We calculate the time-dependent nonlinear transport current through an interacting quantum dot in the single-electron tunneling (SET) regime. We show that an additional dc current is generated by the electron-electron interaction by adiabatic out-of-phase modulation of the gate and bias voltage. This current can arise only when two SET resonance conditions are simultaneously satisfied. We propose an adiabatic transport spectroscopy where lock-in measurement of a "time-averaged stability diagram" probes interactions, tunnel asymmetries, and changes in the ground state spin degeneracy.

Pair tunneling resonance in the single-electron transport regime

We predict a new electron pair tunneling (PT) resonance in nonlinear transport through quantum dots with positive charging energies exceeding the broadening due to thermal and quantum fluctuations. The PT resonance shows up in the single-electron transport (SET) regime as a peak in the derivative of the nonlinear conductance, d(2)I/dV(2), when the electrochemical potential of one electrode matches the average of two subsequent charge addition energies. For a single level quantum dot (Anderson model) we find the analytic peak shape and the dependence on temperature, magnetic field, and junction asymmetry and compare with the inelastic cotunneling peak which is of the same order of magnitude. In experimental transport spectroscopy the PT resonance may be mistaken for a weak SET resonance judging only by the voltage dependence of its position. Our results provide essential clues to avoid such erroneous interpretation.

Pumping of vibrational excitations in the coulomb-blockade regime in a suspended carbon nanotube

Low-temperature transport spectroscopy measurements on a suspended few-hole carbon nanotube quantum dot are presented, showing a gate-dependent harmonic excitation spectrum which, strikingly, occurs in the Coulomb-blockade regime. The quantized excitation energy corresponds to the scale expected for longitudinal vibrations of the nanotube. The electronic transport processes are identified as cotunnel-assisted sequential tunneling, resulting from nonequilibrium occupation of the mechanical mode. They appear only above a high-bias threshold at the scale of electronic nanotube excitations. We discuss models for the pumping process that explain the enhancement of the nonequilibrium occupation and show that it is connected to a subtle interplay between electronic and vibrational degrees of freedom.

Nonequilibrium dynamics of anisotropic large spins in the kondo regime: time-dependent numerical renormalization group analysis

We investigate the time-dependent Kondo effect in a single-molecule magnet (SMM) strongly coupled to metallic electrodes. Describing the SMM by a Kondo model with large spin S>1/2, we analyze the underscreening of the local moment and the effect of anisotropy terms on the relaxation dynamics of the magnetization. Underscreening by single-channel Kondo processes leads to a logarithmically slow relaxation, while finite uniaxial anisotropy causes a saturation of the SMM's magnetization. Additional transverse anisotropy terms induce quantum spin tunneling and a pseudospin-1/2 Kondo effect sensitive to the spin parity.

Kondo-transport spectroscopy of single molecule magnets

We demonstrate that in a single molecule magnet strongly coupled to electrodes the Kondo effect involves all magnetic excitations. This Kondo effect is induced by the quantum tunneling of the magnetic moment. Importantly, the Kondo temperature TK can be much larger than the magnetic splittings. We find a strong modulation of the Kondo effect as a function of the transverse anisotropy parameter or a longitudinal magnetic field. Both for integer and half-integer spin this can be used for an accurate transport spectroscopy of the magnetic states in low magnetic fields on the order of the easy-axis anisotropy parameter. We set up a relationship between the Kondo effects for successive integer and half-integer spins.

Electron transport through single Mn12 molecular magnets

We report transport measurements through a single-molecule magnet, the Mn12 derivative [Mn12O12(O2C-C6H4-SAc)16(H2O)4], in a single-molecule transistor geometry. Thiol groups connect the molecule to gold electrodes that are fabricated by electromigration. Striking observations are regions of complete current suppression and excitations of negative differential conductance on the energy scale of the anisotropy barrier of the molecule. Transport calculations, taking into account the high-spin ground state and magnetic excitations of the molecule, reveal a blocking mechanism of the current involving nondegenerate spin multiplets.

Quantum-tunneling-induced Kondo effect in single molecular magnets

We consider transport through a single-molecule magnet strongly coupled to metallic electrodes. We demonstrate that, for a half-integer spin of the molecule, electron and spin tunneling cooperate to produce both quantum tunneling of the magnetic moment and a Kondo effect in the linear conductance. The Kondo temperature depends sensitively on the ratio of the transverse and easy-axis anisotropies in a nonmonotonic way. The magnetic symmetry of the transverse anisotropy imposes a selection rule on the total spin for the occurrence of the Kondo effect which deviates from the usual even-odd alternation.

Spin quantum tunneling in single molecular magnets: fingerprints in transport spectroscopy of current and noise

We demonstrate that transport spectroscopy of single molecular magnets shows signatures of quantum tunneling at low temperatures. We find current and noise oscillations as a function of bias voltage due to a weak violation of spin-selection rules by quantum tunneling processes. The interplay with Boltzmann suppression factors leads to fake resonances with temperature-dependent position which do not correspond to any charge excitation energy. Furthermore, we find that quantum tunneling can completely suppress transport if the transverse anisotropy has a high symmetry.

Vibration-induced Kondo tunneling through metal-organic complexes with even electron occupation number

We investigate transport through a mononuclear transition-metal complex with strong tunnel coupling to two electrodes. The ground state of this molecule is a singlet, while the first excited state is a triplet. We show that a modulation of the tunnel-barrier due to a molecular distortion which couples to the tunneling induces a Kondo-effect, provided the discrete vibrational energy compensates the singlet-triplet gap. We discuss the single-phonon and two-phonon-assisted cotunneling and possible experimental realization of the theory.

Current collapse in tunneling transport through benzene

We investigate the electrical transport through a system of benzene coupled to metal electrodes by electron tunneling. Using electronic structure calculations, a semiquantitative model for the pi electrons of the benzene is derived that includes general two-body interactions. After exact diagonalization of the benzene model the transport is computed using perturbation theory for weak electrode-benzene coupling (golden rule approximation). We include the effect of an applied electric field on the molecular states, as well as radiative relaxation. We predict a current collapse and strong negative differential conductance due to a "blocking" state when the electrode is coupled to the para-position of benzene. In contrast, for coupling to the meta-position, a series of steps in the I-V curve is found.