Magnetotransport on the nano scale.

Transport experiments in strong magnetic fields show a variety of fascinating phenomena like the quantum Hall effect, weak localization or the giant magnetoresistance. Often they originate from the atomic-scale structure inaccessible to macroscopic magnetotransport experiments. To connect spatial information with transport properties, various advanced scanning probe methods have been developed. Capable of ultimate spatial resolution, scanning tunnelling potentiometry has been used to determine the resistance of atomic-scale defects such as steps and interfaces. Here we combine this technique with magnetic fields and thus transfer magnetotransport experiments to the atomic scale. Monitoring the local voltage drop in epitaxial graphene, we show how the magnetic field controls the electric field components. We find that scattering processes at localized defects are independent of the strong magnetic field while monolayer and bilayer graphene sheets show a locally varying conductivity and charge carrier concentration differing from the macroscopic average.

Mott Quantum Criticality in the Anisotropic 2D Hubbard Model.

We present evidence for Mott quantum criticality in an anisotropic two-dimensional system of coupled Hubbard chains at half-filling. In this scenario emerging from variational cluster approximation and cluster dynamical mean-field theory, the interchain hopping t_{⊥} acts as a control parameter driving the second-order critical end point T_{c} of the metal-insulator transition down to zero at t_{⊥}^{c}/t≃0.2. Below t_{⊥}^{c}, the volume of the hole and electron Fermi pockets of a compensated metal vanishes continuously at the Mott transition. Above t_{⊥}^{c}, the volume reduction of the pockets is cut off by a first-order transition. We discuss the relevance of our findings to a putative quantum critical point in layered organic conductors, whose location remains elusive so far.

Interplay between the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida interaction.

The interplay between the Ruderman-Kittel-Kasuya-Yosida interaction and the Kondo effect is expected to provide the driving force for the emergence of many phenomena in strongly correlated electron materials. Two magnetic impurities in a metal are the smallest possible system containing all these ingredients and define a bottom-up approach towards a long-term understanding of concentrated/dense systems. Here we report on the experimental and theoretical investigation of iron dimers buried below a Cu(100) surface by means of low-temperature scanning tunnelling spectroscopy combined with density functional theory and numerical renormalization group calculations. The Kondo effect, in particular the width of the Abrikosov-Suhl resonance, is strongly altered or even suppressed due to magnetic coupling between the impurities. It oscillates as a function of dimer separation revealing that it is related to indirect exchange interactions mediated by the conduction electrons.

Extracting spectral properties from Keldysh Green functions.

We investigate the possibility to assist the numerically ill-posed calculation of spectral properties of interacting quantum systems in thermal equilibrium by extending the imaginary-time simulation to a finite Schwinger-Keldysh contour. The effect of this extension is tested within the standard maximum entropy approach to analytic continuation. We find that the inclusion of real-time data improves the resolution of structures at high energy, while the imaginary-time data are needed to correctly reproduce low-frequency features such as quasiparticle peaks. As a nonequilibrium application, we consider the calculation of time-dependent spectral functions from retarded Green function data on a finite time interval, and compare the maximum entropy approach to direct Fourier transformation and a method based on Padé approximants.

Unconventional superconductivity from local spin fluctuations in the Kondo lattice.

The explanation of heavy-fermion superconductivity is a long-standing challenge to theory. It is commonly thought to be connected to nonlocal fluctuations of either spin or charge degrees of freedom and therefore of unconventional type. Here we present results for the Kondo-lattice model, a paradigmatic model to describe heavy-fermion compounds, obtained from dynamical mean-field theory which captures local correlation effects only. Unexpectedly, we find robust s-wave superconductivity in the heavy-fermion state. We argue that this novel type of pairing is tightly connected to the formation of heavy quasiparticle bands and the presence of strong local spin fluctuations.

Spin-selective Kondo insulator: cooperation of ferromagnetism and the Kondo effect.

We propose the notion of a spin-selective Kondo insulator, which provides a fundamental mechanism to describe the ferromagnetic phase of the Kondo lattice model with antiferromagnetic coupling. This unveils a remarkable feature of the ferromagnetic metallic phase: the majority-spin conduction electrons show metallic while the minority-spin electrons show insulating behavior. The resulting Kondo gap in the minority-spin sector, which is due to the cooperation of ferromagnetism and partial Kondo screening, evidences a dynamically induced commensurability for a combination of minority-spin electrons and parts of localized spins. Furthermore, this mechanism predicts a nontrivial relation between the macroscopic quantities such as electron magnetization, spin polarization, and electron filling.

Multistep approach to microscopic models for frustrated quantum magnets: the case of the natural mineral azurite.

The natural mineral azurite Cu(3)(CO(3))(2)(OH)(2) is a frustrated magnet displaying unusual and controversially discussed magnetic behavior. Motivated by the lack of a unified description for this system, we perform a theoretical study based on density functional theory as well as state-of-the-art numerical many-body calculations. We propose an effective generalized spin-1/2 diamond chain model which provides a consistent description of experiments: low-temperature magnetization, inelastic neutron scattering, nuclear magnetic resonance measurements, magnetic susceptibility as well as new specific heat measurements. With this study we demonstrate that the balanced combination of first principles with powerful many-body methods successfully describes the behavior of this frustrated material.

Thermodynamics of the 3D Hubbard model on approaching the Néel transition.

We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the Néel temperature by using cluster dynamical mean-field theory. In particular, we calculate the energy, entropy, density, double occupancy, and nearest-neighbor spin correlations as a function of chemical potential, temperature, and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle S/N ≈ 0.65(6) at U/t = 8 is sufficient to achieve a Néel state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.

Analytic continuation of quantum Monte Carlo data by stochastic analytical inference.

We present an algorithm for the analytic continuation of imaginary-time quantum Monte Carlo data which is strictly based on principles of Bayesian statistical inference. Within this framework we are able to obtain an explicit expression for the calculation of a weighted average over possible energy spectra, which can be evaluated by standard Monte Carlo simulations, yielding as by-product also the distribution function as function of the regularization parameter. Our algorithm thus avoids the usual ad hoc assumptions introduced in similar algorithms to fix the regularization parameter. We apply the algorithm to imaginary-time quantum Monte Carlo data and compare the resulting energy spectra with those from a standard maximum-entropy calculation.

Continuous-time quantum Monte Carlo and maximum entropy approach to an imaginary-time formulation of strongly correlated steady-state transport.

Recently, Han and Heary [Phys. Rev. Lett. 99, 236808 (2007)] proposed an approach to steady-state quantum transport through mesoscopic structures, which maps the nonequilibrium problem onto a family of auxiliary quantum impurity systems subject to imaginary voltages. We employ continuous-time quantum Monte-Carlo solvers to calculate accurate imaginary time data for the auxiliary models. The spectral function is obtained from a maximum entropy analytical continuation in both Matsubara frequency and complexified voltage. To enable the analytical continuation we construct a kernel which is compatible with the analytical structure of the theory. While it remains a formidable task to extract reliable spectral functions from this unbiased procedure, particularly for large voltages, our results indicate that the method in principle yields results in agreement with those obtained by other methods.

Targeted self-assembly and quantum Monte Carlo magnetic study of an alternating nickel(II) 1D coordination polymer composed of highly preorganized binuclear tectons.

A pyrazolate-based binucleating ligand HL with pyridyl groups in the chelate arms has been used to synthesize the dinickel(II) complex [LNi2(N3)(MeOH)2](ClO4)2 (1) and the corresponding 1D polymeric [LNi2(mu-N3)2]n(NO3)n (2) depending on the amount of NaN3 added. X-Ray crystallography shows that structural parameters of the (LNi2(N3)) units are very similar in both compounds. This is ascribed to pi-pi stacking between the pyridyl rings that leads to rigidification of the framework and a fixed cis-orientation of the remaining coordination sites, which are filled by MeOH molecules in or by a mu1,3-bridging azide that connects the subunits in 2. Variable-temperature magnetic measurements reveal strong antiferromagnetic coupling with parameters g = 2.21 and J = -60.7 cm(-1) for compound 1. Magnetic data for the extended chain 2 have been analyzed by Quantum Monte Carlo (QMC) simulations to give g = 2.34, J1 = -55 cm(-1), and J2 = -12 cm(-1). The known J value for finally allows unambiguous assignment of J1 to the intrasubunit coupling within each bimetallic chain constituent. The alternation ratio gamma = J2/J1 signifies a singlet-dimer ground state of the new 1D polymer 2.

Alternating spin chains: controlled assembly from bimetallic building blocks and QMC simulation of spin correlation.

By using the compartmental dinucleating pyrazolate ligand HL, dinickel(II) complexes [LNi2(micro-N3)(acetone)2]X2 (1: X = CIO4; 2: X = BPh4) and tetranickel(II) complex [{LNi2(micro-N3)(MeOH)2](CI04)4 (3) have been prepared and structurally characterized. Complexes 1 and 2 differ in the torsion along the bridging micro-1,3-azide moiety, while the azido ligands in 3 adopt an unusual micro-1,1,3 bridging mode to connect the two subunits. All three complexes show overall antiferromagnetic coupling and an S = 0 ground state, but the torsion along the azide moiety is a determining factor for the coupling strength. Compounds 1 and 2 serve as preorganized building blocks for the controlled synthesis of alternating 1D polymeric structures 4-6 by replacement of their labile acetone ligands by additional azido ligands. Due to the modular synthetic approach, 4-6 can be described as Heisenberg antiferromagnetic systems with inherent bond alternation (HABA), whereby the organic ligand framework ensures that the individual nickel/azido chains are well isolated in the crystal lattice. Like their precursors, 4-6 are mainly distinguished by torsion along the micro-1,3-azido bridges, both within and between the bimetallic constituents. Magnetic measurements confirm an overall 5 = 0 ground state for 4-6, and coupling parameters have been deduced from quantum Monte Carlo simulations. The two J values for the alternating 1D chains can be clearly assigned on the basis of the magnetostructural correlations established for the bimetallic building blocks. The alternation ratio gamma = J2J1(-1) places the three new systems in the HABA regime for a singlet-dimer ground state.

Can Competition between the crystal field and the Kondo effect cause non-Fermi-liquid-like behavior?

The recently reported unusual behavior of the static and dynamical magnetic susceptibility as well as the specific heat in Ce(1-x)La(x)Ni9Ge4 has raised the question of a possible non-Fermi-liquid ground state in this material. We argue that for a consistent physical picture the crystal-field splitting of two low-lying magnetic doublets of the Ce 4f-shell must be taken into account. Furthermore, we show that for a splitting of the order of the low temperature scale T* of the system a crossover behavior between an SU(4) and an SU(2) Kondo effect is found. The screening of the two doublets occurs on different temperature scales leading to a different behavior of the magnetic susceptibility and the specific heat at low temperatures. The experimentally accessible temperature regime down to 50 mK still lies in the extended crossover regime into a strong-coupling Fermi-liquid fixed point.