Invariants of the single impurity Anderson model and implications for conductance functionals

An exact relation between the conductance maximum $G_0$ at zero temperature and a ratio of lead densities is derived within the framework of the single impurity Anderson model: $G_0={\mathfrak R}[n] \frac{2e^2}{h}$, where ${\mathfrak R}[n]=4\Delta N_{{\cal L},x} \Delta N_{{\cal R},x}/(\Delta N_{{\cal L},x}+\Delta N_{{\cal R},x})^2$ and $\Delta N_{{\cal L},x}$, $\Delta N_{{\cal R},x}$ denote the excess density in the left/right lead at distance $x$ due to the presence of the impurity at the origin, $x=0$. The relation constitutes a parameter-free expression of the conductance of the model in terms of the ground state density that generalizes an earlier result to the generic case of asymmetric lead couplings. It turns out that the specific density ratio, ${\mathfrak R}[n]$, is independent of the distance to the impurity $x$, the (magnetic) band-structure and filling fraction of the contacting wires, the strength of the onsite interaction, the gate voltage and the temperature. Disorder induced backscattering in the contacting wires has an impact on ${\mathfrak R}$ that we discuss. Our result suggests that it should be possible, in principle, to determine experimentally the peak conductance of the Anderson impurity by performing a combination of measurements of ground-state densities.Comment: 5 pages, 3 figures, accepted by EP

A functional renormalization group approach to electronic structure calculations for systems without translational symmetry

A formalism for electronic-structure calculations is presented that is based on the functional renormalization group (FRG). The traditional FRG has been formulated for systems that exhibit a translational symmetry with an associated Fermi surface, which can provide the organization principle for the renormalization group (RG) procedure. We here advance an alternative formulation, where the RG-flow is organized in the energy-domain rather than in k-space. This has the advantage that it can also be applied to inhomogeneous matter lacking a band-structure, such as disordered metals or molecules. The energy-domain FRG ({\epsilon}FRG) presented here accounts for Fermi-liquid corrections to quasi-particle energies and particle-hole excitations. It goes beyond the state of the art GW-BSE, because in {\epsilon}FRG the Bethe-Salpeter equation (BSE) is solved in a self-consistent manner. An efficient implementation of the approach that has been tested against exact diagonalization calculations and calculations based on the density matrix renormalization group is presented. Similar to the conventional FRG, also the {\epsilon}FRG is able to signalize the vicinity of an instability of the Fermi-liquid fixed point via runaway flow of the corresponding interaction vertex. Embarking upon this fact, in an application of {\epsilon}FRG to the spinless disordered Hubbard model we calculate its phase-boundary in the plane spanned by the interaction and disorder strength. Finally, an extension of the approach to finite temperatures and spin S = 1/2 is also given.Comment: 25 pages, 14 figure

Ab initio spin-flip conductance of hydrogenated graphene nanoribbons: Spin-orbit interaction and scattering with local impurity spins

We calculate the spin-dependent zero-bias conductance $G_{\sigma\sigma'}$ in armchair graphene nanoribbons with hydrogen adsorbates employing a DFT-based ab initio transport formalism including spin-orbit interaction. We find that the spin-flip conductance $G_{\sigma\bar{\sigma}}$ can reach the same order of magnitude as the spin-conserving one, $G_{\sigma\sigma}$, due to exchange-mediated spin scattering. In contrast, the genuine spin-orbit interaction appears to play a secondary role, only

Ab initio quantum transport through armchair graphene nanoribbons: Streamlines in the current density

We calculate the local current density in pristine armchair graphene nanoribbons (AGNRs) with varying width, $N_\mathrm{C}$, employing a density-functional-theory-based ab initio transport formalism. We observe very pronounced current patterns (streamlines) with threefold periodicity in $N_\mathrm{C}$. They arise as a consequence of quantum confinement in the transverse flow direction. Neighboring streamlines are separated by stripes of almost vanishing flow. As a consequence, the response of the current to functionalizing adsorbates is very sensitive to their placement: adsorbates located within the current filaments lead to strong backscattering, while adsorbates placed in other regions have almost no impact at all.Comment: 7 pages, 11 figure

Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition

We present a numerical finite size scaling study of the localization length in long cylinders near the integer quantum Hall transition (IQHT) employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent $y$ is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate $|y| > 0.4$, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent $2.62 \pm 0.06$ confirming recent results. Our stability analysis has broad applicability to other observables at IQHT, as well as other critical points where corrections to scaling are present.Comment: 6 pages and 3 figures, plus supplemental material

Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula

Standard first principles calculations of transport through single molecules miss exchange-correlation corrections to the Landauer formula. From Kubo response theory, both the Landauer formula and these corrections in the limit of zero bias are derived and calculations are presented.Comment: 4 pages, 3 figures, final version to appear in Phys. Rev. B, Rapid Communication

Spin locking at the apex of nano-scale platinum tips

Nanostructures based on platinum, such as small clusters or STM-tips, often exhibit an atomistic structure that relies upon one or very few strongly under-coordinated platinum atoms. Here, we analyze a paradigmatic example, an apex atom on a pyramidal platinum cluster employing the density functional theory. We show that such a pristine platinum tip exhibits a spin polarization of the apex atom with a remarkable robustness. Due to a depletion of the projected density of states at the apex position, the apex-magnetization is efficiently locked to about 0.6$\mu_\text{B}$

Current-induced mechanical torque in chiral molecular rotors

A great endeavor has been undertaken to engineer molecular rotors operated by an electrical current. A frequently met operation principle is the transfer of angular momentum taken from the incident flux. In this paper we present an alternative driving agent that works also in situations where angular momentum of the incoming flux is conserved. This situation arises typically with molecular rotors that exhibit an easy axis of rotation. For quantitative analysis we investigate here a classical model, where molecule and wires are represented by a rigid curved path. We demonstrate that in the presence of chirality the rotor generically undergoes a directed motion, provided that the incident current exceeds a threshold value. Above threshold, the corresponding rotation frequency (per incoming particle current) for helical geometries turns out to be $2\pi m/M_1$, where $m/M_1$ is the ratio of the mass of an incident charge carrier and the mass of the helix per winding number

Charge Transport in Single Au|Alkanedithiol|Au Junctions: Coordination Geometries and Conformational Degrees of Freedom

Recent STM molecular break-junction experiments have revealed multiple series of peaks in the conductance histograms of alkanedithiols. To resolve a current controversy, we present here an in-depth study of charge transport properties of Au|alkanedithiol|Au junctions. Conductance histograms extracted from our STM measurements unambiguously confirm features showing more than one set of junction configurations. Based on quantum chemistry calculations, we propose that certain combinations of different sulfur-gold couplings and trans/gauche conformations act as the driving agents. The present study may have implications for experimental methodology: whenever conductances of different junction conformations are not statistically independent, the conductance histogram technique can exhibit a single series only, even though a much larger abundance of microscopic realizations exists.Comment: 19 pages, 9 figures, 1 table; published versio

The internal clock of many-body delocalization

After a decade of many claims to the opposite, there now is a growing consensus that generic disordered quantum wires, e.g. the XXZ-Heisenberg chain, do not exhibit many-body localization (MBL) - at least not in a strict sense within a reasonable window of disorder values $W$. Specifically, computational studies of short wires exhibit an extremely slow but unmistakable flow of physical observables with increasing time and system size (``creep") that is consistently directed away from (strict) localization. Our work sheds fresh light on delocalization physics: Strong sample-to-sample fluctuations indicate the absence of a generic time scale, i.e. of a naive ``clock rate"; however, the concept of an ``internal clock" survives, at least in an ensemble sense. Specifically, we investigate the relaxation of the imbalance $\mathcal{I}(t)$ and its temporal fluctuations $\mathcal{F}(t)$, the entanglement and Renyi entropies, $\mathcal{S}_{\mathrm{e}}(t)$ and $\mathcal{S}_2(t)$, in a 1D system of interacting disordered fermions. We observe that adopting $\mathcal{S}_{\mathrm{e}}(t), \mathcal{S}_2(t)$ as a measure for the internal time per sample reduces the sample-to-sample fluctuations but does not eliminate them. However, a (nearly) perfect collapse of the average $\overline{\mathcal{I}}(t)$ and $\overline{\mathcal{F}}(t)$ for different $W$ is obtained when plotted against $\overline{\mathcal{S}}_{\mathrm{e}}(t)$ or $\overline{\mathcal{S}}_2(t)$, indicating that the average entropy appropriately models the ensemble-averaged internal clock. We take the tendency for faster-than-logarithmic growth of $\overline{\mathcal{S}}_{\mathrm{e}}(t)$ together with smooth dependency on $W$ of all our observables within the entire simulation window as support for the cross-over scenario, discouraging an MBL transition within the traditional parametric window of computational studies.Comment: 15 pages, 12+5 figures, published versio