We have developed an efficient simulation tool 'GOLLUM' for the computation of electrical, spin and thermal transport characteristics of complex nanostructures. The new multi-scale, multi-terminal tool addresses a number of new challenges and functionalities that have emerged in nanoscale-scale transport over the past few years. To illustrate the flexibility and functionality of GOL-LUM, we present a range of demonstrator calculations encompassing charge, spin and thermal transport, corrections to density functional theory such as local density approximation +U (LDA+U) and spectral adjustments, transport in the presence of non-collinear magnetism, the quantum Hall effect, Kondo and Coulomb blockade effects, finite-voltage transport, multi-terminal transport, quantum pumps, superconducting nanostructures, environmental effects, and pulling curves and conductance histograms for mechanically-controlled breakjunction experiments.New J. Phys. 16 (2014) 093029 J Ferrer et al that non-equilibrium transport codes are quite difficult to handle, in part because of their complex input data structures, which can create a steep learning curve, and also because they carry very heavy computational demands. As a consequence, we have devised the new code GOLLUM to be more user friendly, with simple and easy to understand input and output structures, and with no accuracy parameters to tune. We present now a short summary of the features and functionalities of the two programs to better appreciate their differences. SMEAGOL is a non-equilibrium Green's function (NEGF) program that computes the charge and spin transport properties of two-terminal junctions subject to a finite voltage bias. SMEAGOL cannot read a user-defined tight-binding Hamiltonian. Instead, it reads the meanfield Hamiltonian from the program SIESTA [27] and is tightly bound to the old versions of it. SMEAGOL can read from SIESTA Hamiltonians carrying non-collinear spin arrangements as well as the spin-orbit interaction. SIESTA and SMEAGOL have indeed been used successfully to simulate the magnetic anisotropies of atomic clusters [28][29][30] as well as the spin transport functionalities of several atomic chains and molecular junctions subjected to strong spin-orbit interaction [31,32]. However, SMEAGOL does not profit from other recent density functionals. Examples are the van der Waals family of functionals or those based on the local density approximation + U (LDA+U) approach.GOLLUM is a program that computes the charge, spin and electronic contribution to the thermal transport properties of multi-terminal junctions. In contrast to NEGF codes, GOLLUM is based on equilibrium transport theory, which means that it has a simpler structure, is faster, and consumes less memory. The program has been designed for user-friendliness and takes a considerable leap towards the realization of ab initio multi-scale simulations of conventional and more sophisticated transport functionalities.The simpler interface of GOLLUM allows it to read model tight-binding Hamiltonians. Fur...

A quantum circuit rule for combining quantum interference effects in the conductive properties of oligo(phenyleneethynylene) (OPE)-type molecules possessing three aromatic rings was investigated both experimentally and theoretically. Molecules were of the type X-Y-X, where X represents pyridyl anchors with para (p), meta (m) or ortho (o) connectivities and Y represents a phenyl ring with p and m connectivities. The conductances G XmX (G XpX ) of molecules of the form X-m-X (X-p-X), with meta (para) connections in the central ring, were predominantly lower (higher), irrespective of the meta, para or ortho nature of the anchor groups X, demonstrating that conductance is dominated by the nature of quantum interference in the central ring Y. The single-molecule conductances were found to satisfy the quantum circuit rule G ppp /G pmp ¼ G mpm /G mmm . This demonstrates that the contribution to the conductance from the central ring is independent of the para versus meta nature of the anchor groups. S tudies of the electrical conductance of single molecules attached to metallic electrodes not only probe the fundamentals of quantum transport but also provide the knowledge needed to develop future molecular-scale devices and functioning circuits [1][2][3][4][5][6][7][8][9] . Owing to their small size (on the scale of Angstroms) and the large energy gaps (on the scale of eV), transport through single molecules can remain phase coherent even at room temperature, and constructive or destructive quantum interference (QI) can be utilized to manipulate their room temperature electrical 10-13 and thermoelectrical 14,15 properties. In previous studies, it was reported theoretically and experimentally that the conductance of a phenyl ring with meta (m) connectivity is lower than the isomer with para (p) connectivity by several orders of magnitude [16][17][18][19][20][21][22][23][24][25] . This arises because partial de Broglie waves traversing different paths through the ring are perfectly out of phase leading to destructive QI in the case of meta coupling, while for para or ortho coupling they are perfectly in phase and exhibit constructive QI. (See, for example, equation 8 of ref. 26.) It is therefore natural to investigate how QI in molecules with multiple aromatic rings can be utilized in the design of more complicated networks of interference-controlled molecular units.The basic unit for studying QI in single molecules is the phenyl ring, with thiol 17,21 , methyl thioether 27 , amine 17 or cyanide 19 anchors directly connecting the aromatic ring to gold electrodes. Recently, Arroyo et al. 28,29 studied the effect of QI in a central phenyl ring by varying the coupling to various anchor groups, including two variants of thienyl anchors. However, the relative importance of QI in central rings compared with QI in anchor groups has not been studied systematically because the thienyl anchors of Arroyo et al. 28,29 were five-membered rings, which exhibit only constructive interference. To study the relative effect of QI in anchors,...

Graphene, a single-layer network of carbon atoms, has outstanding electrical and mechanical properties . Graphene ribbons with nanometre-scale widths (nanoribbons) should exhibit half-metallicity and quantum confinement. Magnetic edges in graphene nanoribbons have been studied extensively from a theoretical standpoint because their coherent manipulation would be a milestone for spintronic and quantum computing devices . However, experimental investigations have been hampered because nanoribbon edges cannot be produced with atomic precision and the graphene terminations that have been proposed are chemically unstable . Here we address both of these problems, by using molecular graphene nanoribbons functionalized with stable spin-bearing radical groups. We observe the predicted delocalized magnetic edge states and test theoretical models of the spin dynamics and spin-environment interactions. Comparison with a non-graphitized reference material enables us to clearly identify the characteristic behaviour of the radical-functionalized graphene nanoribbons. We quantify the parameters of spin-orbit coupling, define the interaction patterns and determine the spin decoherence channels. Even without any optimization, the spin coherence time is in the range of microseconds at room temperature, and we perform quantum inversion operations between edge and radical spins. Our approach provides a way of testing the theory of magnetism in graphene nanoribbons experimentally. The coherence times that we observe open up encouraging prospects for the use of magnetic nanoribbons in quantum spintronic devices.

Experiments using a mechanically controlled break junction and calculations based on density functional theory demonstrate a new magic ratio rule (MRR) that captures the contribution of connectivity to the electrical conductance of graphene-like aromatic molecules. When one electrode is connected to a site i and the other is connected to a site i' of a particular molecule, we assign the molecule a "magic integer" Mii'. Two molecules with the same aromatic core but different pairs of electrode connection sites (i,i' and j,j', respectively) possess different magic integers Mii' and Mjj'. On the basis of connectivity alone, we predict that when the coupling to electrodes is weak and the Fermi energy of the electrodes lies close to the center of the HOMO-LUMO gap, the ratio of their conductances is equal to (Mii'/Mjj')(2). The MRR is exact for a tight-binding representation of a molecule and a qualitative guide for real molecules.

Controlling the electrical conductance and in particular the occurrence of quantum interference in single-molecule junctions through gating effects, has potential for the realization of highperformance functional molecular devices. In this work, we used an electrochemically-gated, mechanically-controllable break junction technique to tune the electronic behaviour of thiophene-based molecular junctions that show destructive quantum interference (DQI) features. By varying the voltage applied to the electrochemical gate at room temperature, we