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This tutorial outlines the basic theoretical concepts and tools which underpin the fundamentals of phase-coherent electron transport through single molecules. The key quantity of interest is the transmission coefficient T(E), which yields the electrical conductance, current-voltage relations, the thermopower S and the thermoelectric figure of merit ZT of single-molecule devices. Since T(E) is strongly affected by quantum interference (QI), three manifestations of QI in single-molecules are discussed, namely Mach-Zehnder interferometry, Breit-Wigner resonances and Fano resonances. A simple MATLAB code is provided, which allows the novice reader to explore QI in multi-branched structures described by a tight-binding (Huckel) Hamiltonian. More generally, the strengths and limitations of materials-specific transport modelling based on density functional theory are discussed.
Topological insulators are a new class of materials that have attracted significant attention in contemporary condensed matter physics. They are different from the regular insulators and they display novel quantum properties that also involve the ide
We present a general analytical formula and an ab initio study of quantum interference in multi-branch molecules. Ab initio calculations are used to investigate quantum interference in a benzene-1,2-dithiolate (BDT) molecule sandwiched between gold e
This mini review focuses on conductance measurements through molecular junctions containing few tens of molecules, which are fabricated along two approaches: (i) conducting atomic force microscope contacting a self-assembled monolayers on metal surfa
We have used the electromigration technique to fabricate a $rm{C_{{60}}}$ single-molecule transistor (SMT). We present a full experimental study as a function of temperature, down to 35 mK, and as a function of magnetic field up to 8 T in a SMT wit
Electronic transport properties for single-molecule junctions have been widely measured by several techniques, including mechanically controllable break junctions, electromigration break junctions or by means of scanning tunneling microscopes. In par