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The function of nano-scale devices critically depends on the choice of materials. For electron transport junctions it is natural to characterize the materials by their conductance length dependence, $beta$. Theoretical estimations of $beta$ are made employing two primary theories: complex band structure and DFT-NEGF Landauer transport. Both reveal information on $beta$ of individual states; i.e. complex Bloch waves and transmission eigenchannels, respectively. However, it is unclear how the $beta$-values of the two approaches compare. Here, we present calculations of decay constants for the two most conductive states as determined by complex band structure and standard DFT-NEGF transport calculations for two molecular and one semi-conductor junctions. Despite the different nature of the two methods, we find strong agreement of the calculated decay constants for the molecular junctions while the semi-conductor junction shows some discrepancies. The results presented here provide a template for studying the intrinsic, channel resolved length dependence of the junction through complex band structure of the central material in the heterogeneous nano-scale junction.
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For systems that can be modeled as a single-particle lattice extended along a privileged direction as, e.g., quantum wires, the so-called eigenvalue method provides full information about the propagating and evanescent modes as a function of energy. This complex-band structure method can be applied either to lattices consisting of an infinite succession of interconnected layers described by the same local Hamiltonian or to superlattices: Systems in which the spatial periodicity involves more than one layer. Here, for time-dependent systems subject to a periodic driving, we present an adapted version of the superlattice scheme capable of obtaining the Floquet states and the Floquet quasienergy spectrum. Within this scheme the time periodicity is treated as existing along spatial dimension added to the original system. The solutions at a single energy for the enlarged artificial system provide the solutions of the original Floquet problem. The method is suited for arbitrary periodic excitations including strong and anharmonic drivings. We illustrate the capabilities of the methods for both time-independent and time-dependent systems by discussing: (a) topological superconductors in multimode quantum wires with spin-orbit interaction and (b) microwave driven quantum dot in contact with a topological superconductor.
Topology is familiar mostly from mathematics, but also natural sciences have found its concepts useful. Those concepts have been used to explain several natural phenomena in biology and physics, and they are particularly relevant for the electronic structure description of topological insulators and graphene systems. Here, we introduce topologically distinct graphene forms - graphene spirals - and employ density-functional theory to investigate their geometric and electronic properties. We found that the spiral topology gives rise to an intrinsic Rashba spin-orbit splitting. Through a Hamiltonian constrained by space curvature, graphene spirals have topologically protected states due to time-reversal symmetry. In addition, we argue that the synthesis of such graphene spirals is feasible and can be achieved through advanced bottom-up experimental routes that we indicate in this work.
This mini-review is intended as a short introduction to electron flow in nanostructures. Its aim is to provide a brief overview of this topic for people who are interested in the thermodynamics of quantum systems but know little about nanostructures. We particularly emphasize devices that work in the steady-state, such as simple thermoelectrics, but also mention cyclically driven heat engines. We do not aim to be either complete or rigorous, but use a few pages to outline some of the main ideas in the topic.
Since its inception in 2001, the science and technology of epitaxial graphene on hexagonal silicon carbide has matured into a major international effort and is poised to become the first carbon electronics platform. A historical perspective is presented and the unique electronic properties of single and multilayered epitaxial graphenes on electronics grade silicon carbide are reviewed. Early results on transport and the field effect in Si-face grown graphene monolayers provided proof-of-principle demonstrations. Besides monolayer epitaxial graphene, attention is given to C-face grown multilayer graphene, which consists of electronically decoupled graphene sheets. Production, structure, and electronic structure are reviewed. The electronic properties, interrogated using a wide variety of surface, electrical and optical probes, are discussed. An overview is given of recent developments of several device prototypes including resistance standards based on epitaxial graphene quantum Hall devices and new ultrahigh frequency analog epitaxial graphene amplifiers.
We investigate the dispersion characteristics and the effective properties of acoustic waves propagating in a one-dimensional duct equipped with periodic thermoacoustic coupling elements. Each coupling element consists in a classical thermoacoustic regenerator subject to a spatial temperature gradient. When acoustic waves pass through the regenerator, thermal-to-acoustic energy conversion takes place and can either amplify or attenuate the wave, depending on the direction of propagation of the wave. The presence of the spatial gradient naturally induces a loss of reciprocity. This study provides a comprehensive theoretical model as well as an in-depth numerical analysis of the band structure and of the propagation properties of this thermoacoustically-coupled, tunable, one-dimensional metamaterial. Among the most significant findings, it is shown that the acoustic metamaterial is capable of supporting non-reciprocal thermoacoustic Bloch waves that are associated with a particular form of unidirectional energy transport. Remarkably, the thermoacoustic coupling also allows achieving effective zero compressibility and zero refractive index that ultimately lead to the phase invariance of the propagating sound waves. This single zero effective property is also shown to have very interesting implications in the attainment of acoustic cloaking.
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