Phonon band structure and electron-phonon interactions in metallic nanowires

Abstract

We present first-principles calculations of the phonon band structure and electron-phonon coupling in thin metallic nanowires. A full Brillouin zone analysis of the phonons is mandatory for the investigation of the nanowire structural stability: all the examined unstrained nanowires show instabilities whose wavevectors are located off the zone center. The unstable phonon modes are transverse, leading to a transition without a gap opening, in contrast with the usual Peierls distortion picture. Electron-phonon coupling yields orders-of-magnitude changes depending on the nanowire structure.PACS numbers: 71.15.Mb,73.21.Hb, Metallic nanowires consisting of a single chain of evenly spaced atoms (monowires) have long been a theorist's playground : they have inspired many model systems for electrons, phonons and their coupling. One dimensional (1D) metallic systems were shown to be unstable against longitudinal distortion (i.e. pairing) by Fröhlich[1] and Peierls [2] in the 50s. This is, however, a simplified situation, and more general distortions must be considered. Batra [3] showed that transverse distortions can give rise to a different type of transition, which does not open a gap around the Fermi level (a phenomenon he coined Gapless Peierls Transition -GPT). The consequences of electron-phonon coupling (EPC) in monowires have been the focus of recent studies, e.g.[4], in particular to determine the effect of phonons on conductivity. Peierls transitions have been seen in first-principles simulations of carbon nanotubes [5,6], and the issue of whether superconductivity can survive in 1D, despite Peierls transitions, is an open question. For both normal and superconductivity in 1D, understanding the interplay between structure, stability, and metallicity is essential for nanotechnological applications.Nanowires or nanotubes with diameters superior to a few nanometers are produced nowadays for many different atomic species. In the past decade, it has also become possible to experimentally create and examine wires comprising just a few or even one strand of atoms. The most impressive success has been with gold [7,8], but other metals have also been used in different experimental setups [9,10]. The potential applications of thin nanowires include integrating electronics on a molecular scale, improving scanning microscope tips, and increasing data storage densities if the wires are magnetic.In the first thin gold nanowires visualized with an electron microscope [7], a large distance was observed between neighboring atoms along the wire. This distance was explained using first-principles calculations[11] to be an average distance between second neighbors in a zigzag (ZZ) structure, obtained by a transverse period-doubling of the monowire. Structures with small angles ( 60 • ) between successive bonds have been found theoretically for many metals. Analogous ZZ structures, with an angle larger than 120 degrees, were proposed to be stable only for some metals (see e.g. Ref. 12).Although these striking examples point to the ...

Pressure-enabled phonon engineering in metals

“…We use a 16 × 16 × 16 k-point grid, an 8 × 8 × 8 q-point grid, and a plane wave cutoff of 10.0 hartree for Al and 40.0 hartree for Cu. We use norm-conserving Martin-Troulliers pseudopotentials (22), the accuracy of which was tested in previous works (8,14). The electrical resistivity is calculated according to the lowest-order variational solution to the Boltzmann equation, as outlined in several previous works (8-10).…”

“…It also has been shown that the phonon-mediated properties, including the electrical resistivity and the superconducting transition temperature, can be altered under pressure (11-13). It has been suggested that the electrical transport properties due to the electron-phonon interaction in aluminum show a particularly strong response to interatomic spacing, particularly when the system is subject to extreme quantum confinement (14,15).Studies of the effect of pressure on the superconducting properties of aluminum suggest that superconductivity is suppressed through a reduction in the critical temperature, T c , as the pressure is increased (11,12,(16)(17)(18). It also has been reported that the electron-phonon coupling constant, λ, decreases in aluminum under pressure (11,16), but a quantitative extension to the electrical resistivity under pressure is lacking.…”

“…It also has been shown that the phonon-mediated properties, including the electrical resistivity and the superconducting transition temperature, can be altered under pressure (11-13). It has been suggested that the electrical transport properties due to the electron-phonon interaction in aluminum show a particularly strong response to interatomic spacing, particularly when the system is subject to extreme quantum confinement (14,15).…”

“…These metals are chosen because Al shows a pronounced reaction to changes in interatomic spacing (11,14,16,18) and has a simple, nearly spherical Fermi surface that makes it easy to treat computationally, whereas Cu typically is used for interconnects in industrial applications and has a lower intrinsic resistivity than aluminum. We show that upon pressurizing each metal, the electrical resistivity decreases.…”

Free-Standing Si and Ge, and Ge/Si Core-Shell Semiconductor Nanowires

“…Another example is the low-eld mobility, which for not too low temperatures is limited due to scattering on acoustic phonons. Phonon spectra are also useful to determine the stability of structures [33].…”