Edge effect and significant increase of the superconducting transition onset temperature of 2D superconductors in flat and curved geometries

Abstract

In this paper, we present a simple method to model the curvature activated phonon softening in a 2D superconducting layer. The superconducting transition temperature T c in the case of a 2D rectangular sheet, a hollow cylinder and a hollow sphere of one coherence length thickness is calculated by the quantum mechanical electron-phonon scattering matrix, and a series of collective lattice vibrations in the surface state. We will show that being extremely thin in a flat rectangular shape is not enough to significantly enhance the T c through phonon softening. However, if a curvature is added, T c can be strongly enhanced. The increase in T c with respect to the bulk is greatest in a hollow sphere, intermediate in a hollow cylinder and weakest for the rectangular sheet, when systems of identical length scale are considered. In addition, we find that the edge effect of such a 2D sheet has a strong broadening effect on T c in addition to the effect of order parameter phase fluctuations.

A theoretical quest for high temperature superconductivity on the example of low-dimensional carbon structures

“…As the carbon ring (Sample G) consists of ~100 atoms only, the tilt angle between the adjacent atoms is about 360/100 = 3.6 degrees which is ~8 times smaller than the (4,2) SWCNT. The few degrees of curvature do not amend the electronic band diagram and the electronic DOS remarkably 23 , as demonstrated in the Methods section. Modifying the lattice vibrations is sufficient to dramatically tune T c of such weakly-curved low-dimensional carbon-based superconductors 23 .…”

“…Rw , , , , , , , and are defined in the Methods section. By comparing Tables 1 and 2 , modifying is accurate enough to provide a good reliability when considering the effect of weak curvature and dimensionality in the carbon nanotubes 23 .…”

“…However, the Debye temperature of the carbon chain is even higher than the SWCNT 30 , 31 , and therefore using the scale factor to predict the T c of the carbon nanowire is even more accurate. In the absence of phonon softening due to curvature, the electron phonon coupling is lowered 23 , 28 , 32 , and therefore unfolding the Sample B to Sample C lowers T c by 1.5 times. Removal of the kinks leads to Sample D with a 23 K T c .…”

Superconductivity in ultra-thin carbon nanotubes and carbyne-nanotube composites: An ab-initio approach

“…Another relative spring constant circular z K of the SWCNT is necessary to obtain the full approximated wavefunction of the SWCNT, which can be found by resolving the lattice vibration into radial and tangential components [11].…”

“…The Josephson interaction induced by quantum tunneling of Cooper pairs stabilizes then the superconducting phase order parameter and triggers a dimensional crossover from a 1D fluctuating state at high temperatures to a 3D phase coherent state with vanishing electrical resistance [5,6,7,8,9,10]. By drawing a parallel to the geometry of the non-superconducting graphene, a strong curvature of the graphene sheet is believed to be the main ingredient to activate the superconductivity in thin carbon nanotubes [1,11]. The BCS theory states that a large electronic density of states (DOS) at the Fermi level and a high Debye frequency are the essential ingredients for a high T c in the case of classical phonon-mediated BCS superconductors [8].…”