Density of states ind-wave superconductors of finite size

Abstract

We consider the effect of the finite size in the ab-plane on the surface density of states (DoS) in clean d -wave superconductors. In the bulk, the DoS is gapless along the nodal directions, while the presence of a surface leads to formation of another type of the low-energy states, the midgap states with zero energy. We demonstrate that finiteness of the superconductor in one of dimensions provides the energy gap for all directions of quasiparticle motion except for θ = 45• (θ is the angle between the trajectory and the surface normal); then the angle-averaged DoS behaves linearly at small energies. This result is valid unless the crystal is 0• -or 45• , where α is the angle between the a-axis and the surface normal). In the special case of α = 0• , the spectrum is gapped for all trajectories θ; the angle-averaged DoS is also gapped. In the special case of α = 45• , the spectrum is gapless for all trajectories θ; the angle-averaged DoS is then large at low energies. In all the cases, the angle-resolved DoS consists of energy bands that are formed similarly to the Kronig-Penney model. The analytical results are confirmed by a self-consistent numerical calculation.

Discrete density of states

“…It's seen from Eqs. (20) and (22) that, DDOS/CDOS reaches to its minimum value (2/3) at ground state energy (ε =ε 0 = α 2 1 ) in where the error of CDOS is maximum. In fact, for non-zero energy eigenvalues in a free domain where confinement parameters go to zero,ε >>ε 0 condition can be fulfilled since ground state energy goes to zero (ε 0 → 0) and DDOS is directly reduced to CDOS.…”

Quantum size effects in ultra-thin YBa2Cu3O7-x films

“…The nodeless energy gap has been reported for optimally doped YBCO, underdoped La 2 − x Sr x CuO 4 , and Bi 2 Sr 2-x La x CuO 6+δ lms [8][9][10] . Theoretically, it was proposed that the scattering 11 , disorder 12 , or large superconducting phase uctuations 13,14 may result in the fully gapped state of the d-wave superconductor. All this evidence gives hope that it is feasible to build fully gapped devices from the high-T c superconductors which can be used for quantum applications.…”

In-Plane Anisotropy of Electrical Transport in Y0.85Tb0.15Ba2Cu3O7−x Films

“…Currently, high-kinetic-inductance devices are based on disordered low-temperature superconductors such as NbN [1][2][3], NbTiN [4], NbSi [5], natural Josephson weak-link arrays formed in granular aluminum [6], artificial objects such as Josephson junction arrays [7,8], or semiconductor structures with induced superconductivity [9]. An alternative approach to high-kinetic-inductance materials for quantum applications could be based on hightemperature cuprate superconductors, where a fully gapped state is created by finite-size effects, reductions in the doping level, or phase fluctuations [10][11][12][13][14][15][16]. Cuprate superconductors have low charge carrier densities and, hence, they have high kinetic inductance, which can be calculated as follows:…”