High temperature superconductivity from the two-dimensional semiconductors without magnetism

We examine the possibility of high temperature superconductivity from two-dimensional semiconductor without antiferromagnetic fluctuations. The weak coupling BCS theory is applied, especially where the Fermi level is near the bottom of the conduction band. Due to screening, the attractive interaction is local in k-space. The density of states(DOS) does not have a peak near the bottom of the band, but k-dependent contribution to DOS has a diverging peak at the bottom. These features lead to high temperature superconductivity which may explain the possible superconductivity of WO3. PACS. 74.20.-z Theories and models of superconducting state – 74.20.Fg BCS theory and its development One of the most spectacular discoveries in condensed matter physics is undoubtedly the high Tc cuprates superconductors(HTSC)[1]. Many properties are not simply described by the standard classical BCS theory[2]. The common features of the HTSC are: (a) high superconductive transition Tc ∼ 100K. (b) quasi two-dimensionality, with weakly coupled CuO2 layers (c) antiferromagnetic(AF) fluctuations. The mother materials of HTSC are insulators with AF order below TN . (d) anisotropic superconductive gaps. In order to understand the mechanism of HTSC, there has been efforts to find compounds in which Cu is replaced by an other atom. The compound Ru2SrO4 has the same lattice structure as the HTSC (La, BA)2CuO4, but Cu is replaced by Ru. It is found to have a superconductive phase, however Tc ≃ 1.5K is rather low. There are some experimental results (for example, NMR[4] and muon spin resonance[5] ) to support triplet pairings. The band structure is considerably different from that of typical HTSC. Thus superconductive nature of this layered compound does not seem to be related to HTSC. Recently the signs of high superconductive transition temperature are reported for some doped semiconductors. The NaxWO3−x sodium tungsten bronzes, formed by doping the insulating host WO3 with Na, are n-type semiconductor for x < 0.3. The sample with x = 0.05 shows a sharp metal to insulator transition as temperature is lowered below 100K. It is followed by a sharp drop of resistivity at 91K as temperature is further lowered, it shows signs of superconductivity at 91K. At the same temperature this compound exhibits a sharp diamagnetic step in magnetization[6]. This compound is quasi twodimensional, but does not show any sign of antiferromagnetic fluctuations in sharp contrast to the cuprate high Tc superconductors. Possible superconductive transition is further supported by subsequent measurements of Electron Spin Resonance[7]. There is no sign of antiferromagnetic fluctuations in this compound in sharp contrast to cuprate HTSC, namely the feature (c) above does not apply. This implies that either the mechanism of superconductivity of WO3 is different from the cuprate superconductors or the magnetism does not play an essential role in the high Tc cuprates. The 5d-transition oxidesWO3 and NaxWO3 have nearly the perovskite crystal with W ions occupying the octahedral cation sites. Stoichiometric WO3 is an insulator since the W 5d band is empty; when Na ions are added to WO3, they donate their 3s electron to the W 5d band, resulting in bulk metallic behavior for x ≥ 0.3. For x < 0.3 the NaxWO3 sodium tungsten, is an n-type semiconductor (electron doped). This indicates that there exist two bands: the valence band and the conduction band with the gap G in between. The effect of doping of Na is to add electrons in the conduction band, thus raising the chemical potential μ. Although the superconductivity of WO3 has not been confirmed solidly and it requires further experimental supports, the properties of WO3 motivated us to examine the possibility of high Tc superconductivity from semiconductors without antiferromagnetic fluctuations. For simplicity, 2 M. Kohmoto, I. Chang, and J. Friedel: High Tc superconductivity without magnetism -4 -3 -2 -1 0 1 2 3 kx -4 -3 -2 -1 0 1 2 3 4