China
Africa
Explore chapters and articles related to this topic
Electron states and bands in the cuprates
Published in J. R. Waldram, Superconductivity of Metals and Cuprates, 2017
The Coulomb repulsion has an important effect on an electron gas at low densities. At high densities we think of the electrons as existing in states of definite momentum which extend throughout the container, but at low densities these extended states are replaced by localized states in which each electron sits in a potential box created by the Coulomb repulsions of its neighbours. This state is favoured at low densities because, if the electronic spacing is r, the Coulomb interaction energy is e2/4πϵor whereas the zero-pont kinetic energy of an electron confined in a box of dimension r is ħ2k2/2me ≈ ħ2/2mer2. The different r dependences mean that the Coulomb repulsion has the dominant effect at large r and the zero-point energy at small r. We may say that at high densities the electrons have enough kinetic energy to tunnel through the barrier presented by their neighbours, but at low densities they behave more like classical particles and are trapped in localized states: we then have a Mott insulator. The changeover should take place when r is a few times the Bohr radius αo, and there is no doubt that the hole gas in the cuprates is near this limit.
Competing interactions in unconventional superconductors
Published in A. S. Alexandrov, Theory of Superconductivity From Weak to Strong Coupling, 2003
Therefore, some authors [140,141] dogmatized that the interaction in novel superconductors is essentially repulsive and unretarded and that it also provides high Tc without any phonons. A motivation for this concept can be found in the earlier work by Kohn and Luttinger [57], who showed that the Cooper pairing of repulsive fermions is possible. But the same work clearly showed that the Tc of repulsive fermions is extremely low, well below the mK scale (section 3.6). Nevertheless, BCS and BCS-like theories (including the Kohn–Luttinger consideration) rely heavily on the Fermi-liquid model of the normal state. This model fails in many high-temperature superconductors (chapter 6). There are no obvious a priori reasons for discarding the dogma, if the normal state is not the Fermi liquid. There is little doubt that strong on-site repulsive correlations (Hubbard U) are an essential feature of the cuprates. Indeed all undoped parent compounds are insulators with an insulating gap of about 2 eV or so. But if the repulsive correlations are weak, one would expect a metallic behaviour for the half-filled d-band of copper in cuprates or, at most, a much smaller gap caused by lattice and spin distortions (i.e. due to charge and/or spin density waves [142]). Therefore, it is the strong on-site repulsion of d-electrons in cuprates which results in their parent ‘Mott’ insulating state (section 5.2). Differing from conventional band-structure insulators with completely filled or empty Bloch bands, the Mott insulator arises from a potentially metallic half-filled band due to the Coulomb blockade of electron tunnelling to neighbouring sites, if U > zT(a) [143]. The insulator is antiferromagnetic with one hole and spin-12 per site. In using this model, we have to realize that the insulating properties of the Mott insulator do not depend on the ordering of the spins; they persist above the Néel temperature and arise because the on-site Coulomb repulsion is larger than the half-band width.
Crystal Structures and Electronic States of High-Pressure-Synthesized (1-x)PbVO3-xBiCrO3 Solid Solutions
Published in Journal of Asian Ceramic Societies, 2021
Hajime Yamamoto, Haruna Aizawa, Ikuya Yamada, Kaoru Toda, Atsushi Tanaka, Masaki Azuma, Yuki Sakai, Takumi Nishikubo, Hiroyuki Kimura
The (1 − x)PbVO3–xBiCrO3 samples exhibited Mott insulator features at ambient pressure. As a representative example, the temperature dependence of the electrical resistivity of the 4/8PbVO3–4/8BiCrO3 sample is shown in Figure 7(a). The inset shows the lnρ – 1000/T plot. A clear semiconductive behavior was observed. The activation energy obtained from the Arrhenius plot was Ea = 0.28 eV, which is similar to that observed in perovskite-type tetravalent vanadates and trivalent chromates (Mott insulators) [22,24]. The pressure dependence of the electrical resistivity up to 5 GPa was measured because the external field was expected to induce an insulator-to-metal transition or intermetallic charge transfer, as previously observed for PbVO3, PbCrO3, PbCoO3, and BiNiO3 [2,13,25–27]; results are shown in Figure 7(b). A clear resistivity drop was not observed, indicating that the abovementioned phenomena did not occur up to 5 GPa. Taken together, these results suggest that the valence state of V4+/Cr3+ and the electron localization in the (1 − x)PbVO3–xBiCrO3 solid solutions are quite robust.
Doping and momentum dependence of coupling strength in cuprate superconductors
Published in Philosophical Magazine, 2019
Yingping Mou, Yiqun Liu, Shuning Tan, Shiping Feng
Since the 1986 discovery of superconductivity in cuprate superconductors [1], there has been an intense focus on the understanding of the essential physics of cuprate superconductors [2]. This follows from a fact that the correlation between electrons in cuprate superconductors is so strong that when there is one electron on every copper atom site of their copper-oxide planes, a Mott insulator forms in which no electron motion is possible ([2], see e.g. [3,4]). By removing electrons, the electron motion is restored, and in particular, with the enough fraction of the removed electrons, superconductivity emerges [4–6]. At the temperature above the superconducting (SC) transition temperature , the system becomes a strange-metal ([4], see e.g. [5–9]), where a variety of the electronic orders are associated with various kinds of broken-symmetries. In particular, the resistivity is linear in temperature [8–11], the conductivity exhibits an anomalous power-law dependence on energy [8,12], and the electron Fermi surface (EFS) is broken up into the disconnected Fermi pockets around the nodal region [13–19]. All these anomalous properties arise from the strong interactions between the electrons mediated by the exchange of collective bosonic excitations (see e.g. [20,21]) that are most likely also responsible for the exceptionally high . In this case, it is crucial to elucidate the nature of the strong electron interaction for the understanding of the essential physics of cuprate superconductors.
Autocorrelation of quasiparticle spectral intensities and its connection with quasiparticle scattering interference in cuprate superconductors
Published in Philosophical Magazine, 2019
Deheng Gao, Yingping Mou, Yiqun Liu, Shuning Tan, Shiping Feng
The nature of the quasiparticle excitations in cuprate superconductors is of great interest in the past three decades [1–6]. This follows an experimental fact that the parent compound of cuprate superconductors is a strongly correlated Mott insulator, which is realised by the localisation of an electron at each copper atom of the copper-oxide planes in real-space [7,8]. However, when a small fraction of these electrons are removed from the copper-oxide planes, a process so-called charge-carrier doping, the electronic correlations are altered sufficiently to produce superconductivity, which is characterised by the delocalisation of the electron pairs [1–8]. This remarkable evolution from the localised real-space state of the Mott insulator to the delocalised momentum-space electron pairs of the superconductor therefore leads to a rich phenomenology in cuprate superconductors [9–13]. In particular, since the notable properties of the electronic state are intimately connected to the particular characteristics of the low-energy quasiparticle excitations [1–6], the understanding of the nature of the quasiparticle excitations in cuprate superconductors is thought to be key to the understanding of how a strongly correlated Mott insulator with the localised electronic state becomes a superconductor with the delocalised electron pairing-state.