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Register a new userTheoretical aspects of simple and nested Fermi surfaces for superconductivity in doped semiconductors and high-$T_C$ cuprates
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T. Jarlborg
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The density-of-states at the Fermi energy, $N(E_F)$, is low in doped superconducting semiconductors and high-$T_C$ cuprates. This contrasts with the common view that superconductivity requires a large electron-boson coupling $lambda$ and therefore also a large $N(E_F)$. However, the generic Fermi surfaces (FS) of these systems are relatively simple. Here is presented arguments showing that going from a 3-dimensional multi-band FS to a 2-dimensional and simple FS is energetically favorable to superconductivity. Nesting and few excitations of bosons compensate for a low $N(E_F)$. The typical behavior of the 2-dimensional FS for cuprates, and small 3-dimensional FS pockets in doped semiconductors and diamond, leads to $T_C$ variations as a function of doping in line with what has been observed. Diamond is predicted to attain higher $T_C$ from electron doping than from hole doping, while conditions for superconductivity in Si and Ge are less favorable. A high-$T_C$ material should ideally have few flat and parallel FS sheets with a reasonably large $N(E_F)$.
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Cuprate superconductors have long been known to exhibit an energy gap that persists high above the superconducting transition temperature ($T_c$). Debate has continued now for decades as to whether it is a precursor superconducting gap or a pseudogap arising from some competing correlation. Failure to resolve this has arguably delayed explaining the origins of superconductivity in these highly complex materials. Here we effectively settle the question by calculating a variety of thermodynamic and spectroscopic properties, exploring the effect of a temperature-dependent pair-breaking term in the self-energy in the presence of pairing interactions that persist well above $T_c$. We start by fitting the detailed temperature-dependence of the electronic specific heat and immediately can explain its hitherto puzzling field dependence. Taking this same combination of pairing temperature and pair-breaking scattering we are then able to simultaneously describe in detail the unusual temperature and field dependence of the superfluid density, tunneling, Raman and optical spectra, which otherwise defy explanation in terms a superconducting gap that closes conventionally at $T_c$. These findings demonstrate that the gap above $T_c$ in the overdoped regime likely originates from incoherent superconducting correlations, and is distinct from the competing-order pseudogap that appears at lower doping.
Motivated by the discovery of superconductivity in boron-doped (B-doped) diamond, we investigate the localization and superconductivity in heavily doped semiconductors. The competition between Anderson localization and s-wave superconductivity is investigated from the microscopic point of view. The effect of microscopic inhomogeneity and the thermal fluctuation in superconductivity are taken into account using the self-consistent 1-loop-order theory with respect to superconducting fluctuation. The crossover from superconductivity in the host band to that in the impurity band is described on the basis of the disordered three-dimensional attractive Hubbard model for binary alloys. We show that superconductor-insulator transition (SIT) accompanies the crossover. We point out an enhancement of Cooper pairing in the crossover regime. Further localization of the electron wave function gives rise to incoherent Cooper pairs and the pseudogap above T_c. A global phase diagram is drawn for host band superconductivity, impurity band superconductivity, Anderson localization, Fermi liquid state, and pseudogap state. A theoretical interpretation is proposed for superconductivity in the doped diamond, SiC, and Si.
We present the resistively-determined upper critical field H^{rho}_{c2}(T) and the irreversibility lines H^{rho}_{irr}(T) of various high-T_c cuprates, deduced from measurements in 61-T pulsed magnetic fields applied parallel to the c-axis. The SHAPE of both H^{rho}_{c2}(T) and H^{rho}_{irr}(T) depends monotonically on the anisotropy of the material and none of the samples show saturation of H^{rho}(T) at low temperatures. The anomalous positive curvature, d^2 H^{rho}/dT^2 > 0, is the strongest in materials with the largest normal-state anisotropy, regardless of whether anisotropy is varied by changing the carrier concentration or by comparing a variety of optimally-doped compounds.
We discuss evolution of the Fermi surface (FS) topology with doping in electron doped cuprates within the framework of a one-band Hubbard Hamiltonian, where antiferromagnetism and superconductivity are assumed to coexist in a uniform phase. In the lightly doped insulator, the FS consists of electron pockets around the $(pi,0)$ points. The first change in the FS topology occurs in the optimally doped region when an additional hole pocket appears at the nodal point. The second change in topology takes place in the overdoped regime ($sim18%$) where antiferromagnetism disappears and a large $(pi,pi)$-centered metallic FS is formed. Evidence for these two topological transitions is found in recent Hall effect and penetration depth experiments on Pr$_{2-x}$Ce$_{x}$CuO$_{4-delta}$ (PCCO) and with a number of spectroscopic measurements on Nd$_{2-x}$Ce$_{x}$CuO$_{4-delta}$ (NCCO).
The mechanism by which the Fermi surface of high-$T_c$ cuprates undergoes a dramatic change from a large hole-like barrel to small arcs or pockets on entering the pseudogap phase remains a question of fundamental importance. Here we calculate the normal-state Hall coefficient from the resonating-valence-bond spin-liquid model developed by Yang, Rice and Zhang. In this model, reconstruction of the Fermi surface occurs via an intermediate regime where the Fermi surface consists of both hole- and electron-like pockets. We find that the doping $(x)$ dependence of the Hall number transitions from $1+x$ to $x$ over this narrow doping range. At low temperatures, a switch from a downturn to an upturn in the Hall coefficient signals the departure of the electron-like pockets from the Fermi surface.
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