다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

This article reviews the physics of high-temperature superconductors from the point of view of the doping of a Mott insulator. The basic electronic structure of cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. The normal state in this region exhibits pseudogap phenomenon. In contrast, the quasiparticles in the superconducting state are well defined and behave according to theory. This review introduces Anderson's idea of the resonating valence bond and argues that it gives a qualitative account of the data. The importance of phase fluctuations is discussed, leading to a theory of the transition temperature, which is driven by phase fluctuations and the thermal excitation of quasiparticles. However, an argument is made that phase fluctuations can only explain pseudogap phenomenology over a limited temperature range, and some additional physics is needed to explain the onset of singlet formation at very high temperatures. A description of the numerical method of the projected wave function is presented, which turns out to be a very useful technique for implementing the strong correlation constraint and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the $t\text{\ensuremath{-}}J$ model, with the goal of putting the resonating valence bond idea on a more formal footing. The slave boson is introduced to enforce the constraint againt double occupation and it is shown that the implementation of this local constraint leads naturally to gauge theories. This review follows the historical order by first examining the U(1) formulation of the gauge theory. Some inadequacies of this formulation for underdoping are discussed, leading to the SU(2) formulation. Here follows a rather thorough discussion of the role of gauge theory in describing the spin-liquid phase of the undoped Mott insulator. The difference between the high-energy gauge group in the formulation of the problem versus the low-energy gauge group, which is an emergent phenomenon, is emphasized. Several possible routes to deconfinement based on different emergent gauge groups are discussed, which leads to the physics of fractionalization and spin-charge separation. Next the extension of the SU(2) formulation to nonzero doping is described with a focus on a part of the mean-field phase diagram called the staggered flux liquid phase. It will be shown that inclusion of the gauge fluctuation provides a reasonable description of the pseudogap phase. It is emphasized that $d$-wave superconductivity can be considered as evolving from a stable U(1) spin liquid. These ideas are applied to the high-${T}_{c}$ cuprates, and their implications for the vortex structure and the phase diagram are discussed. A possible test of the topological structure of the pseudogap phase is described.

/pdf/doping-a-mott-insulator-physics-of-high-temperature-55r49vtp31.pdf

Doping a Mott insulator: Physics of high-temperature superconductivity

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

This article reviews the effort to understand the physics of high temperature superconductors from the point of view of doping a Mott insulator. The basic electronic structure of the cuprates is reviewed, emphasizing the physics of strong correlation and establishing the model of a doped Mott insulator as a starting point. A variety of experiments are discussed, focusing on the region of the phase diagram close to the Mott insulator (the underdoped region) where the behavior is most anomalous. We introduce Anderson's idea of the resonating valence bond (RVB) and argue that it gives a qualitative account of the data. The importance of phase fluctuation is discussed, leading to a theory of the transition temperature which is driven by phase fluctuation and thermal excitation of quasiparticles. We then describe the numerical method of projected wavefunction which turns out to be a very useful technique to implement the strong correlation constraint, and leads to a number of predictions which are in agreement with experiments. The remainder of the paper deals with an analytic treatment of the t-J model, with the goal of putting the RVB idea on a more formal footing. The slave-boson is introduced to enforce the constraint of no double occupation. The implementation of the local constraint leads naturally to gauge theories. We give a rather thorough discussion of the role of gauge theory in describing the spin liquid phase of the undoped Mott insulator. We next describe the extension of the SU(2) formulation to nonzero doping. We show that inclusion of gauge fluctuation provides a reasonable description of the pseudogap phase.

Doping a Mott Insulator: Physics of High Temperature Superconductivity

We present an experimental review of the nature of the pseudogap in the cuprate superconductors. Evidence from various experimental techniques points to a common phenomenology. The pseudogap is seen in all high-temperature superconductors and there is general agreement on the temperature and doping range where it exists. It is also becoming clear that the superconducting gap emerges from the normal state pseudogap. The d-wave nature of the order parameter holds for both the superconducting gap and the pseudogap. Although an extensive body of evidence is reviewed, a consensus on the origin of the pseudogap is as lacking as it is for the mechanism underlying high-temperature superconductivity.

/pdf/the-pseudogap-in-high-temperature-superconductors-an-22i3tjkdfn.pdf

The pseudogap in high-temperature superconductors: an experimental survey

We study within BCS theory the properties of an effective Hamiltonian to describe conduction by holes through an oxygen anion network. The Hamiltonian contains an on-site repulsive interaction ${U}_{p}$ and a modulated hopping interaction $\ensuremath{\Delta}t$ that yields a larger hopping amplitude between sites when other holes are present on those sites. The superconducting state is found to be $s$ wave with an energy-dependent gap. Superconductivity is restricted to low hole densities and the critical temperature increases with the hopping amplitude. The particular form of the interaction allows for superconductivity even in the presence of large Coulomb repulsion, up to $\frac{{U}_{p}}{\ensuremath{\Delta}t}\ensuremath{\approx}30$. We discuss the behavior of the tunneling density of states, specific heat, gap ratio, and coherence length as a function of hole density and parameters in the Hamiltonian, and the relationship between our results and existing, as well as possible future, experimental results on high-${T}_{c}$ oxides. Our model provides a natural explanation for the spread in gap values observed in different experiments, for the observed broadening of the resistive transition in a field, and for the observed superconducting glass behavior.

Superconducting state in an oxygen hole metal.

The electron Green's function in the superconducting state can be solved either at discrete Matsubara frequencies along the imaginary axis, or as a function of a continuous variable along the real frequency axis. The former is considerably more convenient to calculate than the latter. We derive a formally exact analytic continuation of the imaginary-axis solutions to the real frequency axis. The procedure is applicable to more general problems involving Green's functions. We apply our method to calculating the tunneling density of states for superconducting lead.

Iterative analytic continuation of the electron self-energy to the real axis.

We discuss predictions of the hole-pairing mechanism of superconductivity for various experimentally measurable properties of the high-${\mathit{T}}_{\mathit{c}}$ oxides. The model considered describes conduction by holes through the oxygen anion network in the high-${\mathit{T}}_{\mathit{c}}$ oxides, and pairing originates in a term in the Hamiltonian describing an enhanced hopping amplitude for a hole in the presence of other holes. The model includes on-site and nearest-neighbor Coulomb repulsions and different hopping amplitudes within and between planes. We use information from experiments to determine suitable ranges of parameters in the model and examine various properties of the superconducting state within this model using BCS theory. Among the most notable predictions of the model for the high-${\mathit{T}}_{\mathit{c}}$ oxides are: (1) the superconducting state is nearly isotropic despite the anisotropic band structure; (2) the pressure dependence of ${\mathit{T}}_{\mathit{c}}$ is very different for pressure applied perpendicular and parallel to the planes; and (3) the upper critical field and effective mass decrease rapidly and monotonically with hole doping, as a crossover occurs between strong- and weak-coupling regimes.

Hole superconductivity and the high-Tc oxides.

Terahertz spectroscopy of nanomaterials is one of the most active areas of terahertz physics thanks to its ability to reveal charge-carrier confinement on length scales of tens to hundreds of nanometers. Structural confinement modifies the experimental complex conductivity, such that it is Drude-like at high frequencies but suppressed at low frequencies. This response is often described as a consequence of carrier backscattering off nanoparticle boundaries and modeled using the sometimes controversial Drude-Smith formula. In this paper, it is demonstrated that the terahertz conductivity of a structurally confined Drude gas of electrons is actually suppressed at low frequencies due to carrier confinement on the diffusion length scale and not due to backscattering. A new conductivity formula is derived based on diffusion that is found to be very similar to the Drude-Smith conductivity formula, thereby explaining many of the previous successes of the Drude-Smith model.

/pdf/microscopic-origin-of-the-drude-smith-model-e2cvr5wj7w.pdf

Microscopic origin of the Drude-Smith model

We critique a Pad\'e analytic continuation method whereby a rational polynomial function is fit to a set of input points by means of a single matrix inversion. This procedure is accomplished to an extremely high accuracy using a symbolic computation algorithm. As an example of this method in action, it is applied to the problem of determining the spectral function of a single-particle thermal Green's function known only at a finite number of Matsubara frequencies with two example self energies drawn from the T-matrix theory of the Hubbard model. We present a systematic analysis of the effects of error in the input points on the analytic continuation, and this leads us to propose a procedure to test quantitatively the reliability of the resulting continuation, thus eliminating the black-magic label frequently attached to this procedure.

https://arxiv.org/pdf/cond-mat/9908477.pdf

Frank Marsiglio

Papers

Superconducting state in an oxygen hole metal.

Iterative analytic continuation of the electron self-energy to the real axis.

Hole superconductivity and the high-Tc oxides.

Microscopic origin of the Drude-Smith model

Reliable Padé analytical continuation method based on a high-accuracy symbolic computation algorithm