arXiv subjects
Publications and source records attributed to F. Marsiglio.
An introduction to and overview of the contents of this Special Issue are given. 32 classes of superconducting materials are discussed, grouped under the three categories "conventional", "possibly unconventional" and "unconventional" according to the mechanism believed to give rise to superconductivity.
We give a brief review of superconductivity at ambient pressure in elements, alloys, and simple three-dimensional compounds. Historically these were the first superconducting materials studied, and based on the experimental knowledge gained from them the BCS theory of superconductivity was developed in 1957. Extended to include the effect of phonon retardation, the theory is believed to describe the subset of superconducting materials known as `conventional superconductors', where superconductivity is caused by the electron-phonon interaction. These include the elements, alloys and simple compounds discussed in this article and several other classes of materials discussed in other articles in this Special Issue.
In a recent experiment [M. Feld et al., Nature 480, 75 (2011); B. Froehlich et al., Phys. Rev. Lett. 109,130403 (2012)], a pairing gap was detected in a two-dimensional (2D) Fermi gas with attractive interaction at temperatures where superfluidity does not occur. The question remains open as to whether this gap is a pseudogap phenomenon or is due to a molecular state. In this paper, by using a t-matrix approach, we reproduce quite well the experimental data for a 2D Fermi gas, and set the boundary between the pseudogap and molecular regimes. We also show that pseudogap phenomena occurring in 2D and 3D can be related through a variable spanning the BCS-BEC crossover in a universal way.
Superconductivity at temperatures up to 190 K at high pressures has recently been observed in $H_2S$ and interpreted as conventional BCS-electron-phonon-driven superconductivity.\cite{h2s} Instead we propose that it is another example of the mechanism of hole superconductivity at work. Within this mechanism high temperature superconductivity arises when holes conduct through negatively charged anions in close proximity. We propose that electron transfer from $H$ to $S$ leads to conduction by holes in a nearly full band arising from direct overlap of $S^=$ $p$ orbitals in a planar structure. The superconductivity is non-phononic and is driven by pairing of heavily dressed hole carriers to lower their kinetic energy. Possible explanations for the observed lower critical temperature of $D_2S$ are discussed. We predict that high temperature superconductivity will also be found in other sulfides under high pressure such as $Li_2S$, $Na_2S$ and $K_2S$.
We survey polaron formation in the BLF-SSH model using acoustic phonons in the adiabatic limit. Multiple different numerical optimization routines and strong coupling analytical calculations are used to find a robust ground state energy for a wide range of coupling strengths. The electronic configuration and accompanying ionic distortions of the polaron were determined, as well as a non-zero critical coupling strength for polaron formation in two and three dimensions.
The Kronig-Penney model describes what happens to electron states when a confining potential is repeated indefinitely. This model uses a square well potential; the energies and eigenstates can be obtained analytically for a the single well, and then Bloch's Theorem allows one to extend these solutions to the periodically repeating square well potential. In this work we describe how to obtain simple numerical solutions for the eigenvalues and eigenstates for any confining potential within a unit cell, and then extend this procedure, with virtually no extra effort, to the case of periodically repeating potentials. In this way one can study the band structure effects which arise from differently-shaped potentials. One of these effects is the electron-hole mass asymmetry. More realistic unit cell potentials generally give rise to higher electron-hole mass asymmetries.
We present numerically exact solutions to the problem of a single electron interacting through a long range interaction with optical phonons in two and three dimensions. Comparisons are made with results for the standard Holstein model, and with perturbative approaches from both the weak coupling and strong coupling sides. We find, in agreement with earlier work, that the polaron effective mass increases (decreases) in the weak (strong) coupling regime, respectively. However, in two dimensions, the decrease in effective mass still results in too large an effective mass to be relevant in realistic models of normal metals. In three dimensions the decrease can be more relevant, but exists only over a very limited range of coupling strengths.
Spin-orbit coupling plays an important role in various properties of very different materials. Moreover efforts are underway to control the degree and quality of spin-orbit coupling in materials with a concomitant control of transport properties. We calculate the frequency dependent optical conductivity in systems with both Rashba and Dresselhaus spin-orbit coupling. We find that when the linear Dresselhaus spin-orbit coupling is tuned to be equal to the Rashba spin-orbit coupling, the interband optical conductivity disappears. This is taken to be the signature of the recovery of SU(2) symmetry. The presence of the cubic Dresselhaus spin-orbit coupling modifies the dispersion relation of the charge carriers and the velocity operator. Thus the conductivity is modified, but the interband contribution remains suppressed at most but not all photon energies for a cubic coupling of reasonable magnitude. Hence, such a measurement can serve as a diagnostic probe of engineered spin-orbit coupling.
Matrix mechanics is an important component of an undergraduate education in quantum mechanics. In this paper we present several examples of the use of matrix mechanics to solve for a number of three dimensional problems involving central forces. These include examples with which the student is familiar, such as the Coulomb interaction. In this case we obtain excellent agreement with exact analytical methods. More importantly, other interesting `non-solvable' examples, such as the Yukawa potential, can be solved as well. Much less mathematical expertise is required for these methods, while some minimal familiarity with the usage of numerical diagonalization software is necessary.
The electronic ground state for Lithium is $1s^22s$, and not $1s^22p$. The traditional argument for why this is so is based on a screening argument that claims that the $2p$ electron is better shielded by the $1s$ electrons, and therefore higher in energy then the configuration that includes the $2s$ electron. We show that this argument is flawed, and in fact the actual reason for the ordering is because the electron-electron interaction energy is higher for the $2p-1s$ repulsion than it is for the $2s-1s$ repulsion.
The two electron configuration in the Helium atom is known to very high precision. Yet, we tend to refer to this configuration as a $1s\uparrow 1s\downarrow$ singlet, where the designations refer to Hydrogen orbitals. The high precision calculations utilize basis sets that are suited for high accuracy and ease of calculation, but do not really aid in our understanding of the electron configuration in terms of product states of Hydrogen orbitals. Since undergraduate students are generally taught to think of Helium, and indeed, the rest of the periodic table, in terms of Hydrogenic orbitals, we present in this paper a detailed spectral decomposition of the two electron ground state for Helium in terms of these basis states. The $1s\uparrow 1s\downarrow$ singlet contributes less than 93% to the ground state configuration, with other contributions coming from both bound and continuum Hydrogenic states.
The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double well potentials that are accessible to the undergraduate student. We describe a method for obtaining the numerically exact eigenenergies and eigenstates for such a model, along with the energies obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact solution is accessible with elementary mathematics, though numerical solutions are required. We also find that the WKB approximation is remarkably accurate, not just for the ground state, but for the excited states as well.
When an electron interacts with phonons, the electron can exhibit either free electron-like or polaron-like properties. The latter tends to occur for very strong coupling, and results in a phonon cloud accompanying the electron as it moves, thus raising its mass considerably. We summarize this behaviour for the Holstein model in one, two and three dimensions, and note that the crossover occurs for fairly low coupling strengths compared to those attributed to real materials exhibiting conventional superconductivity.
We investigate the physical properties of the Ba$_{1-x}$K$_x$BiO$_3$ compounds with a focus on the optical properties. Results from the simple Holstein model, describing a single band coupled to an oxygen breathing mode with parameters derived from first principles calculations, are in excellent agreement with a broad range of experimental information. It accounts for an insulating parent compound at $x=0$ %, with a direct- (optical) and an indirect-gap, and a metal insulator transition around $x = 0.38$. Strong electron-phonon coupling leads to spectral weight redistribution over a frequency scale much larger than the characteristic phonon frequency and to strongly anharmonic phonons. We find that the metallic phase in the vicinity of phase boundary is close to the polaronic regime.
The Dynamic Hubbard Model represents the physics of a multi-band Hubbard model by using a pseudo-spin degree of freedom to dynamically modify the on-site Coulomb interaction. Here we use a dimer system to obtain analytical results for this model. The spectral function and the optical conductivity are calculated analytically for any number of electrons, and the distribution of optical spectral weight is analyzed in great detail. The impact of polaron-like effects due to overlaps between pseudo-spin states on the optical spectral weight distribution is derived analytically. Our conclusions support results obtained previously with different models and techniques: holes are less mobile than electrons.
The superconducting pairing instability---as determined by a divergence of the two-particle susceptibility---is obtained in the mean field (BCS) approximation in the thermodynamic limit. The usual practice is to examine this property for a finite lattice. We illustrate that, while the conclusions remain unchanged, the technical features are very different in the thermodynamic limit and conform more closely with the usual treatment of phase transitions encountered in, for example, the mean-field paramagnetic-ferromagnetic transition. Furthermore, by going to the extreme dilute limit, one can distinguish three dimensions from one and two dimensions, in which a pairing instability occurs even for two particles.
We utilize an exact variational numerical procedure to calculate the ground state properties of a polaron in the presence of Rashba and linear Dresselhaus spin-orbit coupling. We find that when the linear Dresselhaus spin-orbit coupling approaches the Rashba spin-orbit coupling, the Van-Hove singularity in the density of states will be shifted away from the bottom of the band and finally disappear when the two spin-orbit couplings are tuned to be equal. The effective mass will be suppressed; the trend will become more significant for low phonon frequency. The presence of two dominant spin-orbit couplings will make it possible to tune the effective mass with more varied observables.
We utilize an exact variational numerical procedure to calculate the ground state properties of a polaron in the presence of a Rashba-like spin orbit interaction. Our results corroborate with previous work performed with the Momentum Average approximation and with weak coupling perturbation theory. We find that spin orbit coupling increases the effective mass in the regime with weak electron phonon coupling, and decreases the effective mass in the intermediate and strong electron phonon coupling regime. Analytical strong coupling perturbation theory results confirm our numerical results in the small polaron regime. A large amount of spin orbit coupling can lead to a significant lowering of the polaron effective mass.