Experimental studies of the superconductive properties of fullerides are briefly reviewed. Theoretical calculations of the electron-phonon coupling, in particular for the intramolecular phonons, are discussed extensively. The calculations are compared with coupling constants deduced from a number of different experimental techniques. It is discussed why ${\mathrm{A}}_{3}$${\mathrm{C}}_{60}$ are not Mott-Hubbard insulators, in spite of the large Coulomb interaction. Estimates of the Coulomb pseudopotential ${\mathrm{\ensuremath{\mu}}}^{\mathrm{*}}$, describing the effect of the Coulomb repulsion on the superconductivity, as well as possible electronic mechanisms for the superconductivity, are reviewed. The calculation of various properties within the Migdal-Eliashberg theory and attempts to go beyond this theory are described.

/pdf/superconductivity-in-fullerides-1l7z4d92t8.pdf

Superconductivity in fullerides

The density matrix renormalization group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond condensed matter, and is successfully used in quantum chemistry, statistical mechanics, quantum information theory, and nuclear and high-energy physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview of the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite-temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the dynamical mean field method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and versatile methods in modern computational physics.

/pdf/new-trends-in-density-matrix-renormalization-1yg3uti2g1.pdf

New trends in density matrix renormalization

We present a complete prescription for the numerical calculation of surface Green’s functions and selfenergies of semi-infinite quasi-one-dimensional systems. Our work extends previous results generating a robust algorithm to be used in conjunction with ab initio electronic structure methods. We perform a detailed error analysis of the scheme and find that the highest accuracy is found if no inversion of the usually ill conditioned hopping matrix is involved. Even in this case however a transformation of the hopping matrix that decreases its condition number is needed in order to limit the size of the imaginary part of the wave vectors. This is done in two different ways: either by applying a singular value decomposition and setting a lowest bound for the smallest singular value or by adding a random matrix of small amplitude. By using the first scheme the size of the Hamiltonian matrix is reduced, making the computation considerably faster for large systems. For most energies the method gives high accuracy, however in the presence of surface states the error diverges due to the singularity in the self-energy. A surface state is found at a particular energy if the set of solution eigenvectors of the infinite system is linearly dependent. This is then used as a criterion to detect surface states, and the error is limited by adding a small imaginary part to the energy.

/pdf/algorithm-for-the-construction-of-self-energies-for-b1cxsxyazr.pdf

Algorithm for the construction of self-energies for electronic transport calculations based on singularity elimination and singular value decomposition

Recent studies of charge-transfer salts of the ion bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF or ET) are reviewed, focusing in particular on experimental techniques which involve high magnetic fields and on data obtained since 1996. Novel experimental techniques developed in the past few years, including angle-dependent magnetoresistance oscillations, periodic orbit resonances and Fermi-surface traversal resonances are described in detail; briefer descriptions of more traditional techniques such as the Shubnikov-de Haas effect are also included. The applications of these techniques to the ?, ?, ? and ?'' BEDT-TTF salts is described. Theoretical developments related to the experimental data are also mentioned.

https://iopscience.iop.org/article/10.1088/0034-4885/63/8/201/pdf

Studies of quasi-two-dimensional organic conductors based on BEDT-TTF using high magnetic fields

Quantum cascade lasers are unipolar semiconductor lasers covering a wide range of the infrared and terahertz spectrum. Lasing action is achieved by using optical intersubband transitions between quantized states in specifically designed multiple-quantum-well heterostructures. A systematic improvement of quantum cascade lasers with respect to operating temperature, efficiency, and spectral range requires detailed modeling of the underlying physical processes in these structures. Moreover, the quantum cascade laser constitutes a versatile model device for the development and improvement of simulation techniques in nano- and optoelectronics. This review provides a comprehensive survey and discussion of the modeling techniques used for the simulation of quantum cascade lasers. The main focus is on the modeling of carrier transport in the nanostructured gain medium, while the simulation of the optical cavity is covered at a more basic level. Specifically, the transfer matrix and finite difference methods for solving the one-dimensional Schrodinger equation and Schrodinger-Poisson system are discussed, providing the quantized states in the multiple-quantum-well active region. The modeling of the optical cavity is covered with a focus on basic waveguide resonator structures. Furthermore, various carrier transport simulation methods are discussed, ranging from basic empirical approaches to advanced self-consistent techniques. The methods include empirical rate equation and related Maxwell-Bloch equation approaches, self-consistent rate equation and ensemble Monte Carlo methods, as well as quantum transport approaches, in particular the density matrix and non-equilibrium Green's function formalism. The derived scattering rates and self-energies are generally valid for n-type devices based on one-dimensional quantum confinement, such as quantum well structures.

Modeling techniques for quantum cascade lasers

Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems.

The results of a fully ab initio determination of the vibronic coupling strengths in C 60 and C 60 3- where the vibrational and the electronic structure are treated on an equal footing are presented. We obtain accurate vibrational frequencies and the corresponding coupling constants are obtained without further parameters. We find that the coupling to both the low- and high-frequency molecular modes are important, and their relevance to the Jahn-Teller effect and superconductivity are briefly discussed

Vibronic coupling in C60 and C603

Ab initio determination of electron-molecular vibration constants (em-v) in bis(ethylenedithio) tetrathiafulvalene (BEDT-TTF) and tetrathiafulvalene (TTF)

We present simulation results of deposition growth of surfaces in 2, 3 and 4 dimensions for ballistic deposition where overhangs are present, and for restricted solid on solid deposition where there are no overhangs. The values of the scaling exponents for the two models are found to be different, suggesting that they belong to different universality classes.

Simulations of deposition growth models in various dimensions: The possible importance of overhangs

We investigate the phase diagram of two coupled quantum spin-1/2 chains, a square ladder, allowing for anisotropies both in the interchain and intrachain coupling, using the recently introduced density-matrix renormalization-group ~DMRG! algorithm. We consider open chains up to a length of 23200, while retaining up to 120 states in the truncated basis of the Hilbert space. The phase diagram is discussed in connection with exact results and bosonization analysis. Numerically, we show that the crossover from the critical behavior of the uncoupled disordered spin-1/2 chain to a gapped quantum liquid sets in for infinitesimal interchain coupling, both for ferromagnetic and antiferromagnetic interchain coupling. The Haldane phase of the coupled chains is, even for small interchain couplings, generically described by the Affleck-Kennedy-Lieb-Tasaki model. We also discuss typical shortcomings of the DMRG for some choices of the interaction parameters.

David Y. K. Ko

Papers

Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems.

Vibronic coupling in C60 and C603

Ab initio determination of electron-molecular vibration constants (em-v) in bis(ethylenedithio) tetrathiafulvalene (BEDT-TTF) and tetrathiafulvalene (TTF)

Simulations of deposition growth models in various dimensions: The possible importance of overhangs

Real-space renormalization-group study of the phase diagram of two coupled quantum spin-1/2 chains.