Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

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Topological insulators and superconductors

This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

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Phonons and related crystal properties from density-functional perturbation theory

Quantum ESPRESSO is an integrated suite of open-source computer codes for quantum simulations of materials using state-of-the-art electronic-structure techniques, based on density-functional theory, density-functional perturbation theory, and many-body perturbation theory, within the plane-wave pseudopotential and projector-augmented-wave approaches Quantum ESPRESSO owes its popularity to the wide variety of properties and processes it allows to simulate, to its performance on an increasingly broad array of hardware architectures, and to a community of researchers that rely on its capabilities as a core open-source development platform to implement their ideas In this paper we describe recent extensions and improvements, covering new methodologies and property calculators, improved parallelization, code modularization, and extended interoperability both within the distribution and with external software

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Advanced capabilities for materials modelling with Quantum ESPRESSO.

Weyl and Dirac semimetals are three-dimensional phases of matter with gapless electronic excitations that are protected by topology and symmetry. As three-dimensional analogs of graphene, they have generated much recent interest. Deep connections exist with particle physics models of relativistic chiral fermions, and, despite their gaplessness, to solid-state topological and Chern insulators. Their characteristic electronic properties lead to protected surface states and novel responses to applied electric and magnetic fields. The theoretical foundations of these phases, their proposed realizations in solid-state systems, and recent experiments on candidate materials as well as their relation to other states of matter are reviewed.

Weyl and Dirac semimetals in three-dimensional solids

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.

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Doping a Mott insulator: Physics of high-temperature superconductivity

We propose a new framework for first-principles calculations of heavy-fermion materials. These are described in terms of the Kondo lattice Hamiltonian with the parameters extracted from a realistic density functional based calculation which is then solved using continuous-time quantum Monte Carlo method and dynamical mean field theory. As an example, we show our results for the N\'eel temperatures of cerium-122 compounds ($\mathrm{Ce}{X}_{2}{\mathrm{Si}}_{2}$ with $X=\mathrm{Ru}$, Rh, Pd, Cu, Ag, and Au) where the general trend around the magnetic quantum critical point is successfully reproduced. Our results are organized on a universal Doniach phase diagram in a semiquantitative way.

First-Principles Simulations of Heavy Fermion Cerium Compounds Based on the Kondo Lattice

In the theoretical study of the origin of superconductivity in MgB2, the importance of the two dimensionality of the electronic structure has not been clear. Here we use the related system, and predicted superconductor, Li1−xBC to illustrate the importance the two dimensionality of the σ bands has for (1) the occurrence of high Tc, (2) the possibility of raising the critical temperature, and (3) the lattice instabilities that accompany strong electron–phonon coupling.

http://www2.cpfs.mpg.de/fplo/pub/PhysicaC_387_117.pdf

Role of two dimensionality in MgB2

Two well-studied electronic phases in the actinide compound UNiSn correspond to two well-known topological phases, an insight that provides a new link between correlated systems and topological materials.

Topological Insulator-to-Weyl Semimetal Transition in Strongly Correlated Actinide System UNiSn

A series of cerium-based heavy fermion materials is studied using a combination of local density functional theory and the many-body Gutzwiller approximation. Computed orbital-dependent electronic mass enhancement parameters are compared with available experimental data extracted from measured values of the Sommerfeld coefficient. Gutzwiller density functional theory is shown to remarkably follow the trends across a variety of Ce compounds and to give important insights into the phenomenon of orbital-selective mass renormalization which in turn allows for a better understanding of a wide spread of data.

Orbital-dependent electronic masses in Ce heavy-fermion materials studied via Gutzwiller density-functional theory

Weyl semimetals (WSMs), a new type of topological condensed matter, are currently attracting great interest due to their unusual electronic states and intriguing transport properties such as chiral anomaly induced negative magnetoresistance, a semiquantized anomalous Hall effect, and the debated chiral magnetic effect. These systems are close cousins of topological insulators (TIs) which are known for their disorder-tolerant surface states. Similarly, WSMs exhibit unique topologically protected Fermi-arc surface states. Here, we analyze electron-phonon scattering, a primary source of resistivity in metals at finite temperatures, as a function of the shape of the Fermi arc where we find that the impact on surface transport is significantly dependent on the arc curvature and disappears in the limit of a straight arc. Next, we discuss the effect of strong surface disorder on the resistivity by numerically simulating a tight-binding model with the presence of quenched surface vacancies using the coherent potential approximation and Kubo-Greenwood formalism. We find that the limit of a straight arc geometry is remarkably disorder tolerant, producing surface conductivity that is one to two orders of magnitude larger than a comparable setup with surface states of TI. This is primarily attributed to a significantly different hybridization strength of the surface states with the remaining electrons in two systems. Finally, a simulation of the effects of surface vacancies on TaAs is presented, illustrating the disorder tolerance of the topological surface states in a recently discovered WSM material.

Sergey Y. Savrasov

Papers

First-Principles Simulations of Heavy Fermion Cerium Compounds Based on the Kondo Lattice

Role of two dimensionality in MgB2

Topological Insulator-to-Weyl Semimetal Transition in Strongly Correlated Actinide System UNiSn

Orbital-dependent electronic masses in Ce heavy-fermion materials studied via Gutzwiller density-functional theory

High Surface Conductivity of Fermi Arc Electrons in Weyl semimetals