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 investigate the effect of a time--periodical electromagnetic field on magnetic 3D topological insulators by using Floquet theory. It is found that the external field can change the topology of the undriven system by renormalizing its Dirac mass, leading to a new Weyl semimetal phase. A diamond lattice model is further studied to confirm the above results, where topological phase transitions between quantum anomalous Hall and Weyl semimetal phases take place due to the periodical perturbation.

Floquet Weyl semimetal induced by topological phase transitions

Excitons are spin integer particles that are predicted to condense into a coherent quantum state at sufficiently low temperature, and exciton condensates can be realized at much higher temperature than condensates of atoms because of strong Coulomb binding and small mass. Signatures of exciton condensation have been reported in double quantum wells1-4, microcavities5, graphene6, and transition metal dichalcogenides7. Nonetheless, transport of exciton condensates is not yet understood and it is unclear whether an exciton condensate is a superfluid8,9 or an insulating electronic crystal10,11. Topological insulators (TIs) with massless particles and unique spin textures12 have been theoretically predicted13 as a promising platform for achieving exciton condensation. Here we report experimental evidence of excitonic superfluid phase on the surface of three-dimensional (3D) TIs. We unambiguously confirmed that electrons and holes are paired into charge neutral bound states by the electric field independent photocurrent distributions. And we observed a millimetre-long transport distance of these excitons up to 40 K, which strongly suggests dissipationless propagation. The robust macroscopic quantum states achieved with simple device architecture and broadband photoexcitation at relatively high temperature are expected to find novel applications in quantum computations and spintronics.

Emergence of excitonic superfluid at topological-insulator surfaces

Electron-Phonon Superconductivity Near Charge Density Wave Instability in LaO$_{0.5}$F$_{0.5}$BiS$_{2}$

The precise nature of Cooper pairing in superconducting materials is determined by the underlying symmetry of the crystal lattice. In recent years, non-centrosymmetric superconductors have attracted particular interest, since the lack of inversion symmetry mixes spin singlet and triplet pairing states, and may allow the realization of topological superconductivity. The complex interplay of correlations and topology in these materials pose a particular challenge for numerical simulations. For this reason they are excluded from high-throughput searches for topological materials and instead treated on an individual basis. Here we study the electronic properties of the inversion-broken CeTX$_3$ heavy-fermion compounds, and find topological nodal lines as well as Dirac and Weyl points. The topological nodal lines have a significant effect on the Fermi surface spin structure that has not been considered in prior theoretical studies of the superconducting pairing. Our comprehensive treatment of this group of compounds is a critical first step in high-throughput searches of correlated topological materials.

Correlation-driven renormalization of topological features in the CeTX$_3$ series

We review basic computational techniques for simulations of various magnetic properties of solids. Sev- eral applications to compute magnetic anisotropy energy, spin wave spectra, magnetic susceptibilities and tempera- ture dependent magnetisations for a number of real sys- tems are presented for illustrative purposes.

Sergey Y. Savrasov

Papers

Floquet Weyl semimetal induced by topological phase transitions

Emergence of excitonic superfluid at topological-insulator surfaces

Electron-Phonon Superconductivity Near Charge Density Wave Instability in LaO$_{0.5}$F$_{0.5}$BiS$_{2}$

Correlation-driven renormalization of topological features in the CeTX$_3$ series

Electronic Structure and Magnetic Properties of Solids