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

Noncentrosymmetric superconductors have recently attracted much attention, since the lack of inversion symmetry mixes spin-singlet and -triplet pairing states, which may allow the realization of topological superconductivity In this Letter, we study the electronic properties of the family of inversion-broken $\mathrm{Ce}T{X}_{3}$ heavy-fermion superconductors, finding topological nodal lines as well as Dirac and Weyl points, which are renormalized closer to the Fermi energy by correlations We find that the Weyl nodal lines have a substantial effect on the Fermi surface spin structure of the normal state and lead to line nodes in the superconducting phase

Renormalized quasiparticles, topological monopoles, and superconducting line nodes in heavy-fermion Ce T X 3 compounds

We introduce a theoretical framework for computaions of anisotropic multipolar exchange interactions found in many spin--orbit coupled magnetic systems and propose a method to extract these coupling constants using a density functional total energy calculation. This method is developed using a multipolar expansion of local density matrices for correlated orbitals that are responsible for magnetic degrees of freedom. Within the mean--field approximation, we show that each coupling constant can be recovered from a series of total energy calculations via what we call the ``pair--flip'' technique. This technique flips the relative phase of a pair of multipoles and computes corresponding total energy cost associated with the given exchange constant. To test it, we apply our method to Uranium Dioxide, which is a system known to have pseudospin $J=1$ superexchange induced dipolar, and superexchange plus spin--lattice induced quadrupolar orderings. Our calculation reveals that the superexchange and spin--lattice contributions to the quadrupolar exchange interactions are about the same order with ferro-- and antiferro--magnetic contributions, respectively. This highlights a competition rather than a cooperation between them. Our method could be a promising tool to explore magnetic properties of rare--earth compounds and hidden--order materials.

Anisotropic Multipolar Exchange Interactions in Systems with Strong Spin-Orbit Coupling

Theoretical Physics III, Center for Electronic Correlations and Magnetism,Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany(Dated: December 27, 2012)Continuous–Time Quantum Monte Carlo (CT-QMC) method combined with Dynamical MeanField Theory (DMFT) is used to calculate both Periodic Anderson Model (PAM) and Kondo Lat-tice Model (KLM). Diﬀerent parameter sets of both models are connected by the Schrieﬀer–Wolﬀtransformation. For degeneracy N = 2, a special particle–hole symmetric case of PAM at half ﬁllingwhich always ﬁxes one electron per impurity site is compared with the results of the KLM. Weﬁnd a good mapping between PAM and KLM in the limit of large on–site Hubbard interaction Ufor diﬀerent properties like self–energy, quasiparticle residue and susceptibility. This allows us toextract quasiparticle mass renormalizations for the f electrons directly from KLM. The method isfurther applied to higher degenerate case and to realsitic heavy fermion system CeRhIn

Scaling Between Periodic Anderson and Kondo Lattice Models

Z2 and Chern topological phases such as newly discovered quantum spin Hall and original quantum Hall states hardly both co–exist in a single material due to their contradictory requirement on the time–reversal symmetry (TRS). We show that although the TRS is broken in systems with a periodically driving field, an effective TRS can still be defined provided the ac–field is linearly polarized or certain other conditions are satisfied. The controllable TRS provides us a route to manipulate contradictory phases by tuning the polarization. To demonstrate the idea, we consider a tight-binding model that is relevant to several monolayered materials as a benchmark system. Our calculation shows not only topological Z2 to Chern phase transition occurs but rich Chern phases are also observed. In addition, we also discussed the realization of our proposal in real materials, such as spin-orbit coupled graphene and crystal Bismuth. This opens the possibility of manipulating various topological phases in a single material and can be a promising approach to engineer new electronic states of matter.

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Polarization induced Z2 and Chern topological phases in a periodically driving field.

$Z_{2}$ and Chern topological phases such as newly discovered quantum spin Hall and original quantum Hall states hardly both co--exist in a single material due to their contradictory requirement on the time--reversal symmetry (TRS). We show that although the TRS is broken in systems with a periodically driving ac-field, an effective TRS can still be defined provided the ac--field is linearly polarized or certain other conditions are satisfied. The controllable TRS provides us with a route to manipulate $Z_{2} $ and Chern topological phases in a single material by tuning the polarization of the ac--field. To demonstrate the idea, we consider a generic honeycomb lattice model as a benchmark system that is relevant to electronic structures of several monolayered materials. Our calculation shows that not only the transitions between $Z_{2}$ and Chern phases can be induced but also features such as the dispersion of the edge states can be controlled. This opens the possibility of manipulating various topological phases in a single material and can be a promising approach to engineer some new electronic states of matter.

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Sergey Y. Savrasov

Papers

Renormalized quasiparticles, topological monopoles, and superconducting line nodes in heavy-fermion Ce T X 3 compounds

Anisotropic Multipolar Exchange Interactions in Systems with Strong Spin-Orbit Coupling

Scaling Between Periodic Anderson and Kondo Lattice Models

Polarization induced Z2 and Chern topological phases in a periodically driving field.

Manipulating Z2 and Chern topological phases in a single material using periodically driving fields