An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall states in simple lattice models without a large external magnetic field. A fundamental question is whether qualitatively new states can be realized on the lattice as compared with ordinary fractional quantum Hall states. Here we propose new symmetry-enriched topological states, topological nematic states, which are a dramatic consequence of the interplay between the lattice translational symmetry and topological properties of these fractional Chern insulators. The topological nematic states are realized in a partially filled flat band with a Chern number $N$, which can be mapped to an $N$-layer quantum Hall system on a regular lattice. However, in the topological nematic states the lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Consequently, lattice dislocations become defects with a nontrivial quantum dimension, even when the fractional quantum Hall state being realized is, by itself, Abelian. Our proposal leads to the possibility of realizing the physics of topologically ordered states on high-genus surfaces in the lab even though the sample has only the disk geometry.

We propose general topological order parameters for interacting insulators in terms of the Green’s function at zero frequency. They provide a unified description of various interacting topological insulators including the quantum anomalous Hall insulators and the time-reversal-invariant insulators in four, three, and two dimensions. Since only the Green’s function at zero frequency is used, these topological order parameters can be evaluated efficiently by most numerical and analytical algorithms for strongly interacting systems.

Although iron-based superconductors are multiorbital systems with complicated band structures, we demonstrate that the low-energy physics which is responsible for their high-$T_c$ superconductivity is essentially governed by an effective two-orbital Hamiltonian near half filling. This underlying electronic structure is protected by the $S_4$ symmetry. With repulsive or strong next-nearest-neighbor antiferromagnetic exchange interactions, the model results in a robust $A_{1g}$ $s$-wave pairing which can be mapped exactly to the $d$-wave pairing observed in cuprates. The classification of the superconducting (SC) states according to the $S_4$ symmetry leads to a natural prediction of the existence of two different phases, named the $A$ and $B$ phases. In the $B$ phase, the superconducting order has an overall sign change along the $c$ axis between the top and bottom As (or Se) planes in a single Fe-As (or Fe-Se) trilayer structure, the common building block of iron-based superconductors. The sign change is analogous to the sign change in the $d$-wave superconducting state of cuprates upon 90° rotation. Our derivation provides a unified understanding of iron pnictides and iron chalcogenides, and suggests that cuprates and iron-based superconductors share an identical high-$T_c$ superconducting mechanism.

The logarithmic violations of the area law, i.e., an “area law” with logarithmic correction of the form $S\sim L^{d-1}\log L$, for entanglement entropy are found in both 1D gapless fermionic systems with Fermi points and high-dimensional free fermions. This paper shows that both violations are of the same origin, and that, in the presence of Fermi-liquid interactions, such behavior persists for 2D fermion systems. In this paper, we first consider the entanglement entropy of a toy model, namely, a set of decoupled 1D chains of free spinless fermions, to relate both violations in an intuitive way. We then use multidimensional bosonization to rederive the formula by Gioev and Klich [D. Gioev and I. Klich, Entanglement Entropy of Fermions in Any Dimension and the Widom Conjecture, Phys. Rev. Lett. 96, 100503 (2006).] for free fermions through a low-energy effective Hamiltonian and explicitly show that, in both cases, the logarithmic corrections to the area law share the same origin: the discontinuity at the Fermi surface (points). In the presence of Fermi-liquid (forward-scattering) interactions, the bosonized theory remains quadratic in terms of the original local degrees of freedom, and, after regularizing the theory with a mass term, we are able to calculate the entanglement entropy perturbatively up to second order in powers of the coupling parameter for a special geometry via the replica trick. We show that these interactions do not change the leading scaling behavior for the entanglement entropy of a Fermi liquid. At higher orders, we argue that this should remain true through a scaling analysis.

This paper is an attempt to identify the real essence of simplicity of liquids in John Locke’s understanding of the term. Simple liquids are traditionally defined as many-body systems of classical particles interacting via radially symmetric pair potentials. We suggest that a simple liquid should be defined instead by the property of having strong correlations between virial and potential-energy equilibrium fluctuations in the $NVT$ ensemble. There is considerable overlap between the two definitions, but also some notable differences. For instance, in the new definition simplicity is not a direct property of the intermolecular potential because a liquid is usually only strongly correlating in part of its phase diagram. Moreover, not all simple liquids are atomic (i.e., with radially symmetric pair potentials) and not all atomic liquids are simple. The main part of the paper motivates the new definition of liquid simplicity by presenting evidence that a liquid is strongly correlating if and only if its intermolecular interactions may be ignored beyond the first coordination shell (FCS). This is demonstrated by $NVT$ simulations of the structure and dynamics of several atomic and three molecular model liquids with a shifted-forces cutoff placed at the first minimum of the radial distribution function. The liquids studied are inverse power-law systems ($r^{-n}$ pair potentials with $n=18,6,4$), Lennard-Jones (LJ) models (the standard LJ model, two generalized Kob-Andersen binary LJ mixtures, and the Wahnstrom binary LJ mixture), the Buckingham model, the Dzugutov model, the LJ Gaussian model, the Gaussian core model, the Hansen-McDonald molten salt model, the Lewis-Wahnstrom ortho-terphenyl model, the asymmetric dumbbell model, and the single-point charge water model. The final part of the paper summarizes properties of strongly correlating liquids, emphasizing that these are simpler than liquids in general. Simple liquids, as defined here, may be characterized in three quite different ways: (1) chemically by the fact that the liquid’s properties are fully determined by interactions from the molecules within the FCS, (2) physically by the fact that there are isomorphs in the phase diagram, i.e., curves along which several properties like excess entropy, structure, and dynamics, are invariant in reduced units, and (3) mathematically by the fact that throughout the phase diagram the reduced-coordinate constant-potential-energy hypersurfaces define a one-parameter family of compact Riemannian manifolds. No proof is given that the chemical characterization follows from the strong correlation property, but we show that this FCS characterization is consistent with the existence of isomorphs in strongly correlating liquids’ phase diagram. Finally, we note that the FCS characterization of simple liquids calls into question the physical basis of standard perturbation theory, according to which the repulsive and attractive forces play fundamentally different roles for the physics of liquids.

We present the ultra-low-temperature heat-transport study of iron-based superconductors $\mathrm{Ba}({\mathrm{Fe}}_{1-x}{\mathrm{Ru}}_x{)}_2{\mathrm{As}}_2$ and ${\mathrm{BaFe}}_2({\mathrm{As}}_{1-x}{\mathrm{P}}_x{)}_2$. For optimally doped $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$, a large residual ${\kappa }_0/T$ at zero field and a $\sqrt{H}$ dependence of ${\kappa }_0(H)/T$ are observed, which provide strong evidences for nodes in the superconducting gap. This result demonstrates one more nodal superconductor in iron pnictides. The similarities between isovalent Fe and P dopings strongly suggest that the nodal superconductivity in $\mathrm{Ba}({\mathrm{Fe}}_{0.64}{\mathrm{Ru}}_{0.36}{)}_2{\mathrm{As}}_2$ may have the same origin as in ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.67}{\mathrm{P}}_{0.33}{)}_2$. Furthermore, in underdoped $\mathrm{Ba}({\mathrm{Fe}}_{0.77}{\mathrm{Ru}}_{0.23}{)}_2{\mathrm{As}}_2$ and strongly underdoped ${\mathrm{BaFe}}_2({\mathrm{As}}_{0.82}{\mathrm{P}}_{0.18}{)}_2$, ${\kappa }_0/T$ manifests similar nodal behavior, which result shows the robustness of nodal superconductivity in the underdoped regime and puts constraint on theoretical models.

The electronic structure of multilayer graphenes depends strongly on the number of layers as well as the stacking order. Here we explore the electronic transport of purely ABA-stacked trilayer graphenes in a dual-gated field-effect device configuration. We find both that the zero-magnetic-field transport and the quantum Hall effect at high magnetic fields are distinctly different from the monolayer and bilayer graphenes, and that they show electron-hole asymmetries that are strongly suggestive of a semimetallic band overlap. When the ABA trilayers are subjected to an electric field perpendicular to the sheet, Landau-level splittings due to a lifting of the valley degeneracy are clearly observed.

The interaction between substitutional nitrogen atoms in graphene is studied by performing first-principles calculations. The effective nearest-neighbor interaction between nitrogen dopants is found to be highly repulsive because of the strong electrostatic repulsion between nitrogen atoms. This interaction prevents the full nitrogen-carbon phase separation in nitrogen-doped graphene. Interestingly, there are two relatively stable nitrogen-nitrogen pair configurations, whose stability can be attributed to the anisotropy in the charge redistribution induced by nitrogen doping. We reveal two stable, ordered, semiconducting N-doped graphene structures, ${\mathrm{C}}_3\mathrm{N}$ and ${\mathrm{C}}_{12}\mathrm{N}$, through the cluster-expansion technique and particle-swarm optimization method. In particular, we show that ${\mathrm{C}}_{12}\mathrm{N}$ has a direct band gap of 0.98 eV. The heterojunctions between ${\mathrm{C}}_{12}\mathrm{N}$ and graphene nanoribbons might be a promising basis for organic solar cells.

The nature of the parent compound of a high-temperature superconductor (HTS) often plays a pivotal role in determining its superconductivity. The parent compounds of the cuprate HTSs are antiferromagnetically ordered Mott insulators, while those of the iron-pnictide HTSs are metals with spin-density-wave order. Here we report the electronic identification of two insulating parental phases and one semiconducting parental phase of the newly discovered family of ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$ superconductors. The two insulating phases exhibit Mott-insulator-like signatures, and one of the insulating phases is even present in the superconducting and semiconducting ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$ compounds. However, it is mesoscopically phase-separated from the superconducting or semiconducting phase. Moreover, we find that both the superconducting and semiconducting phases are free of the magnetic and vacancy orders present in the insulating phases, and that the electronic structure of the superconducting phase could be developed by doping the semiconducting phase with electrons. The rich electronic properties discovered in these parental phases of the ${\mathrm{K}}_x{\mathrm{Fe}}_{2-y}{\mathrm{Se}}_2$ superconductors provide the foundation for studying the anomalous behavior in this new class of iron-based superconductors.

We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between quantum Hall states on the torus and simple product states—or patterns—in the thin torus limit, together with a suitable coherent state ansatz for localized quasiholes that respects the modular invariance of the torus. We give a refined and unified account of the application of this method to the Laughlin and Moore-Read states, which may serve as a pedagogical introduction to the nuts and bolts of this technique. Our main result is that the approach is also applicable—without further assumptions—to more complicated non-Abelian states. We demonstrate this in great detail for the level $k=3$ Read-Rezayi state at filling factor $\nu =3/2$. These results may serve as an independent check of other techniques, where the statistics are inferred from conformal block monodromies. Our approach has the benefit of giving rise to intuitive pictures representing the transformation of topological sectors during braiding, and allows for a self-consistent derivation of non-Abelian statistics without heavy mathematical machinery.

Chern insulators are band insulators exhibiting a nonzero Hall conductance but preserving the lattice translational symmetry. We conclusively show that a partially filled Chern insulator at $1/3$ filling exhibits a fractional quantum Hall effect and rule out charge-density-wave states that have not been ruled out by previous studies. By diagonalizing the Hubbard interaction in the flat-band limit of these insulators, we show the following: The system is incompressible and has a 3-fold degenerate ground state whose momenta can be computed by postulating an generalized Pauli principle with no more than 1 particle in 3 consecutive orbitals. The ground-state density is constant, and equal to $1/3$ in momentum space. Excitations of the system are fractional-statistics particles whose total counting matches that of quasiholes in the Laughlin state based on the same generalized Pauli principle. The entanglement spectrum of the state has a clear entanglement gap which seems to remain finite in the thermodynamic limit. The levels below the gap exhibit counting identical to that of Laughlin $1/3$ quasiholes. Both the 3 ground states and excited states exhibit spectral flow upon flux insertion. All the properties above disappear in the trivial state of the insulator—both the many-body energy gap and the entanglement gap close at the phase transition when the single-particle Hamiltonian goes from topologically nontrivial to topologically trivial. These facts clearly show that fractional many-body states are possible in topological insulators.

Several thousand compounds from the Inorganic Crystal Structure Database have been considered as nanograined, sintered-powder thermoelectrics with the high-throughput ab-initio AFLOW framework. Regression analysis unveils that the power factor is positively correlated with both the electronic band gap and the carrier effective mass, and that the probability of having large thermoelectric power factors increases with the increasing number of atoms per primitive cell. Avenues for further investigation are revealed by this work. These avenues include the role of experimental and theoretical databases in the development of novel materials.

The 2007 discovery of quantized conductance in HgTe quantum wells delivered the field of topological insulators (TIs) its first experimental confirmation. While many three-dimensional TIs have since been identified, HgTe remains the only known two-dimensional system in this class. Difficulty fabricating HgTe quantum wells has, moreover, hampered their widespread use. With the goal of breaking this logjam, we provide a blueprint for stabilizing a robust TI state in a more readily available two-dimensional material—graphene. Using symmetry arguments, density functional theory, and tight-binding simulations, we predict that graphene endowed with certain heavy adatoms realizes a TI with substantial band gap. For indium and thallium, our most promising adatom candidates, a modest 6% coverage produces an estimated gap near 80 K and 240 K, respectively, which should be detectable in transport or spectroscopic measurements. Engineering such a robust topological phase in graphene could pave the way for a new generation of devices for spintronics, ultra-low-dissipation electronics, and quantum information processing.

A generic theory of the quasiparticle superconducting gap in underdoped cuprates is derived in the strong-coupling limit, and found to describe the experimental “second gap” in absolute scale. In drastic contrast to the standard pairing gap associated with Bogoliubov quasiparticle excitations, the quasiparticle gap is shown to originate from anomalous kinetic (scattering) processes, with a size unrelated to the pairing strength. Consequently, the $k$ dependence of the gap deviates significantly from the pure $d_{x^2-y^2}$ wave of the order parameter. Our study reveals a new paradigm for the nature of the superconducting gap, and is expected to reconcile numerous apparent contradictions among existing experiments and point toward a more coherent understanding of high-temperature superconductivity.

The in-plane resistivity $\rho$ and thermal conductivity $\kappa$ of the heavy-fermion superconductor ${\mathrm{Ce}}_2{\mathrm{PdIn}}_8$ single crystals were measured down to 50 mK. A field-induced quantum critical point, occurring at the upper critical field $H_{c2}$, is demonstrated from the $\rho (T)\sim T$ near $H_{c2}$ and $\rho (T)\sim T^2$ when further increasing the field. The large residual linear term ${\kappa }_0/T$ at zero field and the rapid increase of $\kappa (H)/T$ at low field give evidence for nodal superconductivity in ${\mathrm{Ce}}_2{\mathrm{PdIn}}_8$. The jump of $\kappa (H)/T$ near $H_{c2}$ suggests a first-order-like phase transition at low temperature. These results mimic the features of the famous ${\mathrm{CeCoIn}}_5$ superconductor, implying that ${\mathrm{Ce}}_2{\mathrm{PdIn}}_8$ may be another interesting compound to investigate for the interplay between magnetism and superconductivity.

Using self-consistent mean-field and functional renormalization-group approaches, we show that $s$-wave pairing symmetry is robust in the heavily electron-doped iron chalcogenides $A{\mathrm{Fe}}_{2-x}{\mathrm{Se}}_2$, where $A=\mathrm{K},\text{}\mathrm{Cs}$. Recent neutron scattering experiments suggest that the effective nearest-neighbor spin exchange may be ferromagnetic in chalcogenides. This is different from the iron pnictides, where the nearest-neighbor magnetic exchange coupling is believed to be antiferromagnetic and leads to strong competition between $s$-wave and $d$-wave pairing in the electron-overdoped region. Our finding of a robust $s$-wave pairing in $(\mathrm{K},\text{}\mathrm{Cs}){\mathrm{Fe}}_{2-x}{\mathrm{Se}}_2$ differs from the $d$-wave pairing result obtained by other theories where nonlocal bare interaction terms and the next-to-nearest-neighbor $J_2$ term are underestimated. Detecting the pairing symmetry in $(\mathrm{K},\text{}\mathrm{Cs}){\mathrm{Fe}}_{2-x}{\mathrm{Se}}_2$ may hence provide important insights regarding the mechanism of superconducting pairing in iron-based superconductors.