Topological insulators and nematic phases from spontaneous symmetry breaking in 2D fermi systems with a quadratic band crossing

Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands

Integer and fractional Chern insulators have been extensively explored in correlated flat band models. Recently, the prediction and experimental observation of fractional quantum anomalous Hall (FQAH) states with spontaneous time-reversal symmetry breaking have garnered attention. While the thermodynamics of integer quantum anomalous Hall (IQAH) states have been systematically studied, our theoretical knowledge on thermodynamic properties of FQAH states has been severely limited. Here, we delve into the general thermodynamic response and collective excitations of both IQAH and FQAH states within the paradigmatic flat Chern-band model with remote band considered. Our key findings include (i) in both ν=1 IQAH and ν=1/3 FQAH states, even without spin fluctuations, the charge-neutral collective excitations would lower the onset temperature of these topological states, to a value significantly smaller than the charge gap, due to band mixing and multiparticle scattering; (ii) by employing large-scale thermodynamic simulations in FQAH states in the presence of strong interband mixing between C=±1 bands, we find that the lowest collective excitations manifest as the zero-momentum excitons in the IQAH state, whereas in the FQAH state, they take the form of magnetorotons with finite momentum; (iii) the unique charge oscillations in FQAH states are exhibited with distinct experimental signatures, which we propose to detect in future experiments.

Hydrogenation of Covalent Organic Framework Induces Conjugated π Bonds and Electronic Topological Transition to Enhance Hydrogen Evolution Catalysis

Recently, many topological materials have been discovered as promising electrocatalysts in chemical conversion processes and energy storage. However, it remains unclear how the topological electronic states specifically modulate the catalytic reaction. Here, the two-dimensional metal phthalocyanine-based covalent organic framework (MPc-COF) is studied by ab initio thermodynamic calculations to clearly reveal the promotional effect on the electrochemical hydrogen evolution reaction (HER) induced by topological gapless bands (TGBs). We find that the prehydrogenated (and fluorinated) H4CdPc-COF(F) shows the best HER performance, with 0.016 V (near zero) overpotential. By tracking changes to the electronic structure and free energy as the prehydrogenation and HER processes occur, we are able to separately attribute the high HER efficiency in part due to the increase of the electron bath by donating electrons to the conjugated π bonds and also to the existence of TGBs. Specifically, the significant catalytic promotion by TGBs is proven to decrease the free energy by 0.218 eV to near zero. When the TGBs are destroyed, e.g., by replacing N with P and opening a band gap, the HER efficiency is reduced. This study opens avenues for deterministically harnessing topological band features to improve electrocatalysis.

Broken Inversion Symmetry in Van Der Waals Topological Ferromagnetic Metal Iron Germanium Telluride

Inversion symmetry breaking is critical for many quantum effects and fundamental for spin-orbit torque, which is crucial for next-generation spintronics. Recently, a novel type of gigantic intrinsic spin-orbit torque is established in the topological van der Waals (vdW) magnet iron germanium telluride. However, it remains a puzzle because no clear evidence exists for interlayer inversion symmetry breaking. Here, the definitive evidence of broken inversion symmetry in iron germanium telluride directly measured by the second harmonic generation (SHG) technique is reported. The data show that the crystal symmetry reduces from centrosymmetric P63/mmc to noncentrosymmetric polar P3m1 space group, giving the threefold SHG pattern with dominant out-of-plane polarization. Additionally, the SHG response evolves from an isotropic pattern to a sharp threefold symmetry upon increasing Fe deficiency, mainly due to the transition from random defects to ordered Fe vacancies. Such SHG response is robust against temperature, ensuring unaltered crystalline symmetries above and below the ferromagnetic transition temperature. These findings add crucial new information to the understanding of this interesting vdW metal, iron germanium telluride: band topology, intrinsic spin-orbit torque, and topological vdW polar metal states.

Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene

Rhombohedral-stacked multilayer graphene hosts a pair of flat bands touching at zero energy, which should give rise to correlated electron phenomena that can be tuned further by an electric field. Moreover, when electron correlation breaks the isospin symmetry, the valley-dependent Berry phase at zero energy may give rise to topologically non-trivial states. Here we measure electron transport through hexagonal boron nitride-encapsulated pentalayer graphene down to 100 mK. We observed a correlated insulating state with resistance at the megaohm level or greater at charge density n = 0 and displacement field D = 0. Tight-binding calculations predict a metallic ground state under these conditions. By increasing D, we observed a Chern insulator state with C = -5 and two other states with C = -3 at a magnetic field of around 1 T. At high D and n, we observed isospin-polarized quarter- and half-metals. Hence, rhombohedral pentalayer graphene exhibits two different types of Fermi-surface instability, one driven by a pair of flat bands touching at zero energy, and one induced by the Stoner mechanism in a single flat band. Our results establish rhombohedral multilayer graphene as a suitable system for exploring intertwined electron correlation and topology phenomena in natural graphitic materials without the need for moiré superlattice engineering.

Carbon Kagome nanotubes-quasi-one-dimensional nanostructures with flat bands

In recent years, a number of bulk materials and heterostructures have been explored due their connections with exotic materials phenomena emanating from flat band physics and strong electronic correlation. The possibility of realizing such fascinating material properties in simple realistic nanostructures is particularly exciting, especially as the investigation of exotic states of electronic matter in wire-like geometries is relatively unexplored in the literature. Motivated by these considerations, we introduce in this work carbon Kagome nanotubes (CKNTs)-a new allotrope of carbon formed by rolling up Kagome graphene, and investigate this material using specialized first principles calculations. We identify two principal varieties of CKNTs-armchair and zigzag, and find both varieties to be stable at room temperature, based on ab initio molecular dynamics simulations. CKNTs are metallic and feature dispersionless states (i.e., flat bands) near the Fermi level throughout their Brillouin zone, along with an associated singular peak in the electronic density of states. We calculate the mechanical and electronic response of CKNTs to torsional and axial strains, and show that CKNTs appear to be more mechanically compliant than conventional carbon nanotubes (CNTs). Additionally, we find that the electronic properties of CKNTs undergo significant electronic transitions-with emergent partial flat bands and tilted Dirac points-when twisted. We develop a relatively simple tight-binding model that can explain many of these electronic features. We also discuss possible routes for the synthesis of CKNTs. Overall, CKNTs appear to be unique and striking examples of realistic elemental quasi-one-dimensional materials that may display fascinating material properties due to strong electronic correlation. Distorted CKNTs may provide an interesting nanomaterial platform where flat band physics and chirality induced anomalous transport effects may be studied together.

Realization of a Two-Dimensional Checkerboard Lattice in Monolayer Cu2N

Two-dimensional checkerboard lattice, the simplest line-graph lattice, has been intensively studied as a toy model, while material design and synthesis remain elusive. Here, we report theoretical prediction and experimental realization of the checkerboard lattice in monolayer Cu₂N. Experimentally, monolayer Cu₂N can be realized in the well-known N/Cu(100) and N/Cu(111) systems that were previously mistakenly believed to be insulators. Combined angle-resolved photoemission spectroscopy measurements, first-principles calculations, and tight-binding analysis show that both systems host checkerboard-derived hole pockets near the Fermi level. In addition, monolayer Cu₂N has outstanding stability in air and organic solvents, which is crucial for further device applications.

Topological Exact Flat Bands in Two-Dimensional Materials under Periodic Strain

We study flat bands and their topology in 2D materials with quadratic band crossing points under periodic strain. In contrast to Dirac points in graphene, where strain acts as a vector potential, strain for quadratic band crossing points serves as a director potential with angular momentum ℓ=2. We prove that when the strengths of the strain fields hit certain "magic" values, exact flat bands with C=±1 emerge at charge neutrality point in the chiral limit, in strong analogy to magic angle twisted-bilayer graphene. These flat bands have ideal quantum geometry for the realization of fractional Chern insulators, and they are always fragile topological. The number of flat bands can be doubled for certain point group, and the interacting Hamiltonian is exactly solvable at integer fillings. We further demonstrate the stability of these flat bands against deviations from the chiral limit, and discuss possible realization in 2D materials.

Bloch theorem dictated wave chaos in microcavity crystals

Universality class of wave chaos emerges in many areas of science, such as molecular dynamics, optics, and network theory. In this work, we generalize the wave chaos theory to cavity lattice systems by discovering the intrinsic coupling of the crystal momentum to the internal cavity dynamics. The cavity-momentum locking substitutes the role of the deformed boundary shape in the ordinary single microcavity problem, providing a new platform for the in situ study of microcavity light dynamics. The transmutation of wave chaos in periodic lattices leads to a phase space reconfiguration that induces a dynamical localization transition. The degenerate scar-mode spinors hybridize and non-trivially localize around regular islands in phase space. In addition, we find that the momentum coupling becomes maximal at the Brillouin zone boundary, so the intercavity chaotic modes coupling and wave confinement are significantly altered. Our work pioneers the study of intertwining wave chaos in periodic systems and provide useful applications in light dynamics control.

Direct geometric probe of singularities in band structure

A quantum system’s energy landscape may have points where multiple energy surfaces are degenerate and that exhibit singular geometry of the wave function manifold, with major consequences for the system’s properties. Ultracold atoms in optical lattices have been used to indirectly characterize such points in the band structure. We measured the non-Abelian transformation produced by transport directly through the singularities. We accelerated atoms along a quasi-momentum trajectory that enters, turns, and then exits the singularities at linear and quadratic band-touching points of a honeycomb lattice. Measurements after transport identified the topological winding numbers of these singularities to be 1 and 2, respectively. Our work introduces a distinct method for probing singularities that enables the study of non-Dirac singularities in ultracold-atom quantum simulators.

Sign-tunable anomalous Hall effect induced by two-dimensional symmetry-protected nodal structures in ferromagnetic perovskite thin films

Magnetism and spin-orbit coupling are two quintessential ingredients underlying topological transport phenomena in itinerant ferromagnets. When spin-polarized bands support nodal points/lines with band degeneracy that can be lifted by spin-orbit coupling, the nodal structures become a source of Berry curvature, leading to a large anomalous Hall effect. However, two-dimensional systems can possess stable nodal structures only when proper crystalline symmetry exists. Here we show that two-dimensional spin-polarized band structures of perovskite oxides generally support symmetry-protected nodal lines and points that govern both the sign and the magnitude of the anomalous Hall effect. To demonstrate this, we performed angle-resolved photoemission studies of ultrathin films of SrRuO₃, a representative metallic ferromagnet with spin-orbit coupling. We show that the sign-changing anomalous Hall effect upon variation in the film thickness, magnetization and chemical potential can be well explained by theoretical models. Our work may facilitate new switchable devices based on ferromagnetic ultrathin films.

External tuning of topological phase transitions induced by interaction driven mass renormalization

Electron-electron interactions can be useful for realizing new nontrivial topological phases of matter. Here, we show by means of a tight-binding model and mean field theory how electron-electron interactions can lead to a topological phase transition. By externally adding or removing electrons from the system a band inversion between two bands with different parity is induced. This leads to a topological nontrivial phase if spin-orbit coupling is present. Besides the toy-model illustrating this mechanism, we also propose SmB₆as a possible playground for experimentally realizing a topological phase transition by external tuning.

Second-Order Josephson Effect in Excitonic Insulators

We show that in electron-hole bilayers with excitonic orders arising from conduction and valence bands formed by atomic orbitals that have different parities, nonzero interlayer tunneling leads to a second-order Josephson effect. This means the interlayer electrical current is related to the phase of the excitonic order parameter as J=J_{c}sin2θ instead of J=J_{c}sinθ and that the system has two degenerate ground states at θ=0,π that can be switched by an interlayer voltage pulse. When generalized to a three dimensional stack of alternating electron-hole planes or a two dimensional stack of chains, the ac Josephson effect implies that electric field pulses perpendicular to the layers and chains can steer the order parameter phase between the two degenerate ground states, making these devices ultrafast memories. The order parameter steering also applies to the excitonic insulator candidate Ta_{2}NiSe_{5}.

Realization of topological Mott insulator in a twisted bilayer graphene lattice model

Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.

Floquet scattering of quadratic band-touching semimetals through a time-periodic potential well

We consider tunneling of quasiparticles through a rectangular quantum well, subject to periodic driving. The quasiparticles are the itinerant charges in two-dimensional and three-dimensional semimetals having a quadratic bandtouching (QBT) point in the Brillouin zone. To analyze the time-periodic Hamiltonian, we assume a non-adiabatic limit where the Floquet theorem is applicable. By deriving the Floquet scattering matrices, we chalk out the transmission and shot noise spectra of the QBT semimetals. The spectra show Fano resonances, which we identify with the (quasi)bound states of the systems.

Orbital Chern Insulator and Quantum Phase Diagram of a Kagome Electron System with Half-Filled Flat Bands

We study the quantum phase diagram of electrons on kagome lattice with half-filled lowest flat bands by considering the antiferromagnetic Heisenberg interaction J, and short-range Coulomb interaction V. In the weak J regime, we identify a fully spin-polarized phase. The presence of finite V drives a spontaneous chiral current, which makes the system an orbital Chern insulator by contributing an orbital magnetization. Such an out-of-plane orbital magnetization allows the presence of a Chern insulating phase independent of the spin orientation in contrast to the spin-orbit coupling induced Chern insulator that disappears with in-plane ferromagnetism constrained by symmetry. Such a symmetry difference provides a criterion to distinguish the physical origin of topological responses in kagome systems. The orbital Chern insulator is robust against small coupling J. By further increasing J, we find that the ferromagnetic topological phase is suppressed, which first becomes partially polarized and then enters a nonmagnetic phase with spin and charge nematicity. The frustrated flat band allows the spin and Coulomb interaction to play an essential role in determining the quantum phases.

Self-Trapped Polarons and Topological Defects in a Topological Mott Insulator

Many-body interactions in topological quantum systems can give rise to new phases of matter, which simultaneously exhibit both rich spatial features and topological properties. In this work, we consider spinless fermions on a checkerboard lattice with nearest and next-to-nearest neighbor interactions. We calculate the phase diagram at half filling, which presents, in particular, an interaction-induced quantum anomalous Hall phase. We study the system at incommensurate fillings using an unrestricted Hartree-Fock ansatz and report a rich zoo of solutions such as self-trapped polarons and domain walls above an interaction-induced topological insulator. We find that, as a consequence of the interplay between the interaction-induced topology and topological defects, these domain walls separate two phases with opposite topological invariants and host topologically protected chiral edge states. Finally, we discuss experimental prospects to observe these novel phenomena in a quantum simulator based on laser-dressed Rydberg atoms in an optical lattice.

Critical topological nodal points and nodal lines/rings in Kagome graphene

Critical topological phases, possessing flat bands, provide a platform to study unique topological properties and transport phenomena under a many-body effect. Here, we propose that critical nodal points and nodal lines or rings can be found in Kagome lattices. After the C3 rotation symmetry of a single-layer Kagome lattice is eliminated, a quadratic nodal point splits into two critical nodal points. When the layered Kagome lattices are stacked into a three-dimensional (3D) structure, critical nodal lines or rings can be generated by tuning the interlayer coupling. Furthermore, we use Kagome graphene as an example to identify that these critical phases could be obtained in real materials. We also discuss flat-band-induced ferromagnetism. It is found that the flat band splits into two spin-polarized bands by hole-doping, and as a result the Dirac-type critical phases evolve into Weyl-type phases.

Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks

We propose a new principle to realize flatbands which are robust in real materials, based on a network superstructure of one-dimensional segments. This mechanism is naturally realized in the nearly commensurate charge-density wave of 1T-TaS_{2} with the honeycomb network of conducting domain walls, and the resulting flatband can naturally explain the enhanced superconductivity. We also show that corner states, which are a hallmark of the higher-order topological insulators, appear in the network superstructure.

Intertwined topological phases induced by emergent symmetry protection

The dual role played by symmetry in many-body physics manifests itself through two fundamental mechanisms: spontaneous symmetry breaking and topological symmetry protection. These two concepts, ubiquitous in both condensed matter and high energy physics, have been applied successfully in the last decades to unravel a plethora of complex phenomena. Their interplay, however, remains largely unexplored. Here we report how, in the presence of strong correlations, symmetry protection emerges from a set of configurations enforced by another broken symmetry. This mechanism spawns different intertwined topological phases, where topological properties coexist with long-range order. Such a singular interplay gives rise to interesting static and dynamical effects, including interaction-induced topological phase transitions constrained by symmetry breaking, as well as a self-adjusted fractional pumping. This work paves the way for further exploration of exotic topological features in strongly-correlated quantum systems.

High-throughput Discovery of Topologically Non-trivial Materials using Spin-orbit Spillage

We present a novel methodology to identify topologically non-trivial materials based on band inversion induced by spin-orbit coupling (SOC) effect. Specifically, we compare the density functional theory (DFT) based wavefunctions with and without spin-orbit coupling and compute the 'spin-orbit-spillage' as a measure of band-inversion. Due to its ease of calculation, without any need for symmetry analysis or dense k-point interpolation, the spillage is an excellent tool for identifying topologically non-trivial materials. Out of 30000 materials available in the JARVIS-DFT database, we applied this methodology to more than 4835 non-magnetic materials consisting of heavy atoms and low bandgaps. We found 1868 candidate materials with high-spillage (using 0.5 as a threshold). We validated our methodology by carrying out conventional Wannier-interpolation calculations for 289 candidate materials. We demonstrate that in addition to Z2 topological insulators, this screening method successfully identified many semimetals and topological crystalline insulators. Importantly, our approach is applicable to the investigation of disordered or distorted as well as magnetic materials, because it is not based on symmetry considerations. We discuss some individual example materials, as well as trends throughout our dataset, which is available at the websites: https://www.ctcms.nist.gov/~knc6/JVASP.html and https://jarvis.nist.gov/ .

Prediction of a topological p + ip excitonic insulator with parity anomaly

Excitonic insulators are insulating states formed by the coherent condensation of electron and hole pairs into BCS-like states. Isotropic spatial wave functions are commonly considered for excitonic condensates since the attractive interaction among the electrons and the holes in semiconductors usually leads to s-wave excitons. Here, we propose a new type of excitonic insulator that exhibits order parameter with p + ip symmetry and is characterized by a chiral Chern number C_c = 1/2. This state displays the parity anomaly, which results in two novel topological properties: fractionalized excitations with e/2 charge at defects and a spontaneous in-plane magnetization. The topological insulator surface state is a promising platform to realize the topological excitonic insulator. With the spin-momentum locking, the interband optical pumping can renormalize the surface electrons and drive the system towards the proposed p + ip instability.

Exotic states can be stabilized in strongly-correlated systems with non-trivial topological properties. Here, Wang et al. propose a topological p-wave excitonic insulator characterized by a chiral Chern number 1/2.

Winding Vector: How to Annihilate Two Dirac Points with the Same Charge

The merging or emergence of a pair of Dirac points may be classified according to whether the winding numbers which characterize them are opposite (+- scenario) or identical (++ scenario). From the touching point between two parabolic bands (one of them can be flat), two Dirac points with the same winding number emerge under appropriate distortion (interaction, etc.), following the ++ scenario. Under further distortion, these Dirac points merge following the +- scenario, that is corresponding to opposite winding numbers. This apparent contradiction is solved by the fact that the winding number is actually defined around a unit vector on the Bloch sphere and that this vector rotates during the motion of the Dirac points. This is shown here within the simplest two-band lattice model (Mielke) exhibiting a flat band. We argue on several examples that the evolution between the two scenarios is general.

Interacting topological insulators: a review

The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful research areas for both experimentalists and theorists. The physics of topological insulators is typically well described by band theory and systems of non-interacting fermions. In contrast, several of the most fascinating effects in condensed matter physics merely exist due to electron-electron interactions, examples include unconventional superconductivity, the Kondo effect, and the Mott-Hubbard transition. The aim of this review article is to give an overview of the manifold directions which emerge when topological bandstructures and correlation physics interfere and compete. These include the study of the stability of topological bandstructures and correlated topological insulators. Interaction-induced topological phases such as the topological Kondo insulator provide another exciting topic. More exotic states of matter such as topological Mott insulator and fractional Chern insulators only exist due to the interplay of topology and strong interactions and do not have any bandstructure analogue. Eventually the relation between topological bandstructures and frustrated quantum magnetism in certain transition metal oxides is emphasized.

Topological quantum phase transitions of Chern insulators in disk geometry

We investigate topological quantum phase transitions (TQPTs) of Chern insulators in two-dimensional honeycomb-lattice disk with six-fold rotational symmetry. By considering the nearest-neighbor, next-nearest-neighbor hopping parameters and the staggered-flux parameter of the Haldane model, we can obtain rich topological quantum phases. The trivial and non-trivial phases of the Haldane model in disk geometry can be distinguished based on chiral edge states, real-space particle densities and local density of states. We also explore the TQPTs of Chern insulators with an external potential which varies with the radius of the disk geometry. Some interesting topological phases with large Chern numbers can be observed when we consider long-distance hoppings. Furthermore, we use a machine learning algorithm as an effective way to automatically identify various topological phases and phase diagrams for the Haldane model in disk geometry.

Non-Dirac Chern insulators with large band gaps and spin-polarized edge states

Based on first-principles calculations and k·p models, we demonstrate that PbC/MnSe heterostructures are a non-Dirac type of Chern insulator with very large band gaps (244 meV) and exotically half-metallic edge states, providing the possibilities of realizing very robust, completely spin polarized, and dissipationless spintronic devices from the heterostructures. The achieved extraordinarily large nontrivial band gap can be ascribed to the contribution of the non-Dirac type electrons (composed of px and py) and the very strong atomic spin-orbit coupling (SOC) interaction of the heavy Pb element in the system. Surprisingly, the band structures are found to be sensitive to the different exchange and correlation functionals adopted in the first-principles calculations. Chern insulators with various mechanisms are acquired from them. These discoveries show that the predicted nontrivial topology in PbC/MnSe heterostructures is robust and can be observed in experiments at high temperatures. The system has great potential to have attractive applications in future spintronics.

Time-Reversal Symmetry-Breaking Nematic Insulators near Quantum Spin Hall Phase Transitions

We study the phase diagram of a model quantum spin Hall system as a function of band inversion and band-coupling strength, demonstrating that when band hybridization is weak, an interaction-induced nematic insulator state emerges over a wide range of band inversion. This property is a consequence of the long-range Coulomb interaction, which favors interband phase coherence that is weakly dependent on momentum and therefore frustrated by the single-particle Hamiltonian at the band inversion point. For weak band hybridization, interactions convert the continuous gap closing topological phase transition at inversion into a pair of continuous phase transitions bounding a state with broken time-reversal and rotational symmetries. At intermediate band hybridization, the topological phase transition proceeds instead via a quantum anomalous Hall insulator state, whereas at strong hybridization interactions play no role. We comment on the implications of our findings for InAs/GaSb and HgTe/CdTe quantum spin Hall systems.

Role of four-fermion interaction and impurity in the states of two-dimensional semi-Dirac materials

We study the effects of four-fermion interaction and impurity on the low-energy states of 2D semi-Dirac materials by virtue of the unbiased renormalization group approach. The coupled flow equations that govern the energy-dependent evolutions of all correlated interaction parameters are derived after taking into account one-loop corrections from the interplay between four-fermion interaction and impurity. Whether and how four-fermion interaction and impurity influence the low-energy properties of 2D semi-Dirac materials are discreetly explored and addressed attentively. After carrying out the standard renormalization group analysis, we find that both trivial insulating and nontrivial semimetal states are qualitatively stable against all four kinds of four-fermion interactions. However, while switching on both four-fermion interaction and impurity, certain insulator-semimetal phase transitions and the distance of Dirac nodal points can be respectively induced and modified due to their strong interplay and intimate competition. Moreover, several non-Fermi liquid behaviors that deviate from the conventional Fermi liquids are exhibited at the lowest-energy limit.

Universality and Stability of the Edge States of Chiral-Symmetric Topological Semimetals and Surface States of the Luttinger Semimetal

We theoretically demonstrate that the chiral structure of the nodes of nodal semimetals is responsible for the existence and universal local properties of the edge states in the vicinity of the nodes. We perform a general analysis of the edge states for an isolated node of a 2D semimetal, protected by chiral symmetry and characterized by the topological winding number N. We derive the asymptotic chiral-symmetric boundary conditions and find that there are N+1 universal classes of them. The class determines the numbers of flatband edge states on either side off the node in the 1D spectrum and the winding number N gives the total number of edge states. We then show that the edge states of chiral nodal semimetals are robust: they persist in a finite-size stability region of parameters of chiral-asymmetric terms. This significantly extends the notion of 2D and 3D topological nodal semimetals. We demonstrate that the Luttinger model with a quadratic node for j=3/2 electrons is a 3D topological semimetal in this new sense and predict that α-Sn, HgTe, possibly Pr_{2}Ir_{2}O_{7}, and many other semimetals described by it are topological and exhibit surface states.

Gapless edge states in (C,O,H)-built molecular system with p-stacking and hydrogen bonds

The gapless edge states have been found in a 2D molecular system built with light atoms: C,O,H. This prediction is done on the basis of combined density functional theory (DFT) and tight-binding calculations. The system does not exhibit any effect of the spin-orbit coupling (SOC), neither intrinsic nor Rashba type. The band structure and the edge states are tuned with a strength of the p-stacking and O...H interactions. The elementary cell of this noncovalent structure, does not have the 3D inversion or rotational symmetry. Instead, the system transforms via a superposition of two reflections: with respect to the xz and xy mirror planes, both containing the non-periodic direction. This superposition is equivalent to the inversion in the 2D subspace, in which the system is periodic. The energy gap obtained with the DFT method is 0.11 eV, and largely opens (above 1 eV) with the GW and hybrid-DFT approaches. The bands inversion is partial, i.e. the Bloch states are mixed, with the "swapping" and "non-swapping" atomic contributions.

New Class of 3D Topological Insulator in Double Perovskite

We predict a new class of 3D topological insulators (TIs) in which the spin-orbit coupling (SOC) can more effectively generate band gap. Band gap of conventional TI is mainly limited by two factors, the strength of SOC and, from electronic structure perspective, the band gap when SOC is absent. While the former is an atomic property, the latter can be minimized in a generic rock-salt lattice model in which a stable crossing of bands at the Fermi level along with band character inversion occurs in the absence of SOC. Thus large-gap TIs or TIs composed of lighter elements can be expected. In fact, we find by performing first-principles calculations that the model applies to a class of double perovskites A₂BiXO₆ (A = Ca, Sr, Ba; X = Br, I) and the band gap is predicted up to 0.55 eV. Besides, surface Dirac cones are robust against the presence of dangling bond at boundary.

Emergent Electromagnetic Induction and Adiabatic Charge Pumping in Noncentrosymmetric Weyl Semimetals

The photovoltaic effect due to the adiabatic quantum phase in noncentrosymmetric Weyl semimetals is studied. We particularly focus on the case in which an external ac electric field is applied. By considering a generalized Weyl Hamiltonian with nonlinear terms, we show that the photocurrent is induced by circularly, rather than linearly, polarized light. This photovoltaic current can be understood as an emergent electromagnetic induction in momentum space; the Weyl node is a magnetic monopole in momentum space, the circular motion of which induces the electric field. This result is distinct from conventional photovoltaic effects, and the estimated photocurrent is ∼10^{-1}-10^{1}  nA, which can be detected experimentally.

Physics of higher orbital bands in optical lattices: a review

The orbital degree of freedom plays a fundamental role in understanding the unconventional properties in solid state materials. Experimental progress in quantum atomic gases has demonstrated that high orbitals in optical lattices can be used to construct quantum emulators of exotic models beyond natural crystals, where novel many-body states such as complex Bose-Einstein condensates and topological semimetals emerge. A brief introduction of orbital degrees of freedom in optical lattices is given and a summary of exotic orbital models and resulting many-body phases is provided. Experimental consequences of the novel phases are also discussed.

Topological Varma Superfluid in Optical Lattices

Topological states of matter are peculiar quantum phases showing different edge and bulk transport properties connected by the bulk-boundary correspondence. While noninteracting fermionic topological insulators are well established by now and have been classified according to a tenfold scheme, the possible realization of topological states for bosons has not been explored much yet. Furthermore, the role of interactions is far from being understood. Here, we show that a topological state of matter exclusively driven by interactions may occur in the p band of a Lieb optical lattice filled with ultracold bosons. The single-particle spectrum of the system displays a remarkable parabolic band-touching point, with both bands exhibiting non-negative curvature. Although the system is neither topological at the single-particle level nor for the interacting ground state, on-site interactions induce an anomalous Hall effect for the excitations, carrying a nonzero Chern number. Our work introduces an experimentally realistic strategy for the formation of interaction-driven topological states of bosons.

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

Topological states of matter have been widely studied as being driven by an external magnetic field, intrinsic spin-orbital coupling, or magnetic doping. Here, we unveil an interaction-driven spontaneous quantum Hall effect (a Chern insulator) emerging in an extended fermion-Hubbard model on a kagome lattice, based on a state-of-the-art density-matrix renormalization group on cylinder geometry and an exact diagonalization in torus geometry. We first demonstrate that the proposed model exhibits an incompressible liquid phase with doublet degenerate ground states as time-reversal partners. The explicit spontaneous time-reversal symmetry breaking is determined by emergent uniform circulating loop currents between nearest neighbors. Importantly, the fingerprint topological nature of the ground state is characterized by quantized Hall conductance. Thus, we identify the liquid phase as a quantum Hall phase, which provides a "proof-of-principle" demonstration of the interaction-driven topological phase in a topologically trivial noninteracting band.

Interaction-Induced Dirac Fermions from Quadratic Band Touching in Bilayer Graphene

We revisit the effect of local interactions on the quadratic band touching (QBT) of the Bernal honeycomb bilayer model using renormalization group (RG) arguments and quantum Monte Carlo (QMC) simulations. We present a RG argument which predicts, contrary to previous studies, that weak interactions do not flow to strong coupling even if the free dispersion has a QBT. Instead, they generate a linear term in the dispersion, which causes the interactions to flow back to weak coupling. Consistent with this RG scenario, in unbiased QMC simulations of the Hubbard model we find compelling evidence that antiferromagnetism turns on at a finite U/t despite the U=0 hopping problem having a QBT. The onset of antiferromagnetism takes place at a continuous transition which is consistent with (2+1)D Gross-Neveu criticality. We conclude that generically in models of bilayer graphene, even if the free dispersion has a QBT, small local interactions generate a Dirac phase with no symmetry breaking and that there is a finite-coupling transition out of this phase to a symmetry-broken state.

Diagnosis of Interaction-driven Topological Phase via Exact Diagonalization

We propose a general scheme for diagnosing interaction-driven topological phases in the weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition.

Chiral Spin-Orbital Liquids with Nodal Lines

Strongly correlated materials with strong spin-orbit coupling hold promise for realizing topological phases with fractionalized excitations. Here, we propose a chiral spin-orbital liquid as a stable phase of a realistic model for heavy-element double perovskites. This spin liquid state has Majorana fermion excitations with a gapless spectrum characterized by nodal lines along the edges of the Brillouin zone. We show that the nodal lines are topological defects of a non-Abelian Berry connection and that the system exhibits dispersing surface states. We discuss some experimental signatures of this state and compare them with properties of the spin liquid candidate Ba_{2}YMoO_{6}.

Multifarious topological quantum phase transitions in two-dimensional topological superconductors

We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers.

PT-symmetric phase in kagome-based photonic lattices

The kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing PT-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a PT-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.

Quadratic Fermi node in a 3D strongly correlated semimetal

Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr₂Ir₂O₇, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr₂Ir₂O₇ is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

5d transition metal iridates provide a platform to study the combined effects of strong spin orbit coupling and strong electronic correlations. Here, the authors find a quadratic band touching in the band structure of Pr₂Ir₂O₇, suggesting it may be tuned to form various strongly correlated topological phases.

Interaction-Driven Topological Insulator in Fermionic Cold Atoms on an Optical Lattice: A Design with a Density Functional Formalism

We design an interaction-driven topological insulator for fermionic cold atoms in an optical lattice; that is, we pose the question of whether we can realize in a continuous space a spontaneous symmetry breaking induced by the interatom interaction into a topological Chern insulator. Such a state, sometimes called a "topological Mott insulator," has yet to be realized in solid-state systems, since this requires, in the tight-binding model, large off-site interactions on top of a small on-site interaction. Here, we overcome the difficulty by introducing a spin-dependent potential, where a spin-selective occupation of fermions in A and B sublattices makes the on-site interaction Pauli forbidden, while a sizeable intersite interaction is achieved by a shallow optical potential with a large overlap between neighboring Wannier orbitals. This puts the system away from the tight-binding model, so that we adopt density functional theory for cold atoms, here extended to accommodate noncollinear spin structures emerging in the topological regime, to quantitatively demonstrate the phase transition to the topological Mott insulator.

Temperature-induced spontaneous time-reversal symmetry breaking on the honeycomb lattice

Phase transitions involving spontaneous time-reversal symmetry breaking are studied on the honeycomb lattice at finite hole doping with next-nearest-neighbor repulsion. We derive an exact expression for the mean-field equation of state in closed form, valid at temperatures much less than the Fermi energy. Contrary to standard expectations, we find that thermally induced intraband particle-hole excitations can create and stabilize a uniform metallic phase with broken time-reversal symmetry as the temperature is raised in a region where the ground state is a trivial metal.

Chiral d-wave superconductivity in doped graphene

A highly unconventional superconducting state with a spin-singlet dx2-y2+/-idxy-wave, or chiral d-wave symmetry has recently been suggested to emerge from electron-electron interactions in doped graphene. It has been argued that graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverge, is particularly likely to be a chiral d-wave superconductor. In this review we summarize the currently mounting theoretical evidence for the existence of a chiral d-wave superconducting state in graphene, obtained with methods ranging from mean-field studies of effective Hamiltonians to angle-resolved renormalization group calculations. We further discuss the multiple distinctive properties of the chiral d-wave superconducting state in graphene, as well as its stability in the presence of disorder. We also review the means of enhancing the chiral d-wave state using proximity-induced superconductivity. The appearance of chiral d-wave superconductivity is intimately linked to the hexagonal crystal lattice and we also offer a brief overview of other materials which have also been proposed to be chiral d-wave superconductors.

Topological mott insulator in three-dimensional systems with quadratic band touching

We argue that a three-dimensional electronic system with the Fermi level at the quadratic band touching point such as HgTe could be unstable with respect to the spontaneous formation of the (topological) Mott insulator at arbitrary weak long-range Coulomb interaction. The mechanism of the instability can be understood as the collision of Abrikosov's non-Fermi liquid fixed point with another, quantum critical, fixed point, which approaches it in the coupling space as the system's dimensionality d→dlow+, with the "lower critical dimension" 2<dlow<4. Arguments for the existence of the quantum critical point based on considerations in the large-N limit in d=3, as well as close to d=2, are given. In the one-loop calculation we find that dlow=3.26, and thus above, but not far from three dimensions. This translates into a temperature or energy window (Tc, T*) over which the non-Fermi liquid scaling should still be observable, before the Mott transition finally takes place at the critical temperature Tc∼T*exp[-zC/(dlow-d)1/2]. We estimate C=π/1.1, dynamical critical exponent z≈1.8, and the temperature scale kBT*≈(4m/melϵ^2)13.6  eV, with m as the band mass and ϵ as the dielectric constant.

Double perovskite heterostructures: magnetism, Chern bands, and Chern insulators

Experiments demonstrating the controlled growth of oxide heterostructures have raised the prospect of realizing topologically nontrivial states of correlated electrons in low dimensions. Here, we study heterostructures consisting of {111} bilayers of double perovskites separated by inert band insulators. In bulk, these double perovskites have well-defined local moments interacting with itinerant electrons leading to high temperature ferromagnetism. Incorporating spin-orbit coupling in the two-dimensional honeycomb geometry of a {111} bilayer, we find a rich phase diagram with tunable ferromagnetic order, topological Chern bands, and a C=±2 Chern insulator regime. Our results are of broad relevance to oxide materials such as Sr_{2}FeMoO_{6}, Ba_{2}FeReO_{6}, and Sr_{2}CrWO_{6}.

Theory of a competitive spin liquid state for weak Mott insulators on the triangular lattice

We propose a novel quantum spin liquid state that can explain many of the intriguing experimental properties of the low-temperature phase of the organic spin liquid candidate materials κ-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. This state of paired fermionic spinons preserves all symmetries of the system, and it has a gapless excitation spectrum with quadratic bands that touch at momentum k[over →]=0. This quadratic band touching is protected by symmetries. Using variational Monte Carlo techniques, we show that this state has highly competitive energy in the triangular lattice Heisenberg model supplemented with a realistically large ring-exchange term.

Featureless and nonfractionalized Mott insulators on the honeycomb lattice at 1/2 site filling

Symmetries are increasingly shown to play various key roles determining the possible phases in condensed matter systems. We study bosonic particles (including electron Cooper pairs) living on the vertices of a honeycomb lattice at a density of 1/2 per site. Here the honeycomb symmetries forbid the usual fermionic band insulating state, and the conventional Mott (“strongly interacting”) insulator involves a whole number of particles frozen on each site, suggesting that featureless (fully symmetric) insulators might not exist in this system. Nevertheless, we explicitly construct quantum states and demonstrate that they are examples of featureless insulators on the honeycomb lattice at 1/2 site filling, with a procedure generalizing to lattices with symmorphic symmetry groups.

Within the Landau paradigm, phases of matter are distinguished by spontaneous symmetry breaking. Implicit here is the assumption that a completely symmetric state exists: a paramagnet. At zero temperature such quantum featureless insulators may be forbidden, triggering either conventional order or topological order with fractionalized excitations. Such is the case for interacting particles when the particle number per unit cell, f , is not an integer. However, can lattice symmetries forbid featureless insulators even at integer f ? An especially relevant case is the honeycomb (graphene) lattice—where free spinless fermions at (the two sites per unit cell mean is half-filling per site) are always metallic. Here we present wave functions for bosons, and a related spin-singlet wave function for spinful electrons, on the honeycomb lattice and demonstrate via quantum to classical mappings that they do form featureless Mott insulators. The construction generalizes to symmorphic lattices at integer f in any dimension. Our results explicitly demonstrate that in this case, despite the absence of a noninteracting insulator at the same filling, lack of order at zero temperature does not imply fractionalization.

Topological quantum phase transitions on the kagomé and square-octagon lattices

We study the topological quantum phase transitions of tight-binding electrons on two representative multi-band lattice models with superimposed staggered fluxes: the kagomé lattice and the square-octagon lattice. By considering the nearest-neighbor and next-nearest-neighbor hopping parameters (t1 and t2) and the staggered flux parameter φ, we obtain rich topological quantum phase transitions for both the lattices. The whole phase diagram for the kagomé lattice in the t2-φ parameter space is obtained. We also illustrate a series of topological quantum phase transitions as well as topological bands of high Chern numbers for the square-octagon lattice. Furthermore, interesting topological flat bands with high flatness ratios (e.g. of about 43) are found in the square-octagon lattice, especially when the next-next-nearest-neighbor hopping (t3) is included.

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.

Correlation effects in two-dimensional topological insulators

Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlation effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.