Second-Order Real Nodal-Line Semimetal in Three-Dimensional Graphdiyne.

Real topological phases featuring real Chern numbers and second-order boundary modes have been a focus of current research, but finding their material realization remains a challenge. Here, based on first-principles calculations and theoretical analysis, we reveal the already experimentally synthesized three-dimensional (3D) graphdiyne as the first realistic example of the recently proposed second-order real nodal-line semimetal. We show that the material hosts a pair of real nodal rings, each protected by two topological charges: a real Chern number and a 1D winding number. The two charges generate distinct topological boundary modes at distinct boundaries. The real Chern number leads to a pair of hinge Fermi arcs, whereas the winding number protects a double drumhead surface bands. We develop a low-energy model for 3D graphdiyne which captures the essential topological physics. Experimental aspects and possible topological transition to a 3D real Chern insulator phase are discussed.

Switching Spinless and Spinful Topological Phases with Projective PT Symmetry.

A fundamental dichotomous classification for all physical systems is according to whether they are spinless or spinful. This is especially crucial for the study of symmetry-protected topological phases, as the two classes have distinct symmetry algebra. As a prominent example, the spacetime inversion symmetry PT satisfies (PT)^{2}=±1 for spinless/spinful systems, and each class features unique topological phases. Here, we reveal a possibility to switch the two fundamental classes via Z_{2} projective representations. For PT symmetry, this occurs when P inverses the gauge transformation needed to recover the original Z_{2} gauge connections under P. As a result, we can achieve topological phases originally unique for spinful systems in a spinless system, and vice versa. We explicitly demonstrate the claimed mechanism with several concrete models, such as Kramers degenerate bands and Kramers Majorana boundary modes in spinless systems, and real topological phases in spinful systems. Possible experimental realization of these models is discussed. Our work breaks a fundamental limitation on topological phases and opens an unprecedented possibility to realize intriguing topological phases in previously impossible systems.

Intrinsic Second-Order Anomalous Hall Effect and Its Application in Compensated Antiferromagnets.

Response properties that are purely intrinsic to physical systems are of paramount importance in physics research, as they probe fundamental properties of band structures and allow quantitative calculation and comparison with experiment. For anomalous Hall transport in magnets, an intrinsic effect can appear at the second order to the applied electric field. We show that this intrinsic second-order anomalous Hall effect is associated with an intrinsic band geometric property-the dipole moment of Berry-connection polarizability (BCP) in momentum space. The effect has scaling relation and symmetry constraints that are distinct from the previously studied extrinsic contributions. Particularly, in antiferromagnets with PT symmetry, the intrinsic effect dominates. Combined with first-principles calculations, we demonstrate the first quantitative evaluation of the effect in the antiferromagnet Mn_{2}Au. We show that the BCP dipole and the resulting intrinsic second-order conductivity are pronounced around band near degeneracies. Importantly, the intrinsic response exhibits sensitive dependence on the Néel vector orientation with a 2π periodicity, which offers a new route for electric detection of the magnetic order in PT-invariant antiferromagnets.

Valley-Layer Coupling: A New Design Principle for Valleytronics.

The current valleytronics research is based on the paradigm of time-reversal-connected valleys in two-dimensional (2D) hexagonal materials, which forbids the fully electric generation of valley polarization by a gate field. Here, we go beyond the existing paradigm to explore 2D systems with a novel valley-layer coupling (VLC) mechanism, where the electronic states in the emergent valleys have a valley-contrasted layer polarization. The VLC enables a direct coupling between a valley and a gate electric field. We analyze the symmetry requirements for a system to host VLC, demonstrate our idea via first-principles calculations and model analysis of a concrete 2D material example, and show that an electric, continuous, wide-range, and switchable control of valley polarization can be achieved by VLC. Furthermore, we find that systems with VLC can exhibit other interesting physics, such as valley-contrasting linear dichroism and optical selection of the valley and the electric polarization of interlayer excitons. Our finding opens a new direction for valleytronics and 2D materials research.

Universal Approach to Magnetic Second-Order Topological Insulator.

We propose a universal practical approach to realize magnetic second-order topological insulator (SOTI) materials, based on properly breaking the time reversal symmetry in conventional (first-order) topological insulators. The approach works for both three dimensions (3D) and two dimensions (2D), and is particularly suitable for 2D, where it can be achieved by coupling a quantum spin Hall insulator with a magnetic substrate. Using first-principles calculations, we predict bismuthene on EuO(111) surface as the first realistic system for a two-dimensional magnetic SOTI. We explicitly demonstrate the existence of the protected corner states. Benefitting from the large spin-orbit coupling and sizable magnetic proximity effect, these corner states are located in a boundary gap ∼83 meV, and hence can be readily probed in experiment. By controlling the magnetic phase transition, a topological phase transition between a first-order TI and a SOTI can be simultaneously achieved in the system. The effect of symmetry breaking, the connection with filling anomaly, and the experimental detection are discussed.

Two-Dimensional Second-Order Topological Insulator in Graphdiyne.

A second-order topological insulator (SOTI) in d spatial dimensions features topologically protected gapless states at its (d-2)-dimensional boundary at the intersection of two crystal faces, but is gapped otherwise. As a novel topological state, it has been attracting great interest, but it remains a challenge to identify a realistic SOTI material in two dimensions (2D). Here, based on combined first-principles calculations and theoretical analysis, we reveal the already experimentally synthesized 2D material graphdiyne as the first realistic example of a 2D SOTI, with topologically protected 0D corner states. The role of crystalline symmetry, the robustness against symmetry breaking, and the possible experimental characterization are discussed. Our results uncover a hidden topological character of graphdiyne and promote it as a concrete material platform for exploring the intriguing physics of higher-order topological phases.

Strain-induced Dirac cone-like electronic structures and semiconductor-semimetal transition in graphdiyne.

By means of first-principles calculations combined with the tight-binding approximation, the strain-induced semiconductor-semimetal transition in graphdiyne is discovered. It is shown that the band gap of graphdiyne increases from 0.47 eV to 1.39 eV with increasing the biaxial tensile strain, while the band gap decreases from 0.47 eV to nearly zero with increasing the uniaxial tensile strain, and Dirac cone-like electronic structures are observed. The uniaxial strain-induced changes of the electronic structures of graphdiyne come from the breaking of geometrical symmetry that lifts the degeneracy of energy bands. The properties of graphdiyne under strains are found to differ remarkably from that of graphene.

T-carbon: a novel carbon allotrope.

A structurally stable crystalline carbon allotrope is predicted by means of the first-principles calculations. This allotrope can be derived by substituting each atom in diamond with a carbon tetrahedron, and possesses the same space group Fd3m as diamond, which is thus coined as T-carbon. The calculations on geometrical, vibrational, and electronic properties reveal that T-carbon, with a considerable structural stability and a much lower density 1.50 g/cm3, is a semiconductor with a direct band gap about 3.0 eV, and has a Vickers hardness 61.1 GPa lower than diamond but comparable with cubic boron nitride. Such a form of carbon, once obtained, would have wide applications in photocatalysis, adsorption, hydrogen storage, and aerospace materials.

Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4.

Frustrated magnets hold the promise of material realizations of exotic phases of quantum matter, but direct comparisons of unbiased model calculations with experimental measurements remain very challenging. Here we design and implement a protocol of employing many-body computation methodologies for accurate model calculations-of both equilibrium and dynamical properties-for a frustrated rare-earth magnet TmMgGaO4 (TMGO), which explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz-Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex-antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics, and we further propose experimental detection of its intriguing properties.

Boron fullerenes B(32+8k) with four-membered rings and B32 solid phases: geometrical structures and electronic properties.

Based on ab initio calculations, we have studied the geometrical, electronic properties and chemical bonding of boron fullerenes B(32+8k) (0 < or = k < or = 7) with four-membered rings and B(32) solid phases. The relative energies and the energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) have been calculated, showing that the stabilities grow with the increase of fullerene size, where the smallest cage B(32) bears the largest HOMO-LUMO gap. The frontier orbitals of B(32+8k) show some similarities with those of the corresponding carbon fullerenes C(24+6k), implying that they may have similar chemical properties. It is found that B(32) cages can condense to form solid phases of simple cubic (sc), face-centered cubic (fcc), body-centered cubic (bcc), and body-centered tetragonal (bct) structures, where the bct phase is observed to be the most stable. Electronic structure calculations reveal that the sc, fcc and bcc phases of B(32) solids are metallic, but the bct phase is a semimetal.

Room temperature ferromagnetism and antiferromagnetism in two-dimensional iron arsenides.

The discovery of two-dimensional (2D) magnetic materials with high critical temperature and intrinsic magnetic properties has attracted significant research interest. By using swarm-intelligence structure search and first-principles calculations, we predict three 2D iron arsenide monolayers (denoted as FeAs-I, II and III) with good energetic and dynamical stabilities. We find that FeAs-I and II are ferromagnets, while FeAs-III is an antiferromagnet. FeAs-I and III have sizable magnetic anisotropy comparable to the magnetic recording materials such as the FeCo alloy. Importantly, we show that FeAs-I and III have critical temperatures of 645 K and 350 K, respectively, which are above room temperature. In addition, FeAs-I and II are metallic, while FeAs-III is semiconducting with a gap comparable to Si. For FeAs-III, there exist two pairs of 2D antiferromagnetic Dirac points below the Fermi level, and it displays a giant magneto band-structure effect. The superior magnetic and electronic properties of the FeAs monolayers make them promising candidates for spintronics applications.

Hourglass Dirac chain metal in rhenium dioxide.

Nonsymmorphic symmetries, which involve fractional lattice translations, can generate exotic types of fermionic excitations in crystalline materials. Here we propose a topological phase arising from nonsymmorphic symmetries-the hourglass Dirac chain metal, and predict its realization in the rhenium dioxide. We show that ReO2 features hourglass-type dispersion in the bulk electronic structure dictated by its nonsymmorphic space group. Due to time reversal and inversion symmetries, each band has an additional two-fold degeneracy, making the neck crossing-point of the hourglass four-fold degenerate. Remarkably, close to the Fermi level, the neck crossing-point traces out a Dirac chain-a chain of connected four-fold-degenerate Dirac loops-in the momentum space. The symmetry protection, the transformation under symmetry-breaking, and the associated topological surface states of the Dirac chain are revealed. Our results open the door to an unknown class of topological matters, and provide a platform to explore their intriguing physics.

d Orbital Topological Insulator and Semimetal in the Antifluorite Cu2S Family: Contrasting Spin Helicities, Nodal Box, and Hybrid Surface States.

We reveal a class of three-dimensional d orbital topological materials in the antifluorite Cu2S family. Derived from the unique properties of low-energy t2g states, their phases are solely determined by the sign of the spin-orbit coupling (SOC): topological insulator (TI) for negative SOC and topological semimetal for positive SOC, both having Dirac cone surface states but with contrasting helicities. With broken inversion symmetry, the semimetal becomes one with a nodal box consisting of butterfly-shaped nodal lines that are robust against SOC. Further breaking the tetrahedral symmetry by strain leads to an ideal Weyl semimetal with four pairs of Weyl points. Interestingly, the Fermi arcs coexist with a surface Dirac cone on the (010) surface, as required by a [Formula: see text] invariant.

Criticality-Enhanced Magnetocaloric Effect in Quantum Spin Chain Material Copper Nitrate.

In this work, a systematic study of Cu(NO3)2·2.5 H2O (copper nitrate hemipentahydrate, CN), an alternating Heisenberg antiferromagnetic chain model material, is performed with multi-technique approach including thermal tensor network (TTN) simulations, first-principles calculations, as well as magnetization measurements. Employing a cutting-edge TTN method developed in the present work, we verify the couplings J = 5.13 K, α = 0.23(1) and Landé factors g∥= 2.31, g⊥ = 2.14 in CN, with which the magnetothermal properties have been fitted strikingly well. Based on first-principles calculations, we reveal explicitly the spin chain scenario in CN by displaying the calculated electron density distributions, from which the distinct superexchange paths are visualized. On top of that, we investigated the magnetocaloric effect (MCE) in CN by calculating its isentropes and magnetic Grüneisen parameter. Prominent quantum criticality-enhanced MCE was uncovered near both critical fields of intermediate strengths as 2.87 and 4.08 T, respectively. We propose that CN is potentially a very promising quantum critical coolant.