arXiv subjects

Zhida Song

Publications and source records attributed to Zhida Song.

At least 55 records · Page 3Linked to original sources

arXiv2018

Topological states from topological crystals

We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be adiabatically deformed (allowing for stacking of trivial states) into a special class of states we call topological crystals. A topological crystal in, for example, three dimensions is a real-space assembly of finite-sized pieces of topological states in one and two dimensions protected by the local symmetry group alone, arranged in a configuration invariant under the spatial group and glued together such there is no open edge or end. As a demonstration of principle, we explicitly enumerate all inequivalent topological crystals for non-interacting time-reversal symmetric electronic insulators with significant spin-orbit coupling and any one of the 230 space groups in three dimensions. Because every topological crystalline insulator can be deformed into a topological crystal, the enumeration of the latter gives topological crystalline insulators a full classification and for each class an explicit real-space construction. We also extend these results to give a unified classification including both strong topological insulators and topological crystalline insulators.

cond-mat.mes-hall↗

arXiv2018

MgTa2N3: A new reference Dirac semimetal

We present a prediction of the Dirac semimetal (DSM) phase in MgTa2N3 based on first-principles calculations and symmetry analysis. In this material, the Fermi level is located exactly at the Dirac point without additional Fermi surface pockets. The band inversion associated with the Dirac cone involves the d orbitals of two structurally inequivalent Ta atoms with octahedral and trigonal prismatic coordination spheres. We further show that the lattice symmetry breaking can realize topological phase transitions from the DSM phase to a triple nodal point semimetal, Weyl semimetal or topological insulator. The topologically protected surface states and the non-protected Fermi arc surface states are also studied.

cond-mat.mtrl-sci↗

arXiv2018

All "Magic Angles" Are "Stable" Topological

We show that the electronic structure of the low-energy bands in the small angle-twisted bilayer graphene consists of a series of semi-metallic and topological phases. In particular we are able to prove, using an approximate low-energy particle-hole symmetry, that the gapped set of bands that exist around all magic angles has what we conjecture to be a stable topological index stabilized by a magnetic symmetry and reflected in the odd winding of the Wilson loop in the Moiré BZ. The approximate, emergent particle-hole symmetry is essential to the topology of graphene: when strongly broken, non-topological phases can appear. Our paper underpins topology as the crucial ingredient to the description of low-energy graphene. We provide a $4$-band short range tight-binding model whose $2$ lower bands have the same topology, symmetry, and flatness as those of the twisted graphene, and which can be used as an effective low-energy model. We then perform large-scale ($11000$ atoms per unit cell, 40 days per $\bf k$-point computing time) ab-initio calculations of a series of small angles, from $3^\circ$ to $1^\circ$, which show a more complex and somewhat qualitatively different evolution of the symmetry of the low-energy bands than that of the theoretical Moiré model, but which confirms the topological nature of the system. At certain angles, we find no insulating filling in graphene at $-4$ electrons per Moiré unit cell. The ab-initio evolution of gaps tends to differ from that of the continuum Moiré model.

cond-mat.mes-hall↗

arXiv2018

Quantitative mappings between symmetry and topology in solids

The study of spatial symmetries was accomplished during the last century, and had greatly improved our understanding of the properties of solids. Nowadays, the symmetry data of any crystal can be readily extracted from standard first-principles calculation. On the other hand, the topological data (topological invariants), the defining quantities of nontrivial topological states, are in general considerably difficult to obtain, and this difficulty has critically slowed down the search for topological materials. Here, we provide explicit and exhaustive mappings from symmetry data to topological data for arbitrary gapped band structure in the presence of time-reversal symmetry and any one of the 230 space groups. The mappings are completed using the theoretical tools of layer construction and symmetry-based indicators. With these results, finding topological invariants in any given gapped band structure reduces to a simple search in the mapping tables provided.

cond-mat.mes-hall↗

arXiv2018

Diagnosis for topological semimetals in the absence of spin-orbital coupling

Topological semimetals are under intensive theoretical and experimental studies. The first step of these studies is always the theoretical (numerical) predication of one of several candidate materials, starting from first principles. In these calculations, it is crucial that all topological band crossings, including their types and positions in the Brillouin zone, are found. While band crossings along high-symmetry lines, which are routinely scanned in numerics, are simple to locate, the ones at generic momenta are notoriously time-consuming to find, and may be easily missed. In this paper, we establish a theoretical scheme of diagnosis for topological semimetals where all band crossings are at generic momenta in systems with time-reversal symmetry and negligible spin-orbital coupling. The scheme only uses the symmetry (inversion and rotation) eigenvalues of the valence bands at high-symmetry points in the BZ as input, and provides the types, numbers and configurations of all topological band crossings, if any, at generic momenta. The nature of new diagnosis scheme allows for full automation and parallelizations, and paves way to high throughput numerical predictions of topological materials.

cond-mat.mes-hall↗

arXiv2018

Catalogue of Topological Electronic Materials

Topological electronic materials are new quantum states of matter hosting novel linear responses in the bulk and anomalous gapless states at the boundary, and are for scientific and applied reasons under intensive research in physics and in materials sciences. The detection for such materials has so far been hindered by the level of complication involved in the calculation of the so-called topological invariants, and is hence considered a specialized task that requires both experience with materials and expertise with advanced theoretical tools. Here we introduce an effective, efficient and fully automated algorithm in obtaining the topological invariants for all non-magnetic materials that are known to human, based on recently developed principles that allow for exhaustive mappings between the symmetry representation of occupied bands and the topological invariants. Our algorithm requires as input only the occupied-band information (energy and wavefunction) at a handful (up to eight) of high-symmetry points in the Brillouin zone, which is readily calculable with any first-principles software. In return, it is capable of providing a detailed topological classification of all non-magnetic materials. Equipped with this method we have scanned through a total of 39519 materials available in structural databases, and found that as many as 8056 of them are actually topological (8889 if spin-orbital coupling is neglected). These are further catalogued into classes of 5005 topological semimetals,1814 topological insulators and 1237 topological crystalline insulators, most of which are new to human knowledge. All the results are available and searchable at http://materiae.iphy.ac.cn/ .

cond-mat.mtrl-sci↗

arXiv2018

Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator $\text{Bi}_{2-x}\text{Sm}_x\text{Se}_3$

A universal mechanism to generate chiral hinge states in the ferromagnetic axion insulator phase is proposed, which leads to an exotic transport phenomena, the quantum anomalous Hall effect (QAHE) on some particular surfaces determined by both the crystalline symmetry and the magnetization direction. A realistic material system Sm doped $\text{Bi}_2\text{Se}_3$ is then proposed to realize such exotic hinge states by combing the first principle calculations and the Green's function techniques. A physically accessible way to manipulate the surface QAHE is also proposed, which makes it very different from the QAHE in ordinary 2D systems.

cond-mat.mes-hall↗

arXiv2017

$(d-2)$-dimensional edge states of rotation symmetry protected topological states

We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands, and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through explicit construction of microscopic models having robust $(d-2)$-dimensional edge states.

cond-mat.mes-hall↗

arXiv2017

Instability of Dirac semimetal phase under strong magnetic field

The quantum limit can be easily reached in the Dirac semimetals under the magnetic field, which will lead to some exotic many-body physics due to the high degeneracy of the topological zeroth Landau bands (LBs). By solving the effective Hamiltonian, which is derived by tracing out the high energy degrees of freedom, at the self-consistent mean field level, we have systematically studied the instability of Dirac semimetal under a strong magnetic field. A charge density wave (CDW) phase and a polarized nematic phase formed by "exciton condensation" are predicted as the ground state for the tilted and untilted bands, respectively. Furthermore, we propose that, distinguished from the CDW phase, the polarized nematic phase can be identified in experiments by anisotropic transport and Raman scattering.

cond-mat.mtrl-sci↗

arXiv2017

Double-Weyl phonons in transition-metal monosilicides

Topological states of electrons and photons have attracted significant interest recently. Topological mechanical states also being actively explored, have been limited to macroscopic systems of kHz frequency. The discovery of topological phonons of atomic vibrations at THz frequency can provide a new venue for studying heat transfer, phonon scattering and electron-phonon interaction. Here, we employed ab initio calculations to identify a class of noncentrosymmetric materials of $M$Si ($M$=Fe,Co,Mn,Re,Ru) having double Weyl points in both their acoustic and optical phonon spectra. They exhibit novel topological points termed "spin-1 Weyl point" at the Brillouin zone~(BZ) center and "charge-2 Dirac point" at the zone corner. The corresponding gapless surface phonon dispersions are double helicoidal sheets whose isofrequency contours form a single non-contractible loop in the surface BZ. In addition, the global structure of the surface bands can be analytically expressed as double-periodic Weierstrass elliptic functions. Our prediction of topological bulk and surface phonons can be experimentally verified by neutron scattering and electron energy loss spectroscopy, opening brand new directions for topological phononics.

cond-mat.mtrl-sci↗

arXiv2017

Topological Dirac Nodal-net Fermions in AlB$_2$-type TiB$_2$ and ZrB$_2$

Based on first-principles calculations and effective model analysis, a Dirac nodal-net semimetal state is recognized in AlB$_2$-type TiB$_2$ and ZrB$_2$ when spin-orbit coupling (SOC) is ignored. Taking TiB$_2$ as an example, there are several topological excitations in this nodal-net structure including triple point, nexus, and nodal link, which are protected by coexistence of spatial-inversion symmetry and time reversal symmetry. This nodal-net state is remarkably different from that of IrF$_4$, which requires sublattice chiral symmetry. In addition, linearly and quadratically dispersed two-dimensional surface Dirac points are identified as having emerged on the B-terminated and Ti-terminated (001) surfaces of TiB$_2$ respectively, which are analogous to those of monolayer and bilayer graphene.

cond-mat.mtrl-sci↗

arXiv2016

Detecting Chiral Magnetic Effect by Lattice Dynamics

In the present paper, we propose that the chiral magnetic effect, the direct consequence of the presence of Weyl points in the band structure, can be detected by its coupling to certain phonon modes, which behave like pseudo scalars under point group transformations. Such coupling can generate resonance between intrinsic plasmon oscillation and the corresponding phonon modes, leading to dramatic modification of the optical response by the external magnetic field, which provides a new way to study chiral magnetic effect by optical measurements.

cond-mat.mtrl-sci↗

arXiv2015

Two-Dimensional Oxide Topological Insulator With Iron-Pnictide Superconductor LiFeAs Structure

By using first-principles calculations, we propose that ZrSiO can be looked as a three-dimensional (3D) oxide weak topological insulator (TI) and its single layer is a long-sought-after 2D oxide TI with a band gap up to 30 meV. Calculated phonon spectrum of the single layer ZrSiO indicates it is dynamically stable and the experimental achievements in growing oxides with atomic precision ensure that it can be readily synthesized. This will lead to novel devices based on TIs, the so called "topotronic" devices, operating under room-temperature and stable when exposed in the air. Thus, a new field of "topotronics" will arise. Another intriguing thing is this oxide 2D TI has the similar crystal structure as the well-known iron-pnictide superconductor LiFeAs. This brings great promise in realizing the combination of superconductor and TI, paving the way to various extraordinary quantum phenomena, such as topological superconductor and Majorana modes. We further find that there are many other isostructural compounds hosting the similar electronic structure and forming a $WHM$-family with $W$ being Zr, Hf or La, $H$ being group IV or group V element, and $M$ being group VI one.

cond-mat.mtrl-sci↗

arXiv2015

Quantum Spin Hall State on Square-like Lattice

We find that quantum spin Hall (QSH) state can be obtained on a square-like or rectangular lattice, which is generalized from two-dimensional (2D) transition metal dichalcogenide (TMD) haeckelites. Band inversion is shown to be controled by hopping parameters and results in Dirac cones with opposite or same vorticity when spin-orbit coupling (SOC) is not considered. Effective k$\cdot$p model has been constructed to show the merging or annihilation of these Dirac cones, supplemented with the intuitive pseudospin texture. Similar to graphene based honeycomb lattice system, the QSH insulator is driven by SOC, which opens band gap at the Dirac cones. We employ the center evolution of hybrid Wannier function from Wilson-loop method, as well as the direct integral of Berry curvature, to identify the $Z_2$ number. We hope our detailed analysis will stimulate further efforts in searching for QSH insulators in square or rectangular lattice, in addition to the graphene based honeycomb lattice.

cond-mat.mes-hall↗

arXiv2015

Large-Gap Two-Dimensional Topological Insulator in Oxygen Functionalized MXene

Two-dimensional (2D) topological insulator (TI) have been recognized as a new class of quantum state of matter. They are distinguished from normal 2D insulators with their nontrivial band-structure topology identified by the $Z_2$ number as protected by time-reversal symmetry (TRS). 2D TIs have intriguing spin-velocity locked conducting edge states and insulating properties in the bulk. In the edge states, the electrons with opposite spins propagate in opposite directions and the backscattering is fully prohibited when the TRS is conserved. This leads to quantized dissipationless "two-lane highway" for charge and spin transportation and promises potential applications. Up to now, only very few 2D systems have been discovered to possess this property. The lack of suitable material obstructs the further study and application. Here, by using first-principles calculations, we propose that the functionalized MXene with oxygen, M$_2$CO$_2$ (M=W, Mo and Cr), are 2D TIs with the largest gap of 0.194 eV in W case. They are dynamically stable and natively antioxidant. Most importantly, they are very likely to be easily synthesized by recent developed selective chemical etching of transition-metal carbides (MAX phase). This will pave the way to tremendous applications of 2D TIs, such as "ideal" conducting wire, multifunctional spintronic device, and the realization of topological superconductivity and Majorana modes for quantum computing.

cond-mat.mtrl-sci↗

arXiv2015

Quantum Spin Hall Effect in 2D Transition Metal Dichalcogenide Haeckelites

By using first-principles calculation, we have found that a family of 2D transition metal dichalcogenide haeckelites with square-octagonal lattice $MX_2$-4-8 ($M$=Mo, W and $X$=S, Se and Te) can host quantum spin hall effect. The phonon spectra indicate that they are dynamically stable and the largest band gap is predicted to be around 54 meV, higher than room temperature. These will pave the way to potential applications of topological insulators. We have also established a simple tight-binding model on a square-like lattice to achieve topological nontrivial quantum states, which extends the study from honeycomb lattice to square-like lattice and broads the potential topological material system greatly.

cond-mat.mtrl-sci↗

arXiv2012

Tune of Magnetism and Electronic Structures of Alkali Metal Carbides with Rocksalt Structure

Electronic structures of carbides with the rocksalt structure were calculated by full potential electronic codes solving the Kohn-Sham equation. Bonding characters were analyzed by constructing tight-binding Hamiltonian based on maximally-localized Wannier functions. It was found that the cations in these compounds act as an electron provider and the frame is formed by the carbon atoms. The electronic states in the vicinity of the Fermi level are mainly from the p-orbitals of C. Pressure and doping are two efficient ways to tune the magnetic and electronic properties of these compounds. It turns out that a spin gapless semiconductor can be obtained by applying hydrostatic pressure up to tens of gigaPascal. Higher pressure induced an insulator to metal transition because of band broadening. Compounds of IA group (Na, K, Rb, Cs) were magnetic semiconductor at ambient conditions. Alloying with IIA elements decrease the magnetic moment according to the law of $3-x$, where $x$ is the relative atomic ratio of the IIA elements to the IA ones. The behaviors of the compounds under the pressure and the doping effects can be understood by a rigid band model.

cond-mat.mtrl-sci↗

arXiv2012

Electronic structure and magnetism in M(=IA, IIA)C compounds with the rocksalt structure

Electronic structures of MC where M is the alkali and alkaline earth metals with the rocksalt structure are calculated by full potential density functional codes. We find that the spin magnetic moment in the compounds is mainly contributed by the spin polarized p-orbitals of carbon. The large distance between the carbon makes the p-orbitals localized, which induces magnetic instability according to the Stoner criterion. The electronic structure can be mapped to the rigid band model. SrC, BaC and RaC are half-metals, while KC, RbC and CsC are magnetic semiconductors

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