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Towards ideal topological materials: Comprehensive database searches using symmetry indicators

Feng Tang, Hoi Chun Po, Ashvin Vishwanath, Xiangang Wan

arXiv:1807.09744v3cond-mat.mes-hallcond-mat.mtrl-sci

TL;DR

Excellent topological-material candidates suitable for realistic applications remain scarce because trivial Fermi-surface states can obscure topological behavior. The paper screens nonmagnetic materials using symmetry indicators and identifies a curated set of nearly ideal candidates, including systems that could expedite experimental progress.

  • Problem

    Excellent topological-material candidates for realistic technological applications remain difficult to find, partly because trivial Fermi-surface states can mask topological behavior.

  • Method

    The study applies symmetry-indicator analysis to ab initio electronic representations of nonmagnetic stoichiometric materials across the 230 space groups.

  • Results

    8% of the thousands of discovered topological-material candidates meet stringent criteria for nearly ideal candidates with cleaner Fermi surfaces.

  • Takeaways & Limitations

    The nearly ideal candidates could expedite experimental progress toward topological-material applications.

Abstract

from arXiv · show

Topological materials (TMs) showcase intriguing physical properties defying expectations based on conventional materials, and hold promise for the development of devices with new functionalities. While several theoretically proposed TMs have been experimentally confirmed, extensive experimental exploration of topological properties as well as applications in realistic devices have been held back due to the lack of excellent TMs in which interference from trivial Fermi surface states is minimized. We tackle this problem in the present work by applying our recently developed method of symmetry indicators to all non-magnetic compounds in the 230 space groups. An exhaustive database search reveals thousands of TM candidates. Of these, we highlight the excellent TMs, the 258 topological insulators and 165 topological crystalline insulators which have either noticeable full band gap or a considerable direct gap together with small trivial Fermi pockets. We also give a list of 489 topological semimetals with the band crossing points located near the Fermi level. All predictions obtained through standard generalized gradient approximation (GGA) calculations were cross-checked with the modified Becke-Johnson (MBJ) potential calculations, appropriate for narrow gap materials. With the electronic and optical behavior around the Fermi level dominated by the topologically non-trivial bands, these newly found TMs candidates open wide possibilities for realizing the promise of TMs in next-generation electronic devices.

I. INTRODUCTION

Topological materials offer robust unconventional properties and potential device applications, but excellent candidates remain scarce because trivial metallic states often obscure their topological responses. This work addresses the discovery problem by applying symmetry-indicator methods systematically to suitable non-magnetic materials in structural databases.

  • Motivation: Robust properties such as surface or edge states, absent backscattering, and topological Fermi arcs could enable low-power, high-speed spintronic, magnetoelectric, and optoelectronic devices.These unconventional properties motivate technological interest in topological materials.
  • Challenges: Excellent topological-material candidates for realistic technological applications remain difficult to find despite intense research efforts.The introduction identifies the scarcity of suitable candidates as a central obstacle.
  • Challenges: Native defects in Bi2Se3-family topological insulators can shift the chemical potential into bulk bands, producing metallic states that mask the insulating bulk’s topological response.Although bulk gaps are typically a few 100 meV, improved insulating behavior required chemistry modification.
  • Challenges: Weyl semimetals such as TaAs commonly combine slightly displaced Weyl points with trivial Fermi pockets, while Na3Bi and Cd3As2 face air-stability and toxicity limitations, respectively.These material-specific issues hinder extensive experimental studies and technological applications.
  • Approach: A symmetry-indicator method categorizes materials as possibly atomic insulators, definitely topologically nontrivial, or definitely hosting symmetry-protected band crossings.The method integrates symmetry-based indicator theory with ab initio calculations and had produced experimentally confirmed predictions.
  • Contribution: The study applies this method to suitable non-magnetic materials from structural databases to systematically discover topological materials.Earlier work predicted many topological crystalline phases, with some predictions experimentally confirmed.

II. MATERIALS SEARCH

The study applies a symmetry-indicator materials-search workflow to nonmagnetic stoichiometric compounds and identifies topological candidates, focusing on those with comparatively clean Fermi surfaces. GGA predictions are cross-checked with MBJ calculations because the methods disagree for a substantial fraction of candidates.

  • Search methodology: The search workflow computes atomic-insulator representation bases and combines them with ab initio irreducible representations at high-symmetry momenta.The procedure is applied for each space group to nonmagnetic stoichiometric compounds.
  • Search methodology: The supplementary materials provide atomic-insulator bases for each space group and tabulate the other nearly ideal candidates found.These resources support use of the symmetry-indicator scheme for diagnosing materials.
  • Candidate selection: 11269 of 17258 materials are identified as topological, although most have dirty Fermi surfaces from coexisting trivial states.The search therefore emphasizes nearly ideal candidates with clean Fermi surfaces rather than listing all identified topological materials.
  • Method validation: Approximately 25% of GGA-identified topological materials are classified as trivial by MBJ calculations.The discrepancy motivates cross-checking both methods and recording their agreements or disagreements in the supplementary tables.

III. TOPOLOGICAL INSULATORS

The search identified strong topological insulators, including Ag2Zr and Ba11Bi14Cd8, with representative cases spanning full-gap and large-direct-gap behavior. Ba11Bi14Cd8 is especially notable for its MBJ-calculated full gap and room-temperature-scale band gap.

  • Strong topological insulators: Ag2Zr is identified as a strong topological insulator from its symmetry indicator (0, 1) in space group 139.Its 46 valence bands have SI group XBS = Z2 × Z8, and the result can also be diagnosed using the Fu-Kane parity criterion.
  • Strong topological insulators: Small pockets contribute only a little density of states at the Fermi level in the discussed topological-insulator candidates.This supports the goal of minimizing interference from trivial Fermi-surface states.
  • Strong topological insulators: Ba11Bi14Cd8 is identified as a strong topological insulator from symmetry indicator (0, 1, 1) in space group 12.Its SI group is XBS = Z2 × Z2 × Z4.
  • Strong topological insulators: ∼34 meV by MBJ calculations is Ba11Bi14Cd8’s band gap, which exceeds room temperature and accompanies a full band gap.The full band gap is shown in the MBJ band plot, motivating interest in robust topological features.

IV. TOPOLOGICAL CRYSTALLINE INSULATORS

The study highlights BaGe and Bi2Se2 as representative topological crystalline insulators with favorable gap properties. Symmetry indicators identify BaGe as a weak TI but require further analysis, while Bi2Se2 is a TCI and weak TI with crystalline-symmetry-protected surface states.

  • Representative materials: BaGe has a sizable direct gap of ∼300 meV, whereas Bi2Se2 has a full bulk gap.These materials were selected as representative candidates for detailed discussion.
  • BaGe: BaGe’s symmetry indicator (1, 0) ∈ Z2 × Z4 shows that it is not a strong TI and must be a weak TI.Its space group is 63, with symmetry-indicator group Z2 × Z4.
  • BaGe: Further analysis, such as computing mirror Chern numbers, is required to determine BaGe’s precise topological crystalline phase.The ambiguity arises because symmetry indicators do not fully determine the topology when the strong index is even.
  • Bi2Se2: Bi2Se2 has symmetry indicator (1, 2), implying that it must be a topological crystalline insulator.Bi2Se2 belongs to space group 164, whose symmetry-indicator group is Z2 × Z4.
  • Bi2Se2: Bi2Se2 has topological invariant (ν0; ν1, ν2, ν3) = (0; 1, 1, 1), indicating that it is a weak TI.Its surface states may be protected by mirror or rotation symmetry.

V. TOPOLOGICAL DIRAC SEMIMETAL

PdO in space group 131 is identified as a representative topological Dirac semimetal, with a symmetry-protected Dirac point near the Fermi energy along the high-symmetry line AM.

  • Topological Dirac semimetal: PdO crystallizes in a tetragonal structure with point group D4h and belongs to Case 3, indicating necessary band crossings near the Fermi energy.The material is in space group 131.
  • Topological Dirac semimetal: A band crossing along the high-symmetry line AM results in a Dirac point.The crossing is shown in Fig. 3.
  • Topological Dirac semimetal: The Dirac point is protected by C4v symmetry.The passage states that this protection makes the Dirac point stable, but the condition is truncated.

VI. DISCUSSION

The study’s topological-property predictions use both GGA and MBJ calculations, with GGA results and MBJ crosschecks tabulated for nearly ideal candidates. Stringent selection criteria identify 8% of nearly ideal topological-material candidates from thousands found, potentially expediting experimental progress.

  • VI. DISCUSSION: Predictions of the materials’ topological properties use both GGA and MBJ methods.The paper discusses representative topological materials in the main text and uses MBJ as an additional method.
  • VI. DISCUSSION: GGA results for other nearly ideal topological-material candidates are tabulated in the supplementary material, alongside MBJ crosschecks for topological and crystalline insulators.The supplementary tables cover candidates identified with GGA and report MBJ crosscheck results for TIs and TCIs.
  • VI. DISCUSSION: 8% of nearly ideal topological-material candidates emerged from the thousands found in the search under stringent criteria.The authors state that this filtering could expedite experimental progress.

VII. METHODS

The study uses WIEN2K ab initio calculations with spin-orbital coupling and PBE-GGA, while noting that GGA tends to underestimate band gaps and can compromise topological-material predictions.

  • Computational approach: WIEN2K calculations included spin-orbital coupling and used the PBE realization of the standard GGA exchange-correlation functional.The authors describe WIEN2K as one of the most accurate packages and included spin-orbital coupling in all calculations.
  • Computational limitations: GGA tends to underestimate band gaps, making GGA-based topological-material predictions unreliable in some cases.The passage identifies band-gap underestimation as important for topological materials.

Supplementary Material · I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING

The screening method uses symmetry indicators to efficiently diagnose topological materials through expansions in an atomic insulator basis. Fractional expansion coefficients and common factors distinguish candidate topological phases, which are summarized by an Abelian-group symmetry indicator.

  • I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING: The method requires only an expansion with respect to the atomic insulator basis, enabling efficient topological-materials screening.The supplementary material explicitly shows 230 atomic insulator bases for the 230 space groups.
  • I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING: 230 atomic insulator bases are explicitly provided for the 230 space groups.Each group has a fixed number of integer-valued atomic-insulator-basis vectors, which may share a common factor.
  • I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING: The topological property is diagnosed by inspecting the expansion coefficients q_i.The coefficients are evaluated against the atomic-insulator basis and its pseudo-inverse.
  • I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING: Integer q_i coefficients indicate that the material could be an atomic insulator.This is the first of three diagnostic cases.
  • I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING: Fractional q_i coefficients whose products q_iC_i are all integers indicate satisfied compatibility relations and a continuous gap at high-symmetry points, lines, and planes.This second case is the relevant case for searching topological materials.
  • I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING: For centrosymmetric space groups, an odd q_sC_s mod C_s identifies a strong topological insulator, while an otherwise classified case yields a topological crystalline insulator.For S4-symmetric noncentrosymmetric space groups, C_s = 2 and q_sC_s mod 2 must be 1 for the stated case.
  • I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING: The common factors define an Abelian group X_BS = Z_j × Z_j+1 × . . . × Z_dAI.Here, j denotes the first atomic-insulator-basis vector whose common factor is larger than 1.
  • I. EFFICIENT TOPOLOGICAL MATERIALS SCREENING: The residues r_m = q_mC_m mod C_m form the symmetry indicator (r_j, r_j+1, . . . , r_dAI), providing a fast diagnosis of topological materials.Each residue is interpreted in the corresponding factor group Z_m.

II. TOPOLOGICAL INSULATORS

The section presents relatively good topological insulators identified through GGA database searches, with MBJ calculations checking whether their predicted topology is preserved or becomes crystalline. It also indicates that GGA and MBJ band structures are plotted for the listed materials.

  • II. TOPOLOGICAL INSULATORS: The database search lists all relatively good topological insulators identified using GGA calculations, together with structure references for the materials.The section focuses on candidates with relatively clean Fermi surfaces.
  • II. TOPOLOGICAL INSULATORS: MBJ calculations verify the GGA band topology: unchanged cases are marked blue, while cases becoming topological crystalline phases are marked red.The color coding is applied to the material names in the table.
  • II. TOPOLOGICAL INSULATORS: GGA- and MBJ-calculated electronic band structures are plotted for the listed topological insulators.These band-structure plots are presented in Sec. VI.

III. TOPOLOGICAL CRYSTALLINE INSULATORS

This section lists relatively good topological crystalline insulators identified through GGA database searches and assesses whether MBJ calculations preserve their predicted topology. The accompanying table reports TCIs with clean Fermi surfaces and distinguishes unchanged topology from strong-insulator outcomes.

  • III. TOPOLOGICAL CRYSTALLINE INSULATORS: The database search lists all relatively good topological crystalline insulators identified using GGA calculations.Structure references are provided for the listed materials.
  • III. TOPOLOGICAL CRYSTALLINE INSULATORS: MBJ calculations further checked whether the GGA-predicted band topology was maintained.Materials retaining the predicted topology are marked in blue, while cases becoming topological insulators under MBJ are marked in red.
  • III. TOPOLOGICAL CRYSTALLINE INSULATORS: The table lists all TCIs with clean Fermi surfaces discovered by GGA calculations.Blue indicates unchanged band topology under MBJ, whereas red indicates that MBJ yields a strong insulator.

IV. TOPOLOGICAL (SEMI-)METALS … VII. ELECTRONIC BAND PLOTS FOR TOPOLOGICAL CRYSTALLINE INSULATORS

The paper catalogs relatively clean topological (semi-)metals from GGA database searches and presents selected electronic band structures with symmetry indicators for topological insulators. The supplied passages provide no substantive content for the atomic-insulator-base or topological-crystalline-insulator sections.

  • IV. TOPOLOGICAL (SEMI-)METALS: The database search lists relatively good topological (semi-)metals identified using GGA calculations.Each material belongs to a specialized space group, with structure references provided for the listed names.
  • IV. TOPOLOGICAL (SEMI-)METALS: Tables III–V compile topological (semi-)metals with relatively clean Fermi surfaces discovered from GGA calculations.The tables are presented in three parts.
  • V. ATOMIC INSULATOR BASE: The supplied passages for the atomic-insulator-base section contain only isolated formatting symbols and no readable scientific statements.Consequently, no substantive result from this section can be summarized from the provided material.
  • VI. ELECTRONIC BAND PLOTS FOR TOPOLOGICAL INSULATORS: The band-plot sections cover the topological insulators and topological crystalline insulators listed in Tables I and II, respectively.The supplied passage introduces band structures for these tabulated materials, although only the topological-insulator subsection contains readable text.
  • VI. ELECTRONIC BAND PLOTS FOR TOPOLOGICAL INSULATORS: Red lines in the plotted electronic band structures denote bands up to the electron filling.This convention is stated for the band plots of the listed TIs and TCIs.
  • VI. ELECTRONIC BAND PLOTS FOR TOPOLOGICAL INSULATORS: Symmetry indicators are explicitly given for each material under both GGA and MBJ predictions.The passage identifies these indicators as part of the electronic-band-structure presentation.
  • VI. ELECTRONIC BAND PLOTS FOR TOPOLOGICAL INSULATORS: The paper does not show band structures for all predicted materials because of the arxiv file size limit (≤10 M).The passage also refers readers to band structures for the remaining materials and topological (semi-)materials, but the supplied text is truncated.
  • VII. ELECTRONIC BAND PLOTS FOR TOPOLOGICAL CRYSTALLINE INSULATORS: No substantive passage for the electronic band plots of topological crystalline insulators is included in the supplied material.The readable band-plot passage mentions TCIs but is labeled under the preceding topological-insulator subsection.
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