Session L54: Computational Studies of Topological Materials

Time-reversal-invariant Weyl semimetals indicated by symmetry indictors and invariants

For the time-reversal(TR)-breaking centrosymmetric systems, an odd number of all the even/odd parity occupied bands, at eight inversion-symmetry-invariant (ISI) momenta, indicates the appearance of Weyl points in the systems. Here, based on the the first-principles calculations and symmetry analysis, we demonstrate that, for the TR-preversing noncentrosymmetric systems with S4 symmetry, the Weyl semimetal phase can be characterised by the nonequality between an invariant $\eta$ and an S4 indicator $z_2$. By applying it, we find that some candicates can be ideal Weyl semimetals in a noncentrosymmetric space group with S4 symmetry. Our first-principles calculations show that four pairs of Weyl points are located in the kx,y = 0 planes, being right at the charge neutrality level. An effective model has been built and captures the nontrivial topology in these materials. Our strategy to find the Weyl points by using symmetry indicators and invariants opens a new route to search for Weyl semimetals in TR-invariant systems.   

Topological crystalline insulator: from symmetry indicators to material discovery

Topological crystalline insulators (TCIs) are insulating electronic phases of matter in which the nontrivial topology is driven by crystalline symmetries. Recent theoretical advances have proposed new rotational-symmetry-protected TCI states that are expected to show unique topologically protected boundary modes. The surface normal to the rotational axis in these TCIs features ''unpinned'' Dirac surface states whose Dirac points are located at generic k points. Also, due to the ''higher-order'' bulk-boundary correspondence, such a 3D TCI supports 1D helical edge states. However, to date, rotational-symmetry-protected TCIs have remained elusive in real materials. We systematically examine the topological properties of the TCI states in Ca₂As. On both the top and side surfaces, we show the presence of topological surface states protected independently by rotational and mirror symmetries [1]. We also discuss the van der Waals material α-Bi₄Br₄ and the pristine bulk bismuth and show that these materials harbor TCI states protected purely by rotation symmetry [2,3], even though these materials have been long thought to be topologically trivial.

[1] Phys. Rev. B, 98, 241104(R) (2018).
[2] 2D Materials 6, 031004 (2019).
[3] PNAS 116, 13255 (2019).   

Emergent dual topology in the three-dimensional Kane-Mele Pt2HgSe3

Recently, the very first large-gap Kane-Mele quantum spin Hall insulator was predicted to be monolayer jacutingaite (Pt₂HgSe₃), a naturally-occurring exfoliable mineral. The stacking of quantum spin Hall monolayers typically leads to a (0;001) weak topological phase, which does not protect the existence of surface states on the (001) surface. Unexpectedly, recent ARPES experiments revealed the presence of surface states dispersing over large areas of the 001-surface Brillouin zone. Such 001-surface states have been shown to be topologically protected by a non-zero mirror Chern number, associated with a nodal line gapped by spin-orbit interactions. Here, we extend the two-dimensional Kane-Mele model to bulk jacutingaite and unveil the microscopic origin of the gapped nodal line and the emerging crystalline topological order. By using maximally-localized Wannier functions, we identify a large non-trivial second nearest-layer hopping term that breaks the standard paradigm of weak topological insulators. Complemented by this term, the predictions of the Kane-Mele model are in remarkable agreement with recent experiments and first-principles simulations, providing an appealing conceptual framework also relevant for other layered materials made of stacked honeycomb lattices.   

Doping induced topological phase transition in Bi: The role of quantum electronic stress

Charge doping is an essential means to tailor materials’ properties. However, besides moving the Fermi level, charge doping is generally not expected to induce topological phase transition (TPT). Surprisingly, using first-principles calculations, here we demonstrate an electron doping induced TPT in bulk Bi from a higher-order topological insulator (HOTI) to a TI. The underlying mechanism is revealed to be driven by an electron doping induced quantum electronic stress (QES), which in turn induces a highly anisotropic lattice expansion to close/reopen the small energy gap in Bi band structure. Our finding significantly resolves an outstanding controversy concerning the topological characterization of bulk Bi among existing experiments and theories, and explains the physical origin of the topologic order in Bi (111) thin films. It sheds new lights to fundamental understanding of topological properties of small band gap materials in relation to doping and QES.   

Possibility of topological properties in 2D cadmium chalcogenide (CdX, X = S, Se, and Te) buckled honeycomb monolayer on substitutional doping

Two-dimensional honeycomb monolayers doped with tin atoms are designed from (111) surface of bulk zinc blende structures of cadmium chalcogenides using first principles density functional theory based calculations. On relaxation the buckled honeycomb monolayer shows signature of band inversion between Sn and Cd orbital at the zone center (Γ point) deep in the valence band and high above in the conduction band. The band inversion, due to hybridization, stays even after inclusion of spin-orbit coupling. The systems were chosen with an intention to exploit the possibility of d-d band inversion. CdSnS has s-s band inversion but CdSnSe and CdSnTe monolayers do show band inversion involving d states. The calculated phonon spectra confirmed the stability of all the systems studied. The details of the electronic structure bring out the importance of s-d band inversion. We also report the topological invariants and analysis of edge state properties and band structure of these materials in ribbon geometry. Such systems can be useful for technological application in the Spintronic domain.   

The electronic and topological properties of plumbene by first-principles calculations

Combining tight-binding (TB) models with first-principles calculations, we investigate the electronic and topological properties of plumbene. “Constructive” coupling effects of topological states are found in the plumbene, causing the system being a normal insulator, opposite to topologically nontrivial states formed in the other group IVA monolayers. Based on this mechanism, several schemes are raised to produce a globally topological state in the plumbene. Interestingly, after the edge modification in the nanoribbon structure, the plumbene can own low-dissipation tunable edge states with good conduction performance despite the topologically trivial behavior.   

Topological States in β-PbO2?

The electronic properties of β-PbO₂, have been controversial for over a century. Experiments find metallic behavior, attributed to its defect structure, to indirect semiconducting for stochiometric samples, with a gap of 0.61 eV. Theory leads to similar ambiguities, and predicts this phase to be metallic (PBE, HSE06) or the opening of too small a bandgap (HSE06). An area where this inconsistency is significant, is when a material property depends on the electronic structure in the vicinity of the Fermi energy, such as topological states. In our work, we use a self-consistent DFT+U approach and find stochiometric β-PbO₂ to be an indirect semiconductor with a band gap of ~0.8 eV, similar to experiment. The larger bandgap requires strains of ~4% to drive β-PbO₂ into a nodal line semimetallic state, which is not protected under the application of spin-orbit-coupling. Moreover, our surface computations do not show any topologically protected states near the Fermi energy. Therefore, our results show that in contrast to previous computations β-PbO₂ is a topologically trivial material, consistent with experiment. Differences to previous work can be attributed to our more accurate description of the optical properties of bulk β-PbO₂.   

Mode-Selective Spontaneous Oscillation of Bandgap in Dirac Wedge Semimetals

This article studies the time-dependent behavior of semimetal Zr₃AgX₃F₂₀ [X=Cd and Hg], M(MoS)₃ and M(MoSe)₃ [M=Li, Na, K, Rb, Tl, In, I] using time-dependent density functional theory. The results show half-occupied Dirac wedge bands. Due to the one-dimensional character, the materials oscillate in a selective mode at a finite temperature. The wedge bands couple to such a phonon mode, resulting in spontaneous oscillation in a rigid period. Especially, the bandgap periodically closes and opens in a large scale, supporting a pulsed current even under a constant biased voltage. Besides, these systems might be long sought time crystals in condensed matters.
  

Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators

Quantum material phases such as Anderson insulator, diffusive metal, Weyl/Dirac semimetal as well as topological insulators show specific wave functions both in real and Fourier spaces. These features are well captured by convolutional neural networks, and the phase diagrams have been obtained, where standard methods are not applicable. One of these examples are the cases of random lattices such as quantum percolation. Here we study the topological insulators with random vacancies, namely the quantum percolation in topological insulators, by analyzing the wave functions via convolutional neural network. The vacancies in topological insulators are especially interesting since peculiar bound states are formed around the vacancies. We show that only a few percent of vacancies derives topological phase transition. The results are confirmed by independent calculations of localization length, density of states, and wave packet dynamics.

Reference:
T. Mano and T. Ohtsuki: arxiv:1910.03194, to appear in J. Phys. Soc. Jpn.   

Predicting Topological Properties of Quantum Materials via Statistical Methods

We discuss the topological phases of correlated and non-correlated (insulating) quantum materials using a statistical method that explores the entire phase space.
Based on model systems we draw fundamental conclusions and discuss the predictive power of this method when applied to real materials.   

Strong-coupling superconductivity and pseudogap in topological flat bands: a quantum Monte Carlo study

We study a two-dimensional model of an isolated narrow topological band at partial filling with local attractive interactions. Exact quantum Monte Carlo calculations show that the ground state is a superconductor with a critical temperature that scales linearly with the interaction strength. We also find a broad pseudogap regime at temperatures above the superconducting phase that exhibits strong pairing fluctuations and a tendency towards electronic phase separation. We discuss the possible relevance of superconductivity in this unusual regime to the Physics of flat band Moiré materials, and as a route to designing higher temperature superconductors.   

Role of van der Waals interactions in topological insulators: bulk, surface and interfaces

It is well-known that van der Waals interactions (vdW) play an important role on structural properties of the prototypical 3D topological insulators Bi₂Se₃ and Bi₂Te₃. However, systematic investigations of different implementations of vdW interactions using density functional theory are lacking. We have performed a comprehensive comparison using both semi-empirical (DFT+D2, DFT+D3, Tkatchenko-Scheffler) and first principles (Langreth-Lundqvist DF, SCAN-rVV10) vdW methods in bulk and surface calculations for these materials, treating structural and electronic properties on equal footing. We find that semi-empirical methods, especially D2 produce structural parameters, electronic dispersion, and the Dirac velocity of the surface state close to the experimental values, while other methods exhibit serious problems when applied to Bi₂Se₃ and Bi₂Te₃. We attribute these differences to the importance of the long range r^-6 tail of the vdW interaction, and we discuss its relevance for the properties of topological interfaces.   

Topological Phases in Hydrogenated Group 13 Monolayers

The topological phases of matters have been a rapid exposed field of research due to its possible applications in spintronics and fault-tolerant quantum computing. Recently, the 2D sheet of gallium (gallenene), a group 13 element, has been synthesized, for which topological properties remain undefined. Using an effective k.p model, symmetry analysis and group theoretical approach with first-principles calculations we studied the topological properties of hydrogenated gallenene (gallenane) and other group 13 elements. Without the inclusion of spin-orbit coupling (SOC) all hydrogenated group-13 sheets that are aluminane, gallenane, indinane and thallinane become nodal line semimetal (NLSM). Interestingly, gallenane under SOC and with 2.6% tensile strain evolves to quantum spin Hall insulator with an energy gap of 28 meV, which makes it promising for room temperature applications. Aluminane preserved its topology even in the presence of SOC due to feeble strength of it. Indinane and thallinane are trivial semimetals under SOC. These findings could offer a new direction in topological research.

J. Phys. Chem. C, 2019, 12342, 25985-25990   

Robust descriptor for high-throughput discovery of alloyed topological insulators based on artificial intelligence

Significant advances have been made in predicting new topological materials using high-throughput empirical descriptors or symmetry-based indicators. To date, these approaches have been applied to materials in existing databases, and are severely limited to systems with well-defined symmetries, leaving a much larger materials space unexplored. Using tetradymites as a prototypical class of examples, we uncover a novel two-dimensional descriptor by applying an artificial intelligence (AI) based approach for fast and reliable identification of the topological characters of a drastically expanded range of materials, without prior determination of their specific symmetries and detailed band structures. By leveraging this descriptor that contains only the atomic number and electronegativity of the constituent species, we have readily scanned over four million alloys in the tetradymite family. Strikingly, nearly two million new topological insulators are identified, revealing a much larger territory of the topological materials world. The present work also attests the increasingly important role of such AI-based approaches in modern materials discovery.