Efficient Topological Materials Discovery Using Symmetry-Indicators

As a mathematical concept topology is used for describing the invariant properties of an object undergoing continuous deformation.In the context of quantum Hall effect of 2D free electron gas under a strong magnetic field,condensed matter physicists introduced topology to physics by relating the robust Hall conductivity with the first-class Chern number(which can take any integer).Especially,topological physics has undergone flourishing developments since 2005 when people proposed time-reversal symmetry protected quantum spin Hall effect(or synonymously,2D topological insulator),whose topological index can take 0 or 1,i.e.a Z2 invariant.Soon after that,topological insulator was generalized to 3D.Considering fruitful spatial symmetries in crystals,various topological crystalline insulating phases were also proposed,such as mirror Chern insulator,Hourglass topological crystalline insulator,high-order topological insulator etc.Other than insulators,metals can also host nontrivial band topology,starting from Weyl semimetal,also including Dirac semimetal,nodal-line semimetal,Hopf-link semimetal etc.Weyl points in Weyl semimetal are not protected by any symmetry while the band crossings in other types of topological semimetals require protection of spatial symmetries.Symmetry not only can protect some topological phase,it can also give implication for some topological phase protected by other symmetry,Fu-Kane parity criterion for centrosymmetric topological insulator being a famous example:according to the symmetry information of inversion eigenvalues at inversion-invariant momenta,one can obtain the Z2 topological invariant(s)quickly.Similarly,one can also exploit other symmetry information to calculate some topological invariant quickly,applicable for insulators.Based on the mismatch between real and reciprocal spaces for all the 230 space groups,a Fu-Kane-like theory,called symmetry-indicator theory gives a complete classification of band topology for electrons based on the symmetry information.Based on the symmetry-indicator theory,we develop a new and efficient algorithm of discovering topological materials by first-principles calculations starting from the atomic insulator basis for each space group.This new algorithm need not pre-assume any targeted kind of topological phase and can uncover all the nontrivial topological materials from symmetry properties including topological(crystalline)insulator and semimetal in one sweep.We apply this algorithm to a database search with thousands of topological materials discovered.This thesis is mainly focused on using symmetry-indicator to diagnose band topology and search for topological material efficiently,including:1.After introducing the symmetry-indicator theory in brief,we demonstrate our algorithm of topological materials discovery using the atomic insulator basis as an anchor in detail2.Because of the high efficiency of our algorithm which could uncover all band topology indicated by symmetry,it is suitable for materials search in a large scale.We thus make a database search for topological materials(firstly we filter out those inappropriate materials,e.g.containing magnetic or radioactive elements,or nonstoichiometric),finding thousands of candidates,providing a fruitful flatform for further theoretical or experimental study in future.This result shows that the topological material are actually ubiquitous in nature.3.In systems with strong Z4symmetry-indicator group,through a further analysis,we find that MoTe2 crystallizing in space group 11,can realize screw-protected ID hinge states and BiBr within space group 12 can realize rotation anomaly.They are verified by later works.4.For systems with strong Z2 symmetry-indicator group,they don't own an inversion center.Although Fu-Kane criterion is not applicable,our method,alternatively,predicts that AgNaO in space group 216,is a strong topological insulator.5.In systems with large-order strong symmetry indicator group including Z8 and Z12,we not only find that many well-known materials,such as superconductor MgB2,graphite etc.are topologically nontrivial discovered by our study.We also find many other topological crystalline insulators for this kind and choose graphite,Pt3Ge,PbPt3,Au4Ti and Ti2Sn to give a detailed analysis.All in all,this thesis provides a newly-developed topological materials discovery algorithm.Compared with conventional algorithm,it is not only highly-efficient,but can also uncover any possible band topology indicated by symmetry.Our algorithm can be generalized to 2D systems,magnetic materials,or even bosonic systems,and is expected to promote topological materials to be applied to devices soon.