Weyl Semimetals In Correlated Electronic Materials

Topological materials have been studied for many years.From topological insulators and topological semimetals,the gapless surface state is the most impor-tant ferture for them.The bulk states in topological insulators are gapped,but in topological semimetals there are some gapless nodes or lines in bulk states.The topological semimetals discovered in experiments include Dirac semimetals,Weyl semimetals,Nodal-line semimetals and the three-fold degeneracy”New fermion”semimetals.In this thesis,we have studied the properties of Weyl semimetals in ferroelectric and ferromagnetic materials,based on first principle calculations.We have also proposed the exist of heavy Weyl fermion states in a heavy fermion systerm.Firstly,based on first-principles calculations and effective model analysis,we propose that a noncentrosymmetric material YCoC₂is a topological semimetal.In the absence of spin-orbit coupling?SOC?,it can host two intersecting nodal loops protected by two mirror planes.In the presence of SOC,one nodal loop is gapped totally while the other one evolves into ten pairs?three nonequivalent positions?of Weyl points,with two pairs of type-I and eight pairs of type-II Weyl nodes.Fermi arc surface states are observed on surface projected dispersions.This material was reported as a superconductor with a critical temperature of T_c=4.2 K,and if so,it will provide a convenient platform to explore topological superconductivity hosting exotic Majorana states and may be used in topological quantum computers.Secondly,by using first-principles calculations,we demonstrate that the ex-perimentally synthesized nonmagnetic HgPbO₃is a unique Weyl ferroelectric semimetal.Its centrosymmetric R?3c phase will undergo a ferroelectric phase tran-sition to the ferroelectric R3c structure.Both phases are semimetallic and the ferroelectric phase owns a spontaneous polarization.Our further study proposed that the R3c phase is a trival semimetal and the R?3c phase is a Weyl semimetal,which hosts six pairs of Weyl nodes near the Fermi surface.In nice agreement with theoretical prediction,our neutron diffraction measurements and CBED ex-periments further revealed the ferroelectric phase transition.The coexistence of ferroelectricity and Weyl nodes in HgPbO₃is an ideal platform for exploring mul-tiphase interaction and mutual control for potential applications of integrated topotronic and ferroelectric devices.The origin of anomalous Hall effect?AHE?in magnetic materials is one of the most intriguing aspect in condensed matter physics and has been a controversial for a long time.Recent studies indicate that the intrinsic AHE is closely related to the Berry curvature of occupied electronic states.In a magnetic Weyl semimetal with broken time-reversal symmetry,there are significant contributions to Berry curvature around Weyl nodes,which would lead to a large intrinsic AHE.Here,we report the measurements of quite large AHE in the half-metallic ferromagnet Co₃Sn₂S₂single crystal.By systematically mapping out the electronic structure of Co₃Sn₂S₂both theoretically and experimentally,we demonstrate that the intrinsic AHE from the Weyl fermions near the Fermi energy is dominating.The intrinsic anomalous Hall conductivity depends linearly on the magnetization and can be reproduced by theoretical simulation,in which the Weyl nodes monotonically move with the constrained magnetic moment on Co atom.The theory and first-principle calculations of weak correlated topological ma-terials have been devolopped quite completed.Because of the abundant interest-ing physical properties,more and more attentions have been moved to strongly correlated materials.In this work,we have studied the topological properties of heavy fermion systerm of CeRu₄Sn₆by LDA+Gutzwiller method.Considering the strong interaction of 4f orbitals of Ce,we obtained the qusipartical band structure and the many-body configurations from LDA+Gutzwiller calculations.Compared to the GGA band structure,there are two major corrections caused by the strong correlation effects.Firstly,the total bandwidth of the 4f bands have been suppressed by approximately two times.Secondly and more importantly for this particular material,the splitting among the 4f-orbitals has been greatly en-hanced leading to two direct consequences,the bands with|J=5/2;J_z=±1/2>character are pushed down to mix strongly with the 4d bands from the Ru atoms and at meanwhile the bands with|J=7/2>character are pushed up to about1.2 eV above the Fermi level.Due to the lack of inversion centre,there may exist Weyl points near the band invertion.We have found eight pairs of Weyl nodes in the whole Brillouin zone by using Wilson-loop method.From the calculations of?010?surface states,the long fermi arc can be easily indentified.Comparing to the topological semimetals found in weakly correlated materials,the properties of the heavy Weyl fermion state introduced here are much sensitive to the external fields that can modify the effective valence of Cerium,which provide great tunability in this system and make it a promising material platform for follow-up studies on the relationship between correlation and topology.