First-principles Studies On The Quantum Topological Hall Effect In Layered Alkali Rhodates

With the rapid development of the information age,the performance of traditional electronic devices is unable to meet people's increasing production and life needs,and the development of higher-performance devices has become an urgent problem to be solved.The quantum anomalous Hall effect?QAHE?has non-trivial topological prop-erties and dissipationless chiral conducting edge states.Therefore,it has not only at-tracted attention in the field of basic physics research,but also hopefully has practical applications in the fields of spintronic devices,low-dissipation devices,and even quan-tum computing.Although experimentally the QAHE has been observed in magnetically doped?Bi,Sb?₂Te₃,but its working temperature is too low and the material system is not rich enough.Therefore,it is very important to find more and better materials which possess QAHE.In this thesis,first-principles calculations are performed on the electronic and topo-logical properties of the layered alkali rhodates A_0.5Rh O₂?A=Li,Na,K,Rb,Cs?.We found that these materials have a special QAHE,called quantum topological Hall effect?QTHE?.This kind of QAHE does not require spin-orbit coupling and ferromagnetism in materials but entirely comes from the scalar spin chirality caused by the non-coplanar antiferromagnetic structure.So it is a new kind of quantum Hall effect.The main con-tents and results are as follows:?1?The electronic properties of K_0.5Rh O₂are mainly determined by the Rh O₂layer and the alkali layer mainly plays a role in adjusting the Fermi energy.By analysing the valence of Rh ions,it is shown that when x=1,the Rh's a_1gorbitals are fully occupied,so the stoichiometric ARh O₂is a semiconductor.When x=0.5,the Rh's a_1gorbitals are only 3/4 partially filled.Thus,they should be metals if the magnetism is not considered.However,the unit cell will be possibly enlarged due to the magnetic structures and thus these materials may still open bandgaps.?2?We carefully calculated the magnetic structures of A_0.5Rh O₂and found that the all-in/all-out non-coplanar antiferromagnetism is not only stable but also has the lowest energy.Thus it is the ground state of A_0.5Rh O₂.By calculating the band struc-tures and anomalous Hall conductivities?AHC?of the non-coplanar antiferromagnetic A_0.5Rh O₂,we find that except for the semi-metallic Rb_0.5Rh O₂,all the other materials Li_0.5Rh O₂,Na_0.5Rh O₂,K_0.5Rh O₂,and Cs_0.5Rh O₂not only open bandgaps that increase as the lattice constant c increase,but also have quantized AHC in their bandgaps,indi-cating they all have QAHE.This QAHE does not come from the spin-orbit coupling or ferromagnetism,but the spin chirality caused by the non-coplanar antiferromagnetism.Thus it is called the QTHE.?3?We calculated the Berry curvature and surface states of A_0.5Rh O₂.It was found that the Berry curvature mainly concentrated at the K and H points in Brillouin zone and the number of topological surface states is the same as the Chern number of the material.In particular,the direction of the surface state is related to the spin chirality in the Rh O₂layer.If the spin chirality of the non-coplanar antiferromagnetic structure in each Rh O₂can be controlled,then different kinds of helical surface states can be constructed.In summary,we have systematically studied the electronic structures and QTHE of A_0.5Rh O₂?A=Li,Na,K,Rb,Cs?materials,determined that the all-in/all-out non-coplanar antiferromagnetic structure is their ground magnetic state,and further studied their QTHE caused by this special non-coplanar antiferromagnetism.Our work could deepen the understanding of the physical mechanism of the topological Hall effect and provides new ideas for finding novel quantum anomalous Hall materials.