The First Principles Calculations Of Strongly Correlated Materials

Strongly correlated electronic systems are often element or compounds consist-ing of d or f-local orbital electrons.In such a system,due to the coupling of multiple degrees of freedom,such as degrees of multi-orbitals,spin-orbit coupling caused by relativistic effects,crystal field effects,etc.,the system often exhibit many complex and novel properties.The most common examples are the colossal magnetoresistance ef-fect,the heavy fermion phenomenon and unconventional superconductivity.Many of these novel quantum states,such as the local-itinerant duality in heavy fermion mate-rials and the pairing mechanism of electrons in unconventional superconductors,have not been well studied.On the one hand,due to the large Coulomb interaction between electrons,often compared with the kinetic energy,the traditional perturbation theory in theoretical approach has encountered great challenges.On the other hand,we should consider the multi-orbitals,Coulomb interaction and temperature effects in numerical calculations.Not only the conventional energy band theory facing severe problems,but also most of strongly correlated numerical calculation methods themselves have many limitations due to the large amount of calculation.At the end of the 20th century,the dynamical mean field theory began to develop.Compared with the single electron approximation in the traditional energy band theory,the dynamical mean field theory takes into account the orbital degree of freedom and can handle many body states.Thus,it was the first to succeeded in Mott metal-insulation transition.However,the early study of dynamical mean field theory was limited to few theoretical models.If the method is to be applied to a rich set of specific materials,the most straightforward idea is to combine the density functional theory of first-principles calculations with the dynamical mean field theory.This thesis introduces the related theory of density functional theory and dynamical mean field method,and applies it to the actual material calculations of strongly correlated electronic systems to explore its physical properties.In this thesis,we have studied several typical strongly correlated materials.The first one is the Mn-based unconventional superconductor Mn P,because of the non-collinear magnetic order of this system and the superconductivity emerging at the edge of non-collinear magnetic order at high pressure.Therefore,the non-collinear magnetic fluctuation may relate to the superconducting pairing symmetry.We studied the mag-netic ground state of the system and the magnetic transition under pressure.We found the magnetic transition consistent with the experiment and explained the mechanism of magnetic phase transition by magnetic interaction with the change of crystal struc-ture.We also studied the electronic structure and transport properties of this material and found two types of Fermi surfaces with quasi-one and quasi-three dimensionality,corresponding to carriers with very different lifetime measured by optical conductiv-ity,respectively.The long lifetime carriers correspond to the quasi-three dimensional Fermi surface,contributing to the transport properties and the short lifetime carriers cor-respond to the quasi-one dimensional Fermi surface,contributing to the magnetic prop-erties.The two-fluid like behavior provides a theoretical basis for the superconducting pairing.Secondly,we studied the heavy fermion spin triplet superconducting material UTe₂.Through magnetic calculation,we found that the system is a two-leg ladder sys-tem coupled by magnetic interaction.From the calculation from electronic structure,it is found that there are two quasi-two dimensional Fermi surfaces in the system.The formation of quasi-two dimensional Fermi surfaces may be related to the structure of ladder type.Finally,we analyze the superconducting energy gap nodal structure as point nodes from the symmetry of the material and it is a topologically trivial superconductor.