Study Of Chiral(d+id) Superconductivity In The Two-dimensional Correlated Electron System

Unconventional superconductivity is the frontier research topic in condensed matter physics.In recent years,superconductivity and magnetism of low-dimensional correlated electron systems have been attracting extensive attention,of which the two-dimensional correlated electron system is one of the current hot topics.Based on the two-dimensional honeycomb lattice,we systematically studied the superconductivity and magnetism of such a kind of correlated electron system using numerical exact diagonalization and constrained-path quantum Monte Carlo method.This thesis can be divided into three parts.In the first part,we study the superconductivity and magnetism in the ionic monolayer honeycomb lattice by using the constrained-path quantum Monte Carlo method.We investigate the dependencies of various electron pairing correlation functions on the lattice-site potentials.Our results show that electrons initially lie in the d+ id paired state when the electron filling is close to half filling.As the lattice-site potential increases,the d+ id electron pairing function turns to decrease,and when the lattice-site potential increases to a certain value,the system evolves into a f wave pairing state.On the lattices with different sizes,our results are consistent,indicating that the system has the superconducting phase transition in the thermodynamic limit.In addition,we also find that the electron pairing correlation function takes a maximum value when the electron filling is near n=1.1.In the second part of the thesis,we study the superconducting characteristics of inhomogeneous double-layer honeycomb lattice by combining the numerical exact diagonalization and constrained-path quantum Monte Carlo method.The results of numerical exact diagonalization show that the electron binding energy changes from zero to negative with the increase of the interlayer Coulomb interaction V when the on-site Coulomb interaction U is close to zero,indicating that V can cause the electron pairing state.When the V value is fixed,the electron binding energy gradually changes to positive with the increase of U.The computed results of the constrained-path quantum Monte Carlo method show that the chiral d+ id pairing correlation function increases sharply with the increase of V when U is close to zero.However,the increasing trend of chiral d+ id pairing correlation function is significantly suppressed with the increase of U.The results of the two kinds of computational methods illustrate that the interlayer Coulomb interaction V is helpful for the formation of chiral superconductivity under the weak on-site Coulomb interaction.The third part is motivated by Steven A.Kivelson et al.'s research work on the checkerboard Hubbard model.We use the constrained-path quantum Monte Carlo method to systematically explore the chiral superconductivity in monolayer inhomogeneous honeycomb lattice.Our results indicate that when the inhomogeneity of the system(represented by the ratio of the hopping integrals within and between honeycombs)increases,the chiral d+ id pairing correlation function increases gradually,while when the inhomogeneity is increased to a certain value,the pairing correlation function turns to decrease.The results indicate that there exists an optimal inhomogeneity,which optimizes the chiral d+ id superconductivity.Further analysis shows that magnetism is not responsible for the inhomogeneity-dependent superconductivity.In terms of the changes of the density of states at the Fermi level and the effective on-site interaction as a function of inhomogeneity,we offer a reasonable explanation for the inhomogeneity-dependent superconductivity.This part of study provides a route for quantum control of chiral d+ id superconductivity.