Constrained-Path Quantum Monte Carlo Study On The Charge,Magnetic And Superconducting Properties In Two-dimensional Layered Unconventional Superconductors

Two-dimensional layered unconventional superconductor is one of the hottest topics in modern condensed-matter physics.Classical superconducting systems include copper-based high-temperature superconductors,iron-based high-temperature superconductors,and the recently discovered twisted-bilayer graphene.One of the common feature of these systems lie in their phase diagram,where magnetic order,charge order and supercon-ducting order demonstrates close relations.It is widely believed that understanding these complex electric states and their correlations has significant meaning.The correlations among magnetic order,charge order,and superconducting order in multi-orbital Hubbard model for copper-based,iron-based and bilayer graphene systems have been systemtically studied in this thesis by using constrained-path quantum Monte-Carlo method.The main works are as follows:Based on the three-band Hubbard model with the newly introduced off-site nematic interaction,we investigated the impact of charge-nemetic fluctuations on d-wave pairing correlations for copper-based high-temperature superconductors.Our numerical result-s suggested that for different charge-transfer energy(e.g.,the on-site energy difference between copper and oxygen atoms),positive and negative nearest on-site nematic inter-action enhanced the charge-nemetic fluctuation near(0,0)and(?,?)respectively.Be-sides,positive(negative)off-site nematic interaction enhanced(suppressed)the spin-spin correlation neart(?,?),while long-range d-wave hole-hole correlations and its vertex con-tribution were strongly suppressed by off-site nematic interaction.These results clearly demonstrated the competitive relation between the nematic and superconducting orders in copper-based superconductors.To further explore and understand the relations between nematic and superconducting states,we also introduced a four-band Hubbard model to check the impacts of different types of Coulomb interactions on nematic and supercon-ducting states.It was shown that the interaction related with Copper d3z2-r2 tends to enhance electric nematic phase and suppress d-wave hole-hole correlations.which confirms the competition between nematic and superconducting orders.Based on the two-orbital Hubbard model for iron-based superconductors,we intro-duced the on-site and off-site nematic interactions to study the relations between nematic fluctuations and superconducting orders.Our numerical results showed that on-site ne-matic fluctuation strongly enhanced all the nematic fluctuation in whole Brillouin zone,especially the(?,?)point.The dominant pairings,such as s±and d wave pairings,were suppressed by on-site nematic fluctuations.By controlling on-site and off-site nematic interactions,we found that the dominant paring correlations increases/decreases upon the nematic fluctuation on(0,0)/(?,?).Our results show that nematic fluctuations at different momentum point has different impacts on superconducting states for iron-based superconductors.Based on the two-orbital Hubbard model for twisted bilayer graphene-we mainly studied the magnetic and superconducting properties.Our numerical simulations reveal that the long-range magnetic order develops for U?3.2t at haf filling when only the on site Hubbard U is considered.Upon doping away from half filling,the analysis based on the pairing correlations and corresponding vertex contributions identifies that pairing with the d+id symmetry is the dominant pairing channel.As the on-site Coulomb inter-action is increased,both spin correlation and effective pairing interaction are enhanced simultaneously,indicating the intimate relation between magnetism and superconductiv-ity.An inclusion of nearest neighbor Coulomb interaction V results in a suppression of the d+id superconductivity,but it can survive in the small V regime.Based on half-filled Hubbard model,we also studied the AA-stacked graphene.Our results showed a dominant chiral d+id wave superconductivity,which is triggered by a perpendicular electric filed.At a fixed electric filed,the effective pairing interaction of chiral d+id superconductivity exhibits an increasing behavior with increasing on-site Coulomb interaction.We attribute the electric filed induced d+id superconductivity to an increased density of states near the Fermi energy and robust antiferromagnetic spin correlation upon turning on electric filed.Our results strongly suggest that the AA-stacked graphene system is a good candidate for chiral d+id superconductor.To conclude,this thesis systematically studied the correlations among magnetic/charge orders and superconducting orders for various hot unconventional superconductors and of-fered useful references on the theoretical analysis on the relation between superconducting orders and magnetic/charge orders.In addition,it has important reference significance in the thesis to regulating the quantum fluctuations of the correlated electronic system.