Electronic Orders Near The Type-Ⅱ Van Hove Singularity In BC₃

Researching on superconductivity is an important field in condensed matter physics.Currently,physicists,on one the hand,are searching for superconductors with higher transition temperature;one the other hand,they are taking great efforts to study the microscopic pairing mechanism and pairing symmetry.For the conventional supercon-ductors,the traditional Bardeen-Cooper-Schrieffer(BCS)theory is well adopted.Since the 1980s,a series of superconductors,such as cuprate superconductors,iron-based su-perconductors occurred.They can not be understood by the conventional BCS theory so that they are called unconventional superconductors.The unconventional properties includes high superconducting temperature beyond McMillan limit,different pairing symmetry from s-wave pairing,correlation with magnetism and so on.In this dissertation,we investigate the electron instability in the single-sheet BC3 when the electron filling is near a type-Ⅱ van Hove singularity using the functional renormalization group.Type-II van Hove momenta are not time-reversal invariant so that equal-spin pairing on such momenta is not forbidden by Pauli exclusion princi-ple.Besides,because of the proximity to the van Hove singularity,there are strong ferromagnetic fluctuations at low energy.This may either lead to ferromagnetic or-der,or trigger triplet pairing.Based on our results,we can give the following con-clusions.For a finite Hubbard interaction of BC3,the ferromagnetic-like spin density wave order dominates in the immediate vicinity of the singularity.Elsewhere near the singularity the p-wave superconductivity prevails.We also find that a small nearest-neighbor Coulomb repulsion can enhance the superconductivity.Our results show that BC3 would be a promising candidate to realize topological p + ip’ superconductivity,but the transition temperature is practically sizable only if the local interaction is mod-erately strong.The Majorana modes in the vortices of odd-parity superconductors can be used in quantum computation,in this sence,we believe it is worth putting efforts on the research of BC3.In the introduction part,we give a brief introduction to the relations among topo-logical superconductor,Majorana fermions,and superconductivity with odd parity.Then,we offer several examples to illustrate the experimental development on intrinsic topological superconductors.In the second chapter,after showing the structure and the band of BC3,we review the previous work on the superconductivity of this material.In the third chapter,we,firstly,introduce the generator functional and flow equation of the general functional renormalization group(FRG)method,and next,give a detailed description of singular-mode FRG which we used in our research.In the forth chapter,we display our main results,including electron order and the symmetry of supercon-ducting gap function with different doping,the phase diagram in the space of(n,U),and the transition temperature in different situations.Finally,in the fifth chapter,we provide a necessary summary of this thesis.