【作者】 李伟；

【导师】 程耕； 刘国柱；

【作者基本信息】 中国科学技术大学 ， 理论物理， 2010， 博士

【摘要】 高温超导和石墨烯是凝聚态物理中受到广泛、深入研究的两个强关联体系,其共同特点是低能元激发是无质量的狄拉克费米子,满足相对论性的狄拉克方程,可用(2+1)维量子场论模型来描述。其中高温超导的低能有效理论是(2+1)维量子电动力学,而石墨烯体系中狄拉克费米子之间存在库仑相互作用。QED3中的动力学手征对称破缺(DCSB)已经被研究超过二十年,而在石墨烯中的研究也已经持续了接近十年。这些研究不仅有助于加深对量子色动力学(QCD)中的DCSB的理解,而且也可以用于广泛理解高温超导和石墨烯中的许多重要物理现象。本论文通过对规范相互作用和库仑相互作用导致的动力学手征对称破缺的讨论,研究了高温超导和石墨烯中的手征量子相变,以及该相变对体系低能物理行为的影响。DCSB可以看作由相互作用导致的费米子-反费米子配对机制。研究表明,当狄拉克费米子之间的相互作用足够强时,狄拉克费米子会通过真空凝聚而获得有限的质量,并同时破坏体系原来的手征对称性。通过对Dyson-Schwinger (DS)方程详细地理论分析和计算,我们确定了在高温超导和石墨烯中DCSB发生的条件,指出规范和库仑相互作用的长程性在DCSB的发生中起关键作用,并将所得结果用于讨论DCSB的物理效应。经过具体计算,我们发现,温度、化学势和杂质散射以及规范场质量等因素都会破坏相互作用的长程性,降低动力学费米子质量生成的可能性,既降低费米子临界味数Nc,也会减小动力学质量m。此外,为了更好地理解石墨烯中手征相变带来的物理效应,我们具体计算了半金属和绝缘体两个相中的比热和磁化率。我们发现,在半金属相中,库仑相互作用会导致比热和磁化率的非费米液体行为；而在绝缘体相中,由于费米子激发具有有限能隙,比热和磁化率被大大压制。可见,比热和磁化率能够很好地区分半金属和绝缘体两个相,这为实验上寻找手征相变提供重要信息。通过这些物理量与实验结果的比较,可以加深对手征相变的物理效应的理解。更多还原

【Abstract】 High temperature superconductor (HTSC) and graphene are two strongly cor-related electron systems those have attracted great research interests in recent years. They share one common feature that the low-energy elementary excitations are mass-less Dirac fermions, arising from the special band structures. These Dirac fermions satisfy relativistic Dirac wave equation and can be described by three-dimensional quantum field theory. The dynamical chiral symmetry breaking caused by gauge field and Coulomb interaction, which can describe the low-energy physics of high tempera-ture superconductor and graphene respectively. The theory describing the low-energy physics of of HTSC is (2+1)-dimension QED(QED3), while that is Coulomb inter-action for the Dirac fermions in graphene. The dynamic chiral symmetry breaking (DCSB) in QED3 has been investigated intensively for more than twenty years and about decade for that in graphene, On the one hand, these investigations may help to gain deeper understanding of DCSB in QCD. On the other hand, this non-perturbative phenomenon can be widely used to understand many important physical phenomena in HTSC and graphene.In this thesis, the chiral quantum phase transition and the consequent effects on low-energy physics of system are studied by discussing on the DCSB driven by gauge field and Coulomb interaction in HTSC and graphene, respectively. The DCSB is realized by forming fermion-anti-fermion pairs mediated by strong gauge (Coulomb) interaction. Research shows that when the interaction between Dirac fermions is strong enough, the Dirac fermions will acquire finite dynamic mass by vacuum condensations and break the original chiral symmetry contemporarily. Through the theoretical anal-ysis and calculation of the Dyson-Schwinger (DS) equation, we have identified the conditions of the occurrence of DCSB in the HTSC and the graphene, pointed out that the long-range nature of gauge (Coulomb) interaction play a key role in DCSB. The results are also used to discuss the physical effects induced by DCSB. After the specific calculations, we found that temperature, chemical potential, impurity scattering even the mass of gauge field will make the interaction become short-ranged and prevent the generation of dynamic mass, then reduce the fermion critical flavor number Nc and dynamical mass m.Furthermore, in order to get a better understanding of the physical effects induced by chiral phase transition in graphene, we calculate the specific heat and susceptibil-ity of the system and show that they exhibit distinct behaviors in the semimetal and insulator phases. In the semimetal phase, the Coulomb interaction will lead to non-Fermi liquid behavior of specific heat and susceptibility; while in the insulating phase, the specific heat and susceptibility are strongly suppressed because of finite gap of fermion excitations. Apparently, both specific heat and susceptibility manifest quite different behaviors in these two phases and can distinguish them clearly, which pro-vides important information on experiment research on chiral phase transition. These quantities can be compared with experimental results and hence may help to understand the physical consequence of chiral phase transition.更多还原