中文摘要：

新二维的系统象拓扑的绝缘体(TI ) 和试验性地调查状况的可能性就一十年以前认为异国情调的 graphene 提议的表面那样。这些状况与一个相对论的系列在电子系统包括 chiral 类型的量阶段转变。调停声子(常规) 在出现在 TI 的表面上的迪拉克半金属配对引起转变进 chiral 在这些无差距的系统的超导的状态，和激子冷凝作用长在狭窄乐队的半导体的物理被想象。以本地吸引力或排斥从显微镜的 Dirac Hamiltonian 开始， Gaussian 近似的 Bardeen-Cooper-Schrieffer 类型在功能的积分的框架被开发。由于一种 ultrarelativistic 分散关系，有量，这被显示出管理零温度的转变到一个超导的状态或激子的批评的点压缩了状态。有批评代表的量转变与常规的极大地不同并且属于 chiral 普遍性班。我们讨论这些结果的应用程序到表面超导性在 TI 在被发现并且估计声子配对的可行性的最近的实验。

英文摘要：

New two-dimensional systems such as the surfaces of topological insulators （TIs） and graphene offer the possibility of experimentally investigating situations considered exotic just a decade ago. These situations include the quantum phase transition of the chiral type in electronic systems with a relativistic spectrum. Phonon-mediated （conventional） pairing in the Dirac semimetal appearing on the surface of a TI causes a transition into a chiral superconducting state, and exciton condensation in these gapless systems has long been envisioned in the physics of narrow-band semiconductors. Starting from the microscopic Dirac Hamiltonian with local attraction or repulsion, the Bardeen- Cooper-Schrieffer type of Gaussian approximation is developed in the framework of functional integrals. It is shown that owing to an ultrarelativistic dispersion relation, there is a quantum critical point governing the zero-temperature transition to a superconducting state or the exciton condensed state. Quantum transitions having critical exponents differ greatly from conventional ones and belong to the chiral universality class. We discuss the application of these results to recent experiments in which surface superconductivity was found in TIs and estimate the feasibility of phonon pairing.