高温超导体(HTC)因其具有高于液态氮沸点（77K）的超导转变温度以及新奇丰富的物理相图，成为了当今凝聚态物理学界最有趣也是最具有挑战性的一大课题，而对于欠掺杂样品，在其超导转变温度之上的赝能隙行为被普遍认为是高温超导的一大核心问题。本文在简要介绍完高温超导材料的化学结构、基本相图及其非BCS性质后，着重从输运性质(包括直流电阻率、光电导率、能斯特效应)、热学性质(比热容)、核磁共振(NMR，包括均匀磁化率、晶格-核自旋弛豫率)、非弹性中子散射(INS)、 扫描隧道谱(STS)、角分辨光电子谱(ARPES)和拉曼光谱(Raman)等方面介绍和讨论了一下赝能隙现象。尔后在简要介绍$t$-$J$ 模型及其不同掺杂情况下的平均场理论及波函数后讨论了一下其符号结构。本文研究正是以$t$-$J$模型及其符号结构作为出发点，给出了该模型的超导基态波函数假设[New Journal of Physics {\bf 13}, 103039 (2011)]；我们在这个超导基态波函数假设中关掉了其超导非对角元长程序，便得到了所谓的低温赝能隙态。在非高斯型的超导涨落下，得到的态在自旋自由度和电荷自由度中均表现出了系统的赝能隙行为，显著地体现在了自旋均匀磁化率、比热容、非Drude电阻率、能斯特效应、以及与在强磁场中出现的小费米口袋所对应的量子振荡现象等等。这些反常的`正常态'性质都与铜氧化合物中实验上观察到的定性上一致。特别是，这样一个模型研究建立起奇特的赝能隙性质与超导基态的非BCS本质之间的本征联系。
The High-Temperature superconductor (HTC) becomes one of the most interesting and most ambitious problems in condensed matter physics, because of its transition temperature which is higher than the boiling point of liquefied nitrogen (77K) and its fantastic phase diagram. For underdoped samples, their pseudogap behavior above the transition temperature is considered as a core problem of HTC. In this thesis，after a short introduction on the chemical structure, basic phase diagram and its non-BCS properties of HTC, we will mainly introduce and discuss the pseudogap phenomenon from transport properties (include DC resistivity, optical conductivity, Nernst effect), thermal property (specific heat), nuclear magnetic resonance(NMR, include uniform susceptibility and lattice-nuclear spin relaxation rate), inelastic neutron scattering (INS), Scanning Tunneling Spectrum (STS), angle-resolved photoelectron spectroscopy (ARPES) and Ramam scattering, etc. Then after a short introduction on $t$-$J$ model and its mean-field theory and wave function solutions on different doping cases, we will discuss its sign structure. This thesis just starts from $t$-$J$ model and its sign structure, then presents the corresponding superconducting ground state wave function ansatz [New Journal of Physics {\bf 13}, 103039 (2011)]; we explore a so-called low-temperature pseudogap state by turning off the superconducting off diagonal long range order in this ansatz. With non-Gaussian superconducting fluctuations, the resulting state exhibits a systematic pseudogap behavior in both spin and charge degrees of freedom, manifested in the uniform spin susceptibility, specific heat, non-Drude resistivity, Nernst effect, as well as the quantum oscillation associated with small Fermi pockets emerging in strong magnetic fields, etc. These anomalous `normal state' properties are found in qualitative consistency with experimental measurements in the cuprates. In particular, such a model study establishes an intrinsic connection between the peculiar pseudogap properties and the non-BCS nature of the superconducting ground state.
