This chapter provides readers who are encountering full quantum effects for the first time, with a comprehensive conceptual understanding of the condensed matter physics problems, and prepares them for further exploration of the intrinsic connection between specific macroscopic phenomena and their underlying microscopic mechanisms. It can introduce, in light-element systems, significant nuclear quantum effects (NQEs) and nonadiabatic effects, including quantum tunneling, quantum fluctuations, zero-point energy, and electron–phonon coupling. These effects have significant influence on the atomic structure (e.g., liquid state of helium), electronic structure (e.g., electron bandgap), thermodynamics (e.g., ultra-low thermal conductivity), optical properties (e.g., absorption spectra and formation of polaron), and quantum paraelectricity. As a prominent example, the superfluid and supersolid in helium systems originate from the NQEs. And nonadiabatic effects affect atomic vibrations (e.g., shift of phonon frequency) and collisions, leading to the breaking and reorganization of chemical bonds. These processes significantly affect ultrafast electron transfer (e.g., novel transfer rate dependence outside Fermi’s golden rule), electron–phonon coupling strength, the formation of charge density waves, phase transition dynamics, Berry phase, and superconductivity.

This chapter focuses on research progress related to full quantum effects in dense hydrogen, hydride compounds, and proton transport through 2D materials and bulk materials where hydrogen does not dominate in content. For dense hydrogen, this chapter describes nuclear quantum effects in high-pressure phase diagram, phase transition, and physical property. For the most common hydride compound, water, this chapter introduces nuclear quantum effects in water hydrogen bond property, water phase diagram, and physical and chemical property of confined water and ice. For other hydride compound, this chapter introduces full quantum effects in hydride superconductivity and nonlinear optical property of mineral hydride. These studies reveal that, full quantum effect not only has significant contribution to existing properties, such as hydrogen bond strength and phase diagram boundary probed by isotope substitution, but also causes novel states and properties, such as room temperature, high-pressure superconductivity of hydrides (e.g., sulfur hydride) and liquid forms of metallic and superconducting hydrogen. After these, this chapter introduces theory of proton tunneling rate, which is important from physical to life sciences. Theory of proton transport in perovskite-type oxides is also illustrated as typical example of nuclear quantum effects on hydrogen conduction in bulk materials. Finally, the chapter introduces work demonstrating importance of proton tunneling in DNA mutation.

This chapter explores, for condensed matter formed by other elements, the novel physical and chemical properties that are dominated by full quantum effects. This includes elementary substances including relatively light elements (e.g., helium (He), lithium (Li), carbon (C), and boron (B)) as well as relatively heavy elements (e.g., oxygen (O) and silicon (Si)), and their compounds. The objects studied include liquid and solid helium, lithium bulk metal and clusters, bulk boron, borophene, boron nitride nanotubes, hexagonal boron nitride, magnesium diboride, diamond, graphene, carbon atoms in organic molecules, strontium titanate, barium ferrite, silicon semiconductors, etc. The related physical and chemical properties include superfluidity, supersolidity, elastic or plastic deformation, heat capacity, high-pressure phase diagram, bonding lengths, diffusion, crystal structure, electron–phonon coupling, bandgap renormalization, thermal expansion coefficient, thermal conductivity, phonon frequency distribution, superconducting temperature and light absorption, etc. Through a variety of fruitful aspects readers would overview the situations where full quantum effect is pronounced and even critical.

In this chapter, we review the basic properties of superconductors, illustrating that they go beyond describing a metal without resistance. We develop London's mesoscopic theory of superconductivity as a quantum mechanical description of the charged superfluid, which accounts for the behavior of the superconductor under electromagnetic fields. Using this theory, we explain the flux quantization for supercurrents flowing in closed loops and derive the energetics of the Josephson junction from the tunneling of Cooper pairs.

Starting from a brief introduction to the Meissner effect and other defining properties of superconductivity, Chapter 1 recapitulates the phenomenological theories, including the two-fluid model and the Ginzburg-Landau theory, and the groundbreaking microscopic theory of Bardeen-Cooper-Schrieffer for describing this macroscopic quantum phenomenon. The Cooper pairing and other basic concepts of superconductivity, such as the gap function, off-diagonal long-range order, quasiparticle excitations, coherence length, penetration depth, type-I and type-II superconductors, and phase fluctuations are also introduced, followed by a summary on the classification and experimental identification for the pairing symmetry of high-Tc superconductors.