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Introduction

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Electronic States in Crystals of Finite Size

Part of the book series: Springer Tracts in Modern Physics ((STMP,volume 270))

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Abstract

The theory of electronic states in crystals is the very basis of modern solid-state physics. In conventional solid-state physics, the theory of electronic states is essentially a theory of electronic states in crystals of infinite size where all electronic states are progressive Bloch waves. A fundamental difficulty of such theory is that any real crystal always has a finite size, and the electronic states in a simple crystal of finite size have not been well understood. The theory of electronic states in conventional solid-state physics cannot treat the boundary effects and the size effects of the finite crystals. The effective mass approximation (EMA) previously used in treating finite crystals is based on the understandings of quantum confinement of plane waves. Some numerical results clearly indicated that EMA might be qualitatively incorrect: The quantum confinement of Bloch waves might be fundamentally different from the quantum confinement of plane waves. The chapter is concluded with a brief introduction to the subject and main findings of the book.

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Notes

  1. 1.

    By including the relativistic effect, (1.13) can be further extended to

    $$\begin{aligned} E^2_j = m^2 c^4 + j^2 \hbar ^2 c^2 \left( \frac{\pi }{L} \right) ^2, \end{aligned}$$

    where c is the speed of light [28].

  2. 2.

    In this book, a position vector is usually written as \({\mathbf {x}}= x_1 {\mathbf {a}}_1 + x_2 {\mathbf {a}}_2 + x_3 {\mathbf {a}}_3\). For quantum films, it is usually assumed that \({\mathbf {a}}_3\) is the only primitive lattice vector out of the film plane.

  3. 3.

    The edge-like states were named side-like states in the first edition.

  4. 4.

    The vertex-like states were named corner-like states in the first edition.

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  1. School of Physics, Peking University, Beijing, P. R. China

    Shang Yuan Ren

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Ren, S.Y. (2017). Introduction. In: Electronic States in Crystals of Finite Size. Springer Tracts in Modern Physics, vol 270. Springer, Singapore. https://doi.org/10.1007/978-981-10-4718-3_1

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  • DOI: https://doi.org/10.1007/978-981-10-4718-3_1

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