Solid State Physics

Solid State Physics

Introduction

What is solid state physics? The definition is impossible. Bridgman: “Science is what scientists do.” Two main parts: Anderson divides physics into “Big Science” and “Minor Physics” or “Great Science.” “Big Science” - cosmology, elementary particle physics.

Condensed matter physics and photonics: soft matter, polymer physics.

Condensed matter: Solid state physics Physics of fluids Polymers are included

Transition: discovered in solid state physics: idea, lasers, computers, memory (SSD), internet, telecommunications, huge change in the society -> (“great science” = prepared wave).

Solid state physics: all solid bodies. What is a solid body? A solid body has a proper volume and a proper shape. This is true within some temperature interval (T macroscopic properties. Conceptual construction: 1) reductionism (modern approach to condensed matter physics). 2) constructionism (after 1926 (Schrödinger equation)).

Isolate a number of elementary particles by which the systems are made. ~ quantum ~ mechanical description of the systems. We will limit only to crystals (ordered solids at the atomic scale).

1) reductionism: to become predictive, we need the easiest possible model. The number of elementary entities should be quite small, and electrons ..., ordered sequence of nuclei + “cloud” of electrons.

+ e.g. We do not distinguish between core electrons and valence or conduction electrons: → good -> lattice ions and valence/conduction electrons (“lettf mode”). Tightly bound electrons that behave like atomic core electrons event if we are in a crystal → valence/conduction electrons in the crystal continuously. They were the outmost electrons in the “isolated atom.”

Find the equilibrium position of the lattice ions and the behaviour of the valence electrons can, electronic band structure of crystals &arr;

2) constructionism: pay attention that constructionism doesn't work always (interactions between electrons and nuclei must not be overlooked and very strong for examples). The property of the entire system is not simply the sum of the properties of the individual parts. For example, superconductivity cannot be explained with a simple reduction of the system to lattice ions and valence electrons.

Introduction of quasiparticles: a way to reduce the intensity of interactions and find how they work and not strong in reality. A quasi-electrons, phonons ~ allow constructionism.

Enclose entire single particle that explains the collective behaviour of the electrons. For example:

Thermal vibrations

We have to take into account them for a finite temperature. Instead of vibrations, we use normal coordinate (an acoustic normal atomic phonons).

Phonon position vibration = diffusion and electron = electron phonon interactions. In perfect crystals, the electrical conductivity would be infinite because there are not electron-phonon coupling (nor equip).

We can classify properties into thermodynamic properties, optic properties (dynamic) and transport properties.

1. Thermodynamic properties: Average value of a quantity is constant (response to small fluctuations). → thermodynamic equilibrium (usual fluctuations negligible). All state functions are a function of temperature (specific heat, ... thermal dilation, melting T, elastic constants, ...).

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Energy quantization → quantum effect

2. Optic properties: of semiconductors and metals
3. Transport properties: external perturbation → temperature gradient, electric field → out-of-equilibrium phenomena.

Electrical conductivity of metals

Thermal conductivity of insulator

Single atom: confined states in very small volume → discrete eigen. Electronic levels in molecules

Many nuclei: higher and higher states → no more bound electrons because they both discrete and almost continuous levels of the stationary electronic states → energy bands → properties of crystals (periodicity, phonon -> phonon energy gaps). All depends on the number of electrons and on the distance between electrons. From this point of view crystals can be classified:

• Metals
• Covalent crystals
• Ionic crystals
• Inert gas crystals

Wavefunction ψ(x, y, z, t) is not measurable; we can measure the square modulus → probability density |ψ|² dx

In the stationary state |ψ| = |ψ|_R and not t. We can treat electrons as independent particles.

Born postulate

P(V) = ∫ |ψ|²d³

Probability per unit volume to find the electron in that volume

In the case of metals, free-electron model, Galvani constant, uniformly distributed (the electron moves freely everywhere continuously). In covalent crystals, there are bonds - regions with high directionality where the probability density is higher (aggregation).

x² < (m₁-E) < 0

E = _{ħ² k²} 2m +V₀ = _p² 2m +V₀

V₀-E < 0

0 < ε = E-T+V

ε_n = _n² 2M, ε₁ = _π² 2M

ε = _n² 2m

φ(x) = N sin k_nx

Energies are quantized