Basic Aspects of the Quantum Theory of Solids : Order and by Daniel I. Khomskii

By Daniel I. Khomskii

Offers the most thoughts and crucial theoretical equipment of the trendy quantum conception of solids for graduate scholars and researchers.

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Why does melting occur at all? How can one explain it qualitatively? Let us extend Fig. 6 a bit. e. this potential actually looks as in Fig. 12. We see that there exists an infinite motion at high enough temperature! The lattice is no longer stable, which means melting. Thus we again see that the melting is intrinsically connected with the anharmonicity of the lattice. 3 Another approach to melting. 4 Anharmonic effects 49 (for one phonon mode). 65) (we use the commutation relation bb† − b† b = 1).

Melting of the crystal. I remind readers that in quantum mechanics the time dependence of the wavefunction is given by ψ(t) = ψ(0) exp iωt. e. ωt = ±i|ω|t, this would give an exponential growth of the corresponding quantities. In our case, when the phonon frequencies cross zero, this would mean an exponential growth of the number of corresponding phonons, or of the respective distortion, which means absolute instability of the initial state, in this case a crystal. Whether such instability would indeed correspond to melting or to a structural transition to a different crystal structure, depends on which particular phonon mode becomes unstable.

It seems that in this case we should expect the insulating state to be the stable state at low temperatures (electrons localized at their sites, an ‘electronic crystal’), and the metallic phase to be the high-temperature phase (delocalized, moving electrons – an electron liquid), similar to melting of an ordinary crystal with increasing temperature. However the actual situation is not so simple. 7 General considerations B 27 T paramagnetic insulator paramagnetic metal A antiferromagnetic insulator P Fig.

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