Electronic Properties of Quantum Wire Networks [thesis] by I. Kuzmenko

By I. Kuzmenko

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Therefore, its Fourier expansion contains only wave vectors k1n = nQ (n is the order of diffraction). This means that only frequencies ωn = nvQ can be excited. In this case it is more convenient to expand the field over Bloch eigenfunctions of an “empty” wire [58]. These functions are labelled by quasimomentum q1 , |q1 | ≤ Q/2, and the band number s. 2) within the s-th band and En = −E0 πr02 nQde−nQd . 3) The excited eigenfrequency ωn = ω[s/2] belongs simultaneously to the top of the lower even band with number s = 2n and to the bottom of the upper odd band with number s = 2n + 1 (this is the result of E(x) = E(−x) parity).

This case is illustrated by the points X1 and X2 in Fig. 3. Consider for example point X1 . Here q1 = Q/2, Q2 = 0. 5). The lower (higher) two lines correspond to even (1, g) and odd (1, u) superpositions of the 1-st array states of the first and second (third and fourth) bands. Similarly, two modes (2, s) with s = 2, 3 are degenerate in zero approximation with unperturbed frequency ω = 1. Therefore the middle two lines describe the same superpositions of the 2-d array states from the second and third bands.

20) For QCB this correlator is calculated in Appendix B. Its analysis leads to the following results. The longitudinal absorption ′ σ11 (q, ω) ∝ (1 − φ21q )δ(ω − ω ˜ 1q ) + φ21q δ(ω − ω ˜ 2q ) contains well pronounced peak on the modified first array frequency and weak peak at √ the second array frequency (the parameter φ1q = εζ1 (q1 )ζ1 (q2 )ω1 (q1 )ω1 (q2 ) is small). The modified frequencies ω ˜ 1q and ω ˜ 2q coincide with the eigenfrequencies ω+1q and ω−2q respectively, if ω1q > ω2q . In the opposite case the signs +, − should be changed to the opposite ones.

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