Set of supplementary notes.

More documents

Recommendations

Info

130 CHAPTER 9. ELECTRONIC INSTABILITIES Figure 9.3: Electron diffraction image shows Bragg scattering from a CDW formed in the compound La 0.29 Ca 0.71 MnO 3 . The real space image is at the top, showing a short scale checkerboard that is the atomic lattice, with a periodic modulation. The bottom figure is the fourier transform, so that the widely spaced bright peaks come from the small unit cell (this compound is based on a cubic perovskite, where the Mn atoms are on a simple cubic lattice), and the less intense peaks in between are the CDW. The two periods (lattice and CDW) are not related, because the CDW period is determined by the fermi surface size and shape, which depends on the electron concentration. Here the presence of an incommensurate ratio of trivalent La to divalent Ca means that the Mn d-bands are only partially filled. [Image courtesy of J. Loudon, P.A. Midgley, N.D. Mathur] 9.1.2 Polyacetylene and solitons One of the celebrated cases of such a CDW occurs in the polymer (CH) n , trans-polyacetylene (Fig. 9.5). Of the 4 valence electrons contributed by each carbon atom, one is involved in a bonding band (non-dispersive) with the H, leaving 3 electrons per atom to be accommodated along the −C − C − C− chain. If the C atoms were equally spaced, then there would be one full and one half-filled band. This half-filled band is unstable to dimerisation by the Peierls mechanism — doubling the lattice period, halves the Brillouin zone. It is often idealised as an alternation of double and single bonds, viz. −C = C − C = C− . The figure Fig. 9.5 shows that there are two different but symmetry-related ground states that can be formed by the dimerisation. One can readily imagine that in a long chain, these two states might join up next to each other, and that situation is visualised in Fig. 9.6. The
9.1. CHARGE DENSITY WAVES 131 Figure 9.4: Phonon dispersion curves in the quasi- one-dimensional organic compound TTF- TCNQ (tetrathiofulvalene tetracyanoquinone) along the direction of the chains in which there is a prominent soft phonon that turns into a periodic lattice distortion at low temperature. (There are many non-dispersing optical modes in the complicated unit cell. )[Mook and Watson, Phys. Rev. Lett. 36, 801 (1976)] Figure 9.5: (a) shows a sketch of the atomic arrangement of polyacetylene, with the C atoms as solid circles, and the H atoms as open circles. The C atoms are not equally spaced, and the structure is often idealised as an alternation of “double” and ”single” bonds, (b) and (c). The two isomers in (b) and (c) are related by a mirror symmetry.
Page 1:
Quantum Condensed Matter Physics Pa
Page 4 and 5:
4 CONTENTS 5.1 Bands and Brillouin
Page 6 and 7:
6 CONTENTS also serves to give impo
Page 8 and 9:
8 CONTENTS
Page 10 and 11:
10 CHAPTER 1. CLASSICAL MODELS FOR
Page 12 and 13:
Page 14 and 15:
Page 16 and 17:
Page 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
24 CHAPTER 2. SOMMERFELD THEORY Fig
Page 26 and 27:
26 CHAPTER 2. SOMMERFELD THEORY 2.4
Page 28 and 29:
28 CHAPTER 2. SOMMERFELD THEORY Res
Page 30 and 31:
30 CHAPTER 2. SOMMERFELD THEORY Thi
Page 32 and 33:
32 CHAPTER 2. SOMMERFELD THEORY
Page 34 and 35:
34 CHAPTER 3. FROM ATOMS TO SOLIDS
Page 36 and 37:
Page 38 and 39:
Page 40 and 41:
Page 42 and 43:
Page 44 and 45:
Page 46 and 47:
Page 48 and 49:
Page 50 and 51:
Page 52 and 53:
Page 54 and 55:
Page 56 and 57:
56 CHAPTER 4. ELECTRONIC STRUCTURE
Page 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Page 72 and 73:
Page 74 and 75:
74 CHAPTER 5. BANDSTRUCTURE OF REAL
Page 76 and 77:
Page 78 and 79:
Page 80 and 81: 80 CHAPTER 5. BANDSTRUCTURE OF REAL
Page 88 and 89: 88 CHAPTER 6. EXPERIMENTAL PROBES O
Page 100 and 101: 100 CHAPTER 7. SEMICONDUCTORS Figur
Page 102 and 103: 102 CHAPTER 7. SEMICONDUCTORS is fo
Page 104 and 105: 104 CHAPTER 7. SEMICONDUCTORS Figur
Page 106 and 107: 106 CHAPTER 8. SEMICONDUCTOR DEVICE
Page 116 and 117: ecessitates variances in circuit th
Page 118 and 119: nc... Freescale Semiconductor, I
Page 124 and 125: 124 CHAPTER 9. ELECTRONIC INSTABILI
Page 146 and 147: 146 CHAPTER 10. FERMI LIQUID THEORY
Page 158: 158 CHAPTER 10. FERMI LIQUID THEORY
show all

Set of supplementary notes.

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?