Advanced Solid State Physics

Outline

Electrons

Magnetic effects and
Fermi surfaces

Magnetism

Linear response

Transport

Crystal Physics

Electron-electron
interactions

Quasiparticles

Structural phase
transitions

Landau theory
of second order
phase transitions

Superconductivity

Quantization

Photons

Exam questions

Appendices

Lectures

Books

Course notes

TUG students

      

Space group: 229 (I m -3 m)

96 symmetry operations:

1	x,y,z	identity
2	-x,-y,z	C2 axis
3	-x,y,-z	C2 axis
4	x,-y,-z	C2 axis
5	z,x,y	C3 axis
6	z,-x,-y	C3 axis
7	-z,-x,y	C3 axis
8	-z,x,-y	C3 axis
9	y,z,x	C3 axis
10	-y,z,-x	C3 axis
11	y,-z,-x	C3 axis
12	-y,-z,x	C3 axis
13	y,x,-z	C2 axis
14	-y,-x,-z	C2 axis
15	y,-x,z	C4 axis
16	-y,x,z	C4 axis
17	x,z,-y	C4 axis
18	-x,z,y	C2 axis
19	-x,-z,-y	C2 axis
20	x,-z,y	C4 axis
21	z,y,-x	C4 axis
22	z,-y,x	C2 axis
23	-z,y,x	C4 axis
24	-z,-y,-x	C2 axis
25	-x,-y,-z	Ci: 0 0 0
26	x,y,-z	mirror plane
27	x,-y,z	mirror plane
28	-x,y,z	mirror plane
29	-z,-x,-y	3-bar axis|inversion center at 0 0 0
30	-z,x,y	3-bar axis|inversion center at 0 0 0
31	z,x,-y	3-bar axis|inversion center at 0 0 0
32	z,-x,y	3-bar axis|inversion center at 0 0 0
33	-y,-z,-x	3-bar axis|inversion center at 0 0 0
34	y,-z,x	3-bar axis|inversion center at 0 0 0
35	-y,z,x	3-bar axis|inversion center at 0 0 0
36	y,z,-x	3-bar axis|inversion center at 0 0 0
37	-y,-x,z	mirror plane
38	y,x,z	mirror plane
39	-y,x,-z	4-bar axis|inversion center at 0 0 0
40	y,-x,-z	4-bar axis|inversion center at 0 0 0
41	-x,-z,y	4-bar axis|inversion center at 0 0 0
42	x,-z,-y	mirror plane
43	x,z,y	mirror plane
44	-x,z,-y	4-bar axis|inversion center at 0 0 0
45	-z,-y,x	4-bar axis|inversion center at 0 0 0
46	-z,y,-x	mirror plane
47	z,-y,-x	4-bar axis|inversion center at 0 0 0
48	z,y,x	mirror plane
49	x+1/2,y+1/2,z+1/2	translation: 1/2 1/2 1/2
50	-x+1/2,-y+1/2,z+1/2	2-fold screw axis|translation: 0 0 1/2
51	-x+1/2,y+1/2,-z+1/2	2-fold screw axis|translation: 0 1/2 0
52	x+1/2,-y+1/2,-z+1/2	2-fold screw axis|translation: 1/2 0 0
53	z+1/2,x+1/2,y+1/2	3-fold screw axis|translation: 1/2 1/2 1/2
54	z+1/2,-x+1/2,-y+1/2	3-fold screw axis|translation: 1/6 -1/6 1/6
55	-z+1/2,-x+1/2,y+1/2	3-fold screw axis|translation: -1/6 1/6 1/6
56	-z+1/2,x+1/2,-y+1/2	3-fold screw axis|translation: 1/6 1/6 -1/6
57	y+1/2,z+1/2,x+1/2	3-fold screw axis|translation: 1/2 1/2 1/2
58	-y+1/2,z+1/2,-x+1/2	3-fold screw axis|translation: -1/6 1/6 1/6
59	y+1/2,-z+1/2,-x+1/2	3-fold screw axis|translation: 1/6 1/6 -1/6
60	-y+1/2,-z+1/2,x+1/2	3-fold screw axis|translation: 1/6 -1/6 1/6
61	y+1/2,x+1/2,-z+1/2	2-fold screw axis|translation: 1/2 1/2 0
62	-y+1/2,-x+1/2,-z+1/2	C2 axis
63	y+1/2,-x+1/2,z+1/2	4-fold screw axis|translation: 0 0 1/2
64	-y+1/2,x+1/2,z+1/2	4-fold screw axis|translation: 0 0 1/2
65	x+1/2,z+1/2,-y+1/2	4-fold screw axis|translation: 1/2 0 0
66	-x+1/2,z+1/2,y+1/2	2-fold screw axis|translation: 0 1/2 1/2
67	-x+1/2,-z+1/2,-y+1/2	C2 axis
68	x+1/2,-z+1/2,y+1/2	4-fold screw axis|translation: 1/2 0 0
69	z+1/2,y+1/2,-x+1/2	4-fold screw axis|translation: 0 1/2 0
70	z+1/2,-y+1/2,x+1/2	2-fold screw axis|translation: 1/2 0 1/2
71	-z+1/2,y+1/2,x+1/2	4-fold screw axis|translation: 0 1/2 0
72	-z+1/2,-y+1/2,-x+1/2	C2 axis
73	-x+1/2,-y+1/2,-z+1/2	Ci: 1/4 1/4 1/4
74	x+1/2,y+1/2,-z+1/2	n-glide plane|translation: 1/2 1/2 0
75	x+1/2,-y+1/2,z+1/2	n-glide plane|translation: 1/2 0 1/2
76	-x+1/2,y+1/2,z+1/2	n-glide plane|translation: 0 1/2 1/2
77	-z+1/2,-x+1/2,-y+1/2	3-bar axis|inversion center at 1/4 1/4 1/4
78	-z+1/2,x+1/2,y+1/2	3-bar axis|inversion center at -1/4 1/4 3/4
79	z+1/2,x+1/2,-y+1/2	3-bar axis|inversion center at 1/4 3/4 -1/4
80	z+1/2,-x+1/2,y+1/2	3-bar axis|inversion center at 3/4 -1/4 1/4
81	-y+1/2,-z+1/2,-x+1/2	3-bar axis|inversion center at 1/4 1/4 1/4
82	y+1/2,-z+1/2,x+1/2	3-bar axis|inversion center at 1/4 -1/4 3/4
83	-y+1/2,z+1/2,x+1/2	3-bar axis|inversion center at -1/4 3/4 1/4
84	y+1/2,z+1/2,-x+1/2	3-bar axis|inversion center at 3/4 1/4 -1/4
85	-y+1/2,-x+1/2,z+1/2	c-glide plane|translation: 0 0 1/2
86	y+1/2,x+1/2,z+1/2	d-glide plane|translation: 1/2 1/2 1/2
87	-y+1/2,x+1/2,-z+1/2	4-bar axis|inversion center at 0 1/2 1/4
88	y+1/2,-x+1/2,-z+1/2	4-bar axis|inversion center at 1/2 0 1/4
89	-x+1/2,-z+1/2,y+1/2	4-bar axis|inversion center at 1/4 0 1/2
90	x+1/2,-z+1/2,-y+1/2	a-glide plane|translation: 1/2 0 0
91	x+1/2,z+1/2,y+1/2	d-glide plane|translation: 1/2 1/2 1/2
92	-x+1/2,z+1/2,-y+1/2	4-bar axis|inversion center at 1/4 1/2 0
93	-z+1/2,-y+1/2,x+1/2	4-bar axis|inversion center at 0 1/4 1/2
94	-z+1/2,y+1/2,-x+1/2	b-glide plane|translation: 0 1/2 0
95	z+1/2,-y+1/2,-x+1/2	4-bar axis|inversion center at 1/2 1/4 0
96	z+1/2,y+1/2,x+1/2	d-glide plane|translation: 1/2 1/2 1/2