Unformatted text preview: n the spectrum).
Kopnin, Salomaa, 1991.
Read and Green, 2000.
2. 4D quantum Hall effect.
Zhang, Hu, 2001
3. Solitons in 1D chains.
Su, Schrieffer, Heeger (1978) Thursday, January 6, 2011 10 Other topological insulators?
1. 2D px+ipy superconductor (“insulator” since its
Bogoliubov quasiparticles have a gap in the spectrum).
Kopnin, Salomaa, 1991.
Read and Green, 2000.
2. 4D quantum Hall effect.
Zhang, Hu, 2001
3. Solitons in 1D chains.
Su, Schrieffer, Heeger (1978)
4. Modern 2D and 3D topological insulators.
Kane and Mele (2005); Zhang, Hughes, Bernevig, (2006);
Moore, Balents, (2007); Fu, Kane, Mele (2007)
Thursday, January 6, 2011 10 AltlandZirnbauer’s tenfold way Thursday, January 6, 2011 11 AltlandZirnbauer’s tenfold way Symmetries: 1. Timereversal Thursday, January 6, 2011 11 AltlandZirnbauer’s tenfold way Symmetries: 1. Timereversal
2. Particlehole Thursday, January 6, 2011 11 AltlandZirnbauer’s tenfold way Symmetries: 1. Timereversal
2. Particlehole
3. Chiral (sublattice) Thursday, January 6, 2011 11 AltlandZirnbauer’s tenfold Symmetries: 1. Timereversal 3. Chiral (sublattice) Cartan label
A (unitary)
AI (orthogonal)
AII (symplectic)
AIII (ch. unit.)
BDI (ch. orth.)
CII (ch. sympl.)
D (BdG)
C (BdG)
DIII (BdG)
CI (BdG) Thursday, January 6, 2011 T C S 0
+1
−1
0
+1
−1
0
0
−1
+1 0
0
0
0
+1
−1
+1
−1
+1
−1 0
0
0
1
1
1
0
0
1
1 From: Ryu, Schnyder, Furusaki, Ludwig, 2010 2. Particlehole respectively, as well as the 11
ty
way
‘Hamiltonian’ lists, for each of t
which the quantum mechanical
The column ‘Cartan label’ is t
space listed in the column ‘Ham
(dating back to the year 1926).
lists the (compact sectors of the
localization physics at long wav U
U
U
U
O
S
S
S
S
S AltlandZirnbauer’s tenfold Symmetries: 1. Timereversal 3. Chiral (sublattice)
IQHE
spinorbit coupling coupling: modern top. ins.
SuSchriefferHeeger solitons
pwave spinpolarized superconductors
3He, phase B swave superconductors
Thursday, January 6, 2011 Cartan label
A (unitary)
AI (orthogonal)
AII (symplectic)
AIII (ch. unit.)
BDI (ch. orth.)
CII (ch. sympl.)
D (BdG)
C (BdG)
DIII (BdG)
CI (BdG) T C S 0
+1
−1
0
+1
−1
0
0
−1
+1 0
0
0
0
+1
−1
+1
−1
+1
−1 0
0
0
1
1
1
0
0
1
1 From: Ryu, Schnyder, Furusaki, Ludwig, 2010 2. Particlehole respectively, as well as the 11
ty
way
‘Hamiltonian’ lists, for each of t
which the quantum mechanical
The column ‘Cartan label’ is t
space listed in the column ‘Ham
(dating back to the year 1926).
lists the (compact sectors of the
localization physics at long wav U
U
U
U
O
S
S
S
S
S 12
the topologically distinct phases within a given symmetry class of topological
insulators (superconductors) are characterized by an integer invariant (Z) or a
Z2 quantity, respectively. The symbol ‘0’ denotes the case when there exists no
topological insulator (superconductor), i.e. when all quantum ground states are
Table from Ryu, Schnyder, Furusaki, Ludwig, 2010
topologically equivalent to the trivial state. Classiﬁcation table of topological
insulators and superconductors
Cartan 0 1 2 3 4 5 d space dimensionality
6
7
8
9
10 Complex case:
A
AIII Z
0 0
Z Z
0...
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 Spring '12
 WarrenE.Pickett
 Physics, Trigraph, Condensed matter physics, z2, Quantum Hall effect, Quantum spin Hall effect

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