Sarbanes Oxley and the Impact on Information Technology

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Sarbanes Oxley and the Impact on Information Technology By: Frank Padavano, IT Managing Director About Accume Partners ○ Founded by Big Four partners in 1994 ○ Proprietary, risk-based internal audit approach ○ Proven business model adds value – Professionals averaging nearly 20 years experience, deployed at competitive rates – Excellent reputation among clients, regulators, and the Big Four – Sarbanes-Oxley - Experience with over 100 SOX clients 2
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Towards Understanding Topological Insulators
Vijay B. Shenoy
Centre for Condensed Matter Theory, IISc Bangalore
shenoy@physics.iisc.ernet.in
ICTS ICMP 2010, Bangalore
1/36Acknowledgement
S.-Q. Shen (Hong Kong), Lectures at ICTS Topology School
Amal Medhi, IISc (for discussions)
Generous funding by DAE and DST
2/36Goal and Outline
Goal { Answer the question: What the !@@! is a topological insulator
(TI)?
Where do TIs t into condensed matter physics?
Symmetries (revise time reversal)
Band theory { metals and insulators
Integer quantum Hall e ect
2D TIs
3D TIs
Why the fuss? What can you do with TIs?
3/36Prerequisites
Graduate quantum mechanics (including second quantization)
Basic solid state physics (@Kittel)
...
A keen desire to understand things and put in the necessary e ort
Follow the maxim (source: T. V. Ramakrishnan):
There are no stupid questions, only stupid answers!
DISCLAIMER: The speaker is NOT an expert! Focus is on elementary
concepts...not on calculations
4/36References
RMP by Hassan and Kane
Physics Today article by Qi and Zhang
Annual Reviews of Condensed Matter by Hassan and Moore
PRB Papers by Rahul Roy
5/361S
0
2
1s
2 3 4 3 2 1P1/2 P0 S3/2 P2 P3/2 S0
2 2 2 2 2 2 2 3 2 2 4 2 2 5 2 2 6
1s 2s 2p 1s 2s 2p 1s 2s 2p 1s 2s 2p 1s 2s 2p 1s 2s 2p
2 3 4 3 2 1P P S P P S
1/2 0 3/2 2 3/2 0
3 2 1 2 3 4 3 2 1F S S0 P1/2 P S3/2 P2 P3/2 S0
4 1/2 0
1 2 3 4 3 2 1S P° P S P P S
0 1/2 0 3/2 2 3/2 0
1 2 3 4 3 2 1S0 P1/2 P0 S3/2 P2 P3/2 S0
Condensed Matter
Operative de nition of condensed matter: A collection/aggregate of
atoms/ions in the non-relativistic regime
\Raw materials" for condensed matter
P E R I O D I C T A B L E
Group
1 18Atomic Properties of the Elements
IA VIIIA
2 1 S Physics Standard Reference 2
1/2 Frequently used fundamental physical constants
For the most accurate values of these and other constants, visit physics.nist.gov/constants Laboratory Data GroupH Hephysics.nist.gov www.nist.gov/srd1 1 second = 9 192 631 770 periods of radiation corresponding to the transitionHydrogen 133 Heliumbetween the two hyperfine levels of the ground state of Cs
1.00794 4.002602
-12 speed of light in vacuum c 299 792 458 m s (exact) 13 14 15 16 17
1s Solids
-34
13.5984 IIA Planck constant h 6.6261 · 10 J s ( /2 ) IIIA IVA VA VIA VIIA 24.5874Liquids
-19
2 1 elementary charge e 1.6022 · 10 C 3 S1/2 4 S0 5 ° 6 7 ° 8 9 ° 10
-31 Gaseselectron mass m 9.1094 · 10 kg
eLi Be 2 B C N O F Nemec 0.5110 MeV Artificially
2 Lithium Beryllium -27 Boron Carbon Nitrogen Oxygen Fluorine Neonproton mass mp 1.6726 · 10 kg Prepared
6.941 9.012182 10.811 12.0107 14.0067 15.9994 18.9984032 20.1797
2 2 2 fine-structure constant 1/137.036
1s 2s 1s 2s -1Rydberg constant R 10 973 732 m
5.3917 9.3227 15 8.2980 11.2603 14.5341 13.6181 17.4228 21.5645R c 3.289 842 · 10 Hz
2 1 11 S 12 S 13 ° 14 15 ° 16 17 ° 18
1/2 0 R hc 13.6057 eV
-23 -1Na Mg Boltzmann constant k 1.3807 · 10 J K Al Si P S Cl Ar
3 Sodium Magnesium Aluminum Silicon Phosphorus Sulfur Chlorine Argon
22.989770 24.3050 26.981538 28.0855 30.973761 32.065 35.453 39.9483 4 5 6 7 8 9 10 11 12
2 2 2 2 2 3 2 4 2 5 2 6
[Ne]3s [Ne]3s [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3p [Ne]3s 3pIIIB IVB VB VIB VIIB VIII IB IIB
5.1391 7.6462 5.9858 8.1517 10.4867 10.3600 12.9676 15.7596
2 1 2 3 4 7 6 5 4 19 S1/2 20 S0 21 D3/2 22 F2 23 F3/2 24 S3 25 S5/2 26 D4 27 F9/2 28 29 30 31 ° 32 33 ° 34 35 ° 36
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
4 Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton
39.0983 40.078 44.955910 47.867 50.9415 51.9961 54.938049 55.845 58.933200 58.6934 63.546 65.409 69.723 72.64 74.92160 78.96 79.904 83.798
2 2 2 2 3 2 5 5 2 6 2 7 2 8 2 10 10 2 10 2 10 2 2 10 2 3 10 2 4 10 2 5 10 2 6
[Ar]4s [Ar]4s [Ar]3d4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p [Ar]3d 4s 4p
4.3407 6.1132 6.5615 6.8281 6.7462 6.7665 7.4340 7.9024 7.8810 7.6398 7.7264 9.3942 5.9993 7.8994 9.7886 9.7524 11.8138 13.9996
2 1 2 3 6 7 6 5 4 1 2 37 S 38 S 39 D 40 F 41 D 42 S 43 S 44 F 45 F 46 S 47 S 48 49 50 51 ° 52 53 ° 54
1/2 0 3/2 2 1/2 3 5/2 5 9/2 0 1/2
Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
5 Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon
85.4678 87.62 88.90585 91.224 92.90638 95.94 (98) 101.07 102.90550 106.42 107.8682 112.411 114.818 118.710 121.760 127.60 126.90447 131.293
2 2 2 2 4 5 5 2 7 8 10 10 10 2 10 2 10 2 2 10 2 3 10 2 4 10 2 5 10 2 6
[Kr]5s [Kr]5s [Kr]4d5s [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s [Kr]4d [Kr]4d 5s [Kr]4d 5s [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p [Kr]4d 5s 5p
4.1771 5.6949 6.2173 6.6339 6.7589 7.0924 7.28 7.3605 7.4589 8.3369 7.5762 8.9938 5.7864 7.3439 8.6084 9.0096 10.4513 12.1298
2 1 4 5 6 5 3
3 4 2 55 S1/2 56 S0 72 F2 73 F3/2 74 D0 75 S5/2 76 D4 77 F9/2 78 D3 79 S1/2 80 81 ° 82 83 ° 84 85 ° 86
Cs Ba Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
6 Cesium Barium Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon
132.90545 137.327 178.49 180.9479 183.84 186.207 190.23 192.217 195.078 196.96655 200.59 204.3833 207.2 208.98038 (209) (210) (222)
2 14 2 2 14 3 2 14 4 2 14 5 2 14 6 2 14 7 2 14 9 14 10 14 10 2 2 3 4 5 6
[Xe]6s [Xe]6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Xe]4f 5d 6s [Hg]6p [Hg]6p [Hg]6p [Hg]6p [Hg]6p [Hg]6p
3.8939 5.2117 6.8251 7.5496 7.8640 7.8335 8.4382 8.9670 8.9588 9.2255 10.4375 6.1082 7.4167 7.2855 8.414 10.7485
2 1 3 87 S 88 S 104 F ? 105 106 107 108 109 110 111 112 114 116
1/2 0 2
Fr Ra Rf Db Sg Bh Hs Mt Uun Uuu Uub Uuq Uuh
7 Francium Radium Rutherfordium Dubnium Seaborgium Bohrium Hassium Meitnerium Ununnilium Unununium Ununbium Ununquadium Ununhexium
(223) (226) (261) (262) (266) (264) (277) (268) (281) (272) (285) (289) (292)
2 14 2 2
[Rn]7s [Rn]7s [Rn]5f 6d 7s ?
4.0727 5.2784 6.0 ?
2 1 4 5 6 7 8 9 6 5 4 3 2 1 2Atomic Ground-state D G° I° I H° F S° D° H° I I° H F° S D 57 3/2 58 4 59 9/2 60 4 61 5/2 62 0 63 7/2 64 2 65 15/2 66 8 67 15/2 68 6 69 7/2 70 0 71 3/2Number Level
La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
1Symbol 58 G° Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium
4
138.9055 140.116 140.90765 144.24 (145) 150.36 151.964 157.25 158.92534 162.500 164.93032 167.259 168.93421 173.04 174.967
2 2 3 2 4 2 5 2 6 2 7 2 7 2 9 2 10 2 11 2 12 2 13 2 14 2 14 2
[Xe]5d6s [Xe]4f5d6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 5d6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 6s [Xe]4f 5d6sCeName 5.5769 5.5387 5.473 5.5250 5.582 5.6437 5.6704 6.1498 5.8638 5.9389 6.0215 6.1077 6.1843 6.2542 5.4259
Cerium
2 3 4 5 6 7 8 9 6 5 4 3 2 1 2 89 D 90 F 91 K 92 L° 93 L 94 F 95 S° 96 D° 97 H° 98 I 99 I° 100 H 101 F° 102 S 103 P° ?140.116 3/2 2 11/2 6 11/2 0 7/2 2 15/2 8 15/2 6 7/2 0 1/2Atomic
† 2Weight [Xe]4f5d6s Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
5.5387 Actinium Thorium Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium Californium Einsteinium Fermium Mendelevium Nobelium Lawrencium
(227) 232.0381 231.03588 238.02891 (237) (244) (243) (247) (247) (251) (252) (257) (258) (259) (262)
2 2 2 2 2 3 2 4 2 6 2 7 2 7 2 9 2 10 2 11 2 12 2 13 2 14 2 14 2Ground-state Ionization
[Rn]6d7s [Rn]6d 7s [Rn]5f 6d7s [Rn]5f 6d7s [Rn]5f 6d7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 6d7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s [Rn]5f 7s 7p?Configuration Energy (eV)
5.17 6.3067 5.89 6.1941 6.2657 6.0260 5.9738 5.9914 6.1979 6.2817 6.42 6.50 6.58 6.65 4.9 ?

12Based upon C. () indicates the mass number of the most stable isotope. For a description of the data, visit physics.nist.gov/data NIST SP 966 (September 2003)
6/36
Period
Actinides LanthanidesCondensed Matter
What happens when we aggregate atoms? Many things...
In fact, the same atoms will give you very di erent things if
aggregated di erently! Eg., carbon atoms give
Di erent arrangement of atoms leads to very di erent emergent
properties!
Again: More is di erent... Di erent mores are more so!
Natural question: What are all the di erent \emergent
states/things/properties" can we obtain by aggregating atoms?
7/36Quantum Condensed Matter Physics
We will dwell mainly on electrons in materials
Electrons in materials experience various things:
...this de nes the \space of Hamiltonians" for the electrons
The ground state (and concomitant excitations) of the electrons
depend on where in the Hamiltonian space you are! There are many
\electronic phases"
One encounters (quantum) phase transitions as one moves about in
the Hamiltonian space!
8/36Electronic Phases
Electrons in materials can organize themselves in many di erent ways
{ \phases/states"...we have
I Metals
I Semi-metals
I Insulators/Semiconductors
I Topological insulators
I Superconductors
I Magnets
I Charge density wave systems
I Spin liquids
I ...
Each of these have a common set of characteristics...(similar in sprint
to: all liquids ow). In this sense each of the above is an \electronic
phase"!
9/36Electronic Phases
The goal of condensed matter research is to discover and understand
\all" the phases of electrons!
Think of a \character table"
...idea is to tabulate phases and their properties...and add to this
table!
This is useful ...and most interesting!
10/36