PH320: Condensed Matter Physics II
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1 PH320: Condensed Matter Physics II Vijay B. Shenoy Centre for Condensed Matter Theory, IISc Bangalore 1 / 12
2 Overview 2 / 12
3 Overview What is this course about? 2 / 12
4 Overview What is this course about? Course outline 2 / 12
5 Overview What is this course about? Course outline Logistics 2 / 12
6 Condensed Matter Physics What is it really? 3 / 12
7 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! 3 / 12
8 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) 3 / 12
9 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) Matter interacts via messengers...gluons, W /Z-bosons, photons 3 / 12
10 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) Matter interacts via messengers...gluons, W /Z-bosons, photons Quarks combine to hadrons... e, g., neutrons and protons 3 / 12
11 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) Matter interacts via messengers...gluons, W /Z-bosons, photons Quarks combine to hadrons... e, g., neutrons and protons They in turn form aggregates nuclei... 3 / 12
12 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) Matter interacts via messengers...gluons, W /Z-bosons, photons Quarks combine to hadrons... e, g., neutrons and protons They in turn form aggregates nuclei......which are now big enough to trap leptons such as electrons... 3 / 12
13 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) Matter interacts via messengers...gluons, W /Z-bosons, photons Quarks combine to hadrons... e, g., neutrons and protons They in turn form aggregates nuclei......which are now big enough to trap leptons such as electrons......and we get atoms! 3 / 12
14 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) Matter interacts via messengers...gluons, W /Z-bosons, photons Quarks combine to hadrons... e, g., neutrons and protons They in turn form aggregates nuclei......which are now big enough to trap leptons such as electrons......and we get atoms!... 3 / 12
15 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) Matter interacts via messengers...gluons, W /Z-bosons, photons Quarks combine to hadrons... e, g., neutrons and protons They in turn form aggregates nuclei......which are now big enough to trap leptons such as electrons......and we get atoms!... There is something interesting going on here: The aggregate of interacting quarks and leptons, the atom, has an identity of its own! 3 / 12
16 Condensed Matter Physics What is it really? Condensed matter is certainly made of matter! Matter = Leptons, quarks (etc.?) Matter interacts via messengers...gluons, W /Z-bosons, photons Quarks combine to hadrons... e, g., neutrons and protons They in turn form aggregates nuclei......which are now big enough to trap leptons such as electrons......and we get atoms!... There is something interesting going on here: The aggregate of interacting quarks and leptons, the atom, has an identity of its own! Moral: An aggregate can look and feel very different from its constituents! 3 / 12
17 Condensed Matter 4 / 12
18 Condensed Matter Operative definition of condensed matter: A collection/aggregate of atoms/ions in the non-relativistic regime 4 / 12
19 Condensed Matter Operative definition of condensed matter: A collection/aggregate of atoms/ions in the non-relativistic regime Raw materials for condensed matter 4 / 12
20 Condensed Matter Operative definition of condensed matter: A collection/aggregate of atoms/ions in the non-relativistic regime Raw materials for condensed matter Period Group 1 IA 1 2 S 1/2 H Hydrogen s S 1/2 Li Lithium s 2 2s Na 2 S 1/2 Sodium [Ne]3s K 2 S 1/2 Potassium 2 IIA 4 Be 1 S 0 Beryllium s 2 2s Mg 1 S 0 Magnesium [Ne]3s Ca 1 S 0 Calcium [Ar]4s [Ar]4s Rb 2 S 1/2 Sr 1 S 0 Rubidium Strontium [Kr]5s [Kr]5s Cs 2 S 1/2 Ba 1 S 0 Cesium Barium [Xe]6s [Xe]6s Fr 2 S 1/2 Ra 1 S 0 Francium Radium (223) [Rn]7s (226) [Rn]7s P E R I O D I C T A B L E Atomic Properties of the Elements 18 VIIIA Frequently used fundamental physical constants Physics Standard Reference 2 For the most accurate values of these and other constants, visit physics.nist.gov/constants Laboratory Data Group 1 second = periods of radiation corresponding to the transition physics.nist.gov He Helium between the two hyperfine levels of the ground state of 133 Cs speed of light in vacuum c m s Solids (exact) Planck constant h J s ( /2 ) Liquids IIIA IVA VA VIA VIIA elementary charge e C Gases electron mass m e kg m ec Artificially B C N O F Ne MeV proton mass m p kg Prepared Boron Carbon Nitrogen Oxygen Fluorine Neon fine-structure constant 1/ Rydberg constant R m R c Hz R hc ev 18 Boltzmann constant k J K 1 Al Si P S Cl Ar Aluminum Silicon Phosphorus Sulfur Chlorine Argon [Ne]3s 2 3p [Ne]3s 2 3p 2 [Ne]3s 2 3p 3 [Ne]3s 2 3p 4 [Ne]3s 2 3p 5 [Ne]3s 2 3p IIIB IVB VB VIB VIIB VIII IB IIB Sc 2 D 22 Ti 3 3/2 F V 4 2 F 24 Cr 7 3/2 S 25 Mn 6 3 S 26 Fe 5 5/2 D 27 Co 4 4 F 9/2 28 Ni Cu Zn Ga Ge As Se Br Kr Scandium Titanium Vanadium Chromium Manganese Iron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton [Ar]3d4s 2 [Ar]3d 2 4s 2 [Ar]3d 3 4s 2 [Ar]3d 5 4s [Ar]3d 5 4s 2 [Ar]3d 6 4s 2 [Ar]3d 7 4s 2 [Ar]3d 8 4s 2 [Ar]3d 10 4s [Ar]3d 10 4s 2 [Ar]3d 10 4s 2 4p [Ar]3d 10 4s 2 4p 2 [Ar]3d 10 4s 2 4p 3 [Ar]3d 10 4s 2 4p 4 [Ar]3d 10 4s 2 4p 5 [Ar]3d 10 4s 2 4p Y 2 D 3/2 Zr 3 F 2 Nb 6 D 1/2 Mo 7 S 3 Tc 6 S 5/2 Ru 5 F Rh 4 F Pd 1 5 9/2 S Ag 2 0 S 1/2 Cd In Sn Sb Te I Xe Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium Palladium Silver Cadmium Indium Tin Antimony Tellurium Iodine Xenon (98) [Kr]4d5s 2 [Kr]4d 2 5s 2 [Kr]4d 4 5s [Kr]4d 5 5s [Kr]4d 5 5s 2 [Kr]4d 7 5s [Kr]4d 8 5s [Kr]4d 10 [Kr]4d 10 5s [Kr]4d 10 5s 2 [Kr]4d 10 5s 2 5p [Kr]4d 10 5s 2 5p 2 [Kr]4d 10 5s 2 5p 3 [Kr]4d 10 5s 2 5p 4 [Kr]4d 10 5s 2 5p 5 [Kr]4d 10 5s 2 5p Hf 3 F 2 Ta 4 F 3/2 W 5 D 0 Re 6 S 5/2 Os 5 D 4 Ir 4 F 9/2 Pt 3 D 3 Au 2 S 1/2 Hg Tl Pb Bi Po At Rn Hafnium Tantalum Tungsten Rhenium Osmium Iridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon (209) (210) (222) [Xe]4f 14 5d 2 6s 2 [Xe]4f 14 5d 3 6s 2 [Xe]4f 14 5d 4 6s 2 [Xe]4f 14 5d 5 6s 2 [Xe]4f 14 5d 6 6s 2 [Xe]4f 14 5d 7 6s 2 [Xe]4f 14 5d 9 6s [Xe]4f 14 5d 10 6s [Xe]4f 14 5d 10 6s 2 [Hg]6p [Hg]6p 2 [Hg]6p 3 [Hg]6p 4 [Hg]6p 5 [Hg]6p F? Rf Db Sg Bh Hs Mt Uun Uuu Uub Uuq Uuh Rutherfordium Dubnium Seaborgium Bohrium Hassium Meitnerium Ununnilium Unununium Ununbium Ununquadium Ununhexium (261) (262) (266) (264) (277) (268) (281) (272) (285) (289) (292) [Rn]5f 14 6d 2 7s 2? 6.0? 3 F 4 2 S 1/2 1 S 0 2 P 1/2 1 S 0 1 S 0 2 P 1/2 1s 2 2s 2 2p 3 P 0 1s 2 2s 2 2p 2 4 S 3/2 1s 2 2s 2 2p 3 3 P 2 1s 2 2s 2 2p 4 2 P 3/2 1s 2 2s 2 2p 5 1s 2 1 S 0 1 S 0 1s 2 2s 2 2p 6 2 P 1/2 3 P 0 4 S 3/2 3 P 2 2 P 3/2 1 S 0 3 P 0 4 S 3/2 3 P 2 2 P 3/2 1 S 0 2 P 1/2 3 P 0 4 S 3/2 3 P 2 2 P 3/2 1 S 0 2 P 1/2 3 P 0 4 S 3/2 3 P 2 2 P 3/2 1 S 0 Symbol Name Atomic Weight Atomic Number Ground-state Configuration Ground-state Level 58 Ce 1 G 4 Cerium [Xe]4f5d6s Ionization Energy (ev) Lanthanides Actinides 57 La Lanthanum [Xe]5d6s Ac Actinium (227) [Rn]6d7s D 58 Ce 1 3/2 G 4 Cerium [Xe]4f5d6s D 90 Th 3 3/2 F 2 Thorium [Rn]6d 2 7s Pr 4 I Nd 5 9/2 I Pm 6 4 H Sm 7 Eu Gd Tb Dy 5 I Ho 4 5/2 F 8 0 S 9 7/2 D 6 2 H 8 I Er 3 15/2 15/2 H Tm 2 6 F 7/2 Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium (145) [Xe]4f 3 6s 2 [Xe]4f 4 6s 2 [Xe]4f 5 6s 2 [Xe]4f 6 6s 2 [Xe]4f 7 6s 2 [Xe]4f 7 5d6s 2 [Xe]4f 9 6s 2 [Xe]4f 10 6s 2 [Xe]4f 11 6s 2 [Xe]4f 12 6s 2 [Xe]4f 13 6s Pa 4 K 11/2 Protactinium [Rn]5f 2 6d7s U 5 L 6 Uranium [Rn]5f 3 6d7s Np 6 L 11/2 Neptunium (237) [Rn]5f 4 6d7s Pu 7 F 95 Am 8 0 S 7/2 Plutonium Americium (244) [Rn]5f 6 7s Cm 9 D 97 Bk 6 98 Cf 5 I 99 Es 4 I 100 Fm Md 2 2 H 15/2 8 15/2 H 6 F 7/2 Curium Berkelium Californium Einsteinium Fermium Mendelevium (243) (247) (247) (251) (252) (257) (258) [Rn]5f 7 7s 2 [Rn]5f 7 6d7s 2 [Rn]5f 9 7s 2 [Rn]5f 10 7s 2 [Rn]5f 11 7s 2 [Rn]5f 12 7s 2 [Rn]5f 13 7s Yb 1 S 0 Ytterbium [Xe]4f 14 6s No 1 S 0 Nobelium (259) [Rn]5f 14 7s Lu 2 D 3/2 Lutetium [Xe]4f 14 5d6s ? Lr 2 P 1/2 Lawrencium (262) [Rn]5f 14 7s 2 7p? 4.9? Based upon 12 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) 4 / 12
21 Condensed Matter 5 / 12
22 Condensed Matter What happens when we aggregate atoms? 5 / 12
23 Condensed Matter What happens when we aggregate atoms? Many things... 5 / 12
24 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! 5 / 12
25 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! Eg., carbon atoms give 5 / 12
26 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! Eg., carbon atoms give 5 / 12
27 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! Eg., carbon atoms give 5 / 12
28 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! Eg., carbon atoms give 5 / 12
29 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! Eg., carbon atoms give Different arrangement of atoms leads to very different emergent properties! 5 / 12
30 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! Eg., carbon atoms give Different arrangement of atoms leads to very different emergent properties! Again: More is different... 5 / 12
31 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! Eg., carbon atoms give Different arrangement of atoms leads to very different emergent properties! Again: More is different... Different mores are more so! 5 / 12
32 Condensed Matter What happens when we aggregate atoms? Many things... In fact, the same atoms will give you very different things if aggregated differently! Eg., carbon atoms give Different arrangement of atoms leads to very different emergent properties! Again: More is different... Different mores are more so! Natural question: What are all the different emergent states/things/properties can we obtain by aggregating atoms? 5 / 12
33 Condensed Matter Why (in particular, ) care? 6 / 12
34 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? 6 / 12
35 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? 6 / 12
36 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? 6 / 12
37 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? 6 / 12
38 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? 6 / 12
39 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? We look to create atom aggregates (materials) with ever better properties 6 / 12
40 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? We look to create atom aggregates (materials) with ever better properties For this we need to know: What atoms to aggregate? What kind of aggregation? How to aggregate them? 6 / 12
41 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? We look to create atom aggregates (materials) with ever better properties For this we need to know: What atoms to aggregate? What kind of aggregation? How to aggregate them? The branch of science that predicts properties of atom aggregates is Condensed Matter Physics 6 / 12
42 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? We look to create atom aggregates (materials) with ever better properties For this we need to know: What atoms to aggregate? What kind of aggregation? How to aggregate them? The branch of science that predicts properties of atom aggregates is Condensed Matter Physics... 6 / 12
43 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? We look to create atom aggregates (materials) with ever better properties For this we need to know: What atoms to aggregate? What kind of aggregation? How to aggregate them? The branch of science that predicts properties of atom aggregates is Condensed Matter Physics... Hence, they ( ) should care! 6 / 12
44 Condensed Matter Why (in particular, Everything that we use is condensed matter! ) care? We look to create atom aggregates (materials) with ever better properties For this we need to know: What atoms to aggregate? What kind of aggregation? How to aggregate them? The branch of science that predicts properties of atom aggregates is Condensed Matter Physics... Hence, they ( ) should care! But why should you care? 6 / 12
45 Condensed Matter Physics 7 / 12
46 Condensed Matter Physics In many cases, atom aggregates can be studied in a purely classical mechanics framework 7 / 12
47 Condensed Matter Physics In many cases, atom aggregates can be studied in a purely classical mechanics framework 7 / 12
48 Condensed Matter Physics In many cases, atom aggregates can be studied in a purely classical mechanics framework 7 / 12
49 Condensed Matter Physics In many cases, atom aggregates can be studied in a purely classical mechanics framework 7 / 12
50 Condensed Matter Physics In many cases, atom aggregates can be studied in a purely classical mechanics framework...this falls under the purview of soft condensed matter 7 / 12
51 Condensed Matter Physics In many cases, atom aggregates can be studied in a purely classical mechanics framework...this falls under the purview of soft condensed matter...and in others, e. g., a metal, quantum mechanics is unavoidable, 7 / 12
52 Condensed Matter Physics In many cases, atom aggregates can be studied in a purely classical mechanics framework...this falls under the purview of soft condensed matter...and in others, e. g., a metal, quantum mechanics is unavoidable, quantum condensed matter (aka hard condensed matter) 7 / 12
53 Condensed Matter Physics In many cases, atom aggregates can be studied in a purely classical mechanics framework...this falls under the purview of soft condensed matter...and in others, e. g., a metal, quantum mechanics is unavoidable, quantum condensed matter (aka hard condensed matter) This is a course primarily on quantum condensed matter 7 / 12
54 Quantum Condensed Matter Physics 8 / 12
55 Quantum Condensed Matter Physics We will dwell mainly on electrons in materials 8 / 12
56 Quantum Condensed Matter Physics We will dwell mainly on electrons in materials Electrons in materials experience various things: 8 / 12
57 Quantum Condensed Matter Physics We will dwell mainly on electrons in materials Electrons in materials experience various things: 8 / 12
58 Quantum Condensed Matter Physics We will dwell mainly on electrons in materials Electrons in materials experience various things:...this defines the space of Hamiltonians for the electrons 8 / 12
59 Quantum Condensed Matter Physics We will dwell mainly on electrons in materials Electrons in materials experience various things:...this defines 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 8 / 12
60 Quantum Condensed Matter Physics We will dwell mainly on electrons in materials Electrons in materials experience various things:...this defines 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 / 12
61 Electronic Phases 9 / 12
62 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have 9 / 12
63 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals 9 / 12
64 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals 9 / 12
65 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors 9 / 12
66 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors Topological insulators 9 / 12
67 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors Topological insulators Superconductors 9 / 12
68 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors Topological insulators Superconductors Magnets 9 / 12
69 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors Topological insulators Superconductors Magnets Charge density wave systems 9 / 12
70 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors Topological insulators Superconductors Magnets Charge density wave systems Spin liquids 9 / 12
71 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors Topological insulators Superconductors Magnets Charge density wave systems Spin liquids... 9 / 12
72 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors Topological insulators Superconductors Magnets Charge density wave systems Spin liquids... Each of these have a common set of characteristics...(similar in sprint to: all liquids flow). In this sense each of the above is an electronic phase! 9 / 12
73 Electronic Phases Electrons in materials can organize themselves in many different ways phases/states...we have Metals Semi-metals Insulators/Semiconductors Topological insulators Superconductors Magnets Charge density wave systems Spin liquids... Each of these have a common set of characteristics...(similar in sprint to: all liquids flow). In this sense each of the above is an electronic phase! 9 / 12
74 What is Metallic about a Metal? 10 / 12
75 What is Metallic about a Metal? Copper is a metal, gold is also...so is sodium...they look so different, and yet we insist that they are the same! 10 / 12
76 What is Metallic about a Metal? Copper is a metal, gold is also...so is sodium...they look so different, and yet we insist that they are the same! Resistivity of metals increases with temperature / 12
77 What is Metallic about a Metal? Copper is a metal, gold is also...so is sodium...they look so different, and yet we insist that they are the same! Resistivity of metals increases with temperature / 12
78 What is Metallic about a Metal? Copper is a metal, gold is also...so is sodium...they look so different, and yet we insist that they are the same! Resistivity of metals increases with temperature......we see that there is something unviersal about it! 10 / 12
79 What is Metallic about a Metal? Copper is a metal, gold is also...so is sodium...they look so different, and yet we insist that they are the same! Resistivity of metals increases with temperature......we see that there is something unviersal about it! Despite their different appearance, there is something deeply common among various metals...this commonality characterizes the metallic state 10 / 12
80 What is this Course About? 11 / 12
81 What is this Course About? Natural next question: What all states are there? This is what condensed matter physicists are after...discover, name, study/characterize states of condensed matter / 12
82 What is this Course About? Natural next question: What all states are there? This is what condensed matter physicists are after...discover, name, study/characterize states of condensed matter... More important question: When should we claim to have discovered a new state? When do we use the term exotic? 11 / 12
83 What is this Course About? Natural next question: What all states are there? This is what condensed matter physicists are after...discover, name, study/characterize states of condensed matter... More important question: When should we claim to have discovered a new state? When do we use the term exotic? We need to prepare ourselves to know when to be surprised 11 / 12
84 What is this Course About? Natural next question: What all states are there? This is what condensed matter physicists are after...discover, name, study/characterize states of condensed matter... More important question: When should we claim to have discovered a new state? When do we use the term exotic? We need to prepare ourselves to know when to be surprised Need to have some idea about states that are already known, what their properties are etc. 11 / 12
85 What is this Course About? Natural next question: What all states are there? This is what condensed matter physicists are after...discover, name, study/characterize states of condensed matter... More important question: When should we claim to have discovered a new state? When do we use the term exotic? We need to prepare ourselves to know when to be surprised Need to have some idea about states that are already known, what their properties are etc. This course is about familiarising the most common states of (quantum) condensed matter, to learn basic condensed matter taxonomy 11 / 12
86 What is this Course About? Natural next question: What all states are there? This is what condensed matter physicists are after...discover, name, study/characterize states of condensed matter... More important question: When should we claim to have discovered a new state? When do we use the term exotic? We need to prepare ourselves to know when to be surprised Need to have some idea about states that are already known, what their properties are etc. This course is about familiarising the most common states of (quantum) condensed matter, to learn basic condensed matter taxonomy The list of states that we shall see in this course is listed in the course outline 11 / 12
87 This Course / 12
88 This Course... Many different experimental probes (X-rays, Transport, ARPES, Neutron, STM, Raman, etc...)... Each phase has a characteristic response to such probes / 12
89 This Course... Many different experimental probes (X-rays, Transport, ARPES, Neutron, STM, Raman, etc...)... Each phase has a characteristic response to such probes / 12
90 This Course... Many different experimental probes (X-rays, Transport, ARPES, Neutron, STM, Raman, etc...)... Each phase has a characteristic response to such probes... Our goal is to understand what the responses of various states are to (some of) such probes / 12
91 This Course... Many different experimental probes (X-rays, Transport, ARPES, Neutron, STM, Raman, etc...)... Each phase has a characteristic response to such probes... Our goal is to understand what the responses of various states are to (some of) such probes... Along the way we will also pick up some technical tools 12 / 12
92 This Course... Many different experimental probes (X-rays, Transport, ARPES, Neutron, STM, Raman, etc...)... Each phase has a characteristic response to such probes... Our goal is to understand what the responses of various states are to (some of) such probes... Along the way we will also pick up some technical tools There have been many recent surprises: Cuprates, Topological Insulators / 12
93 This Course... Many different experimental probes (X-rays, Transport, ARPES, Neutron, STM, Raman, etc...)... Each phase has a characteristic response to such probes... Our goal is to understand what the responses of various states are to (some of) such probes... Along the way we will also pick up some technical tools There have been many recent surprises: Cuprates, Topological Insulators... And even systems that allow for fantastic new directions for controlled experimentation cold atoms 12 / 12
94 This Course... Many different experimental probes (X-rays, Transport, ARPES, Neutron, STM, Raman, etc...)... Each phase has a characteristic response to such probes... Our goal is to understand what the responses of various states are to (some of) such probes... Along the way we will also pick up some technical tools There have been many recent surprises: Cuprates, Topological Insulators... And even systems that allow for fantastic new directions for controlled experimentation cold atoms Our goal is to prepare to attack these! / 12
95 This Course... Many different experimental probes (X-rays, Transport, ARPES, Neutron, STM, Raman, etc...)... Each phase has a characteristic response to such probes... Our goal is to understand what the responses of various states are to (some of) such probes... Along the way we will also pick up some technical tools There have been many recent surprises: Cuprates, Topological Insulators... And even systems that allow for fantastic new directions for controlled experimentation cold atoms Our goal is to prepare to attack these!...and to imagine even more! 12 / 12
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