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QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to...

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Kai Sun University of Michigan, Ann Arbor
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Page 1: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Kai Sun

University of Michigan, Ann Arbor

Page 2: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Plan for today

Overview of solid state physics Course Syllabus

Page 3: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

What is this course about?

Systems under study: Solids• What is a solid?• Solid is different from other states of matter by its

shear modulus (ability to resist the change of shape)• Examples: metal, stone, wood, plastics, glass, …

Methods: All we have learned!• Quantum mechanics• Electromagnetism• Statistical mechanics and thermodynamics• Mechanics • Various math tools (Fourier transform, eigen-problem, …)

Page 4: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

How is this course different from others?

Previous courses (e.g., Mechanics, QM, E&M, Stat Mech,…)• Start from a few fundamental laws• Derive theorems from these laws• Verify the agreement with experiments

Solid state physics• Start by looking at real materials• Think about which laws/theorems apply here

(important step: make simplifications and approximations!)• Evaluate our model and think about how to do better• Prepares you for future research

Page 5: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

What will we learn?

What are nucleons doing in a solid? What are electrons doing in a solid? What are spins doing in a solid? Topics of modern condensed matter Effects of disorder

Page 6: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

What are nucleons doing in a solid?

Picture from wikipedia.com

Simple solids: crystals (we mostly deal with in this course)

Noncrystalline solids

(much more complicated to characterize)

• Why they exhibit such orders?

• How many types of crystal structures are there?

Page 7: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Nucleons don’t stay still at lattice sites!

At finite temperature: thermal fluctuations

• Vibrate around their equilibrium positions

• Interact with each other

Result: waves

Corresponding particles: Phonons

Page 8: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

What are electrons doing in a solid?

Why are there two types of solids: conductors and insulators?

It is a quantum phenomenon

Page 9: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Superconductivity

The search for the best conductor: superconductor

Perfect conductivity (no resistance)

Picture from wikipedia.com

Page 10: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Superconductivity

Meissner effect: B=0

Magnetic levitation

Picture from wikipedia.com

Page 11: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Maglev train

Shanghai Maglev TrainMechanical force Magnetic force

No contact No friction Low noise High speed (300m/h)

Page 12: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

What are spins doing in a solid?

Ferromagnetism 𝑀 ≠ 0

They play a very important role in the magnetism of solids

Paramagnetism 𝑀 = 0

𝑚

Page 13: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Magnetism (more exotic examples)

Anti-ferromagnetic:

Spin liquid:

Page 14: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Topics of modern condensed matter

Topological insulator

Conductor

Topological insulator: insulator inside but metal outside

Page 15: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Topological insulator

Why?Answer: Topology of the quantum wavefunction

Page 16: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Topics of modern condensed matter

Two different scales

High temperature superconductivity

Page 17: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Course Syllabus

Instructor: Prof. Kai SunEmail: [email protected]: 734-764-0730Office: 2245 RandallCourse Homepage: http://www-personal.umich.edu/~sunkai/teaching/Winter_2015/phys463.html

Time and placeTime: 8:30-10:00 am, Tuesdays and ThursdaysPlace: 335 West HallOffice hour: Wednesday 2:00-3:00pm at 2245 Randall

Page 18: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Course Syllabus

Textbook• Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed.• Additional reference (not required): Ashcroft and Mermin, Solid State Physics• Both books are on reserve at the library

PrerequisitePHYSICS 453 or equivalent

Problem Setsbi-weekly

Page 19: QUANTUM LIQUID CRYSTAL PHASES IN STRONGLY … · • Required textbook: Kittel, “Introduction to Solid State Physics” , 8th ed. • Additional reference (not required): Ashcroft

Course work and grading

Course grade will be based on• Problem set: 20%• Final Presentation: 20%

You will form teams of up to 3 members. Each team will give a 15 minute presentation on a topic you choose, illustrating an application of solid state physics.

• Midterm: 30%• Final: 30%


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