PHYS731-0101: Solid State Physics: Survey-Spring 2018 jaydsau

PHYS731-0101: Solid State Physics: Survey-Spring 2018 jaydsau

 

An introduction to phenomena that illustrate basic principles of solid state physics using undergraduate quantum mechanics:

Phys 731 elucidates a set collective quantum phenomena that occur in solid state systems by taking advantage of quantum mechanics at the advanced undergraduate (Griffiths) level (this is what takes this course beyond the undergraduate one) . 

 

 

 

 

 

 

Some of the topics covered are (suggestions welcome):

  • Second quantization for the many-electron gas
  • Screened Coulomb interactions (dielectric function)
  • Fermi surface and Fermi liquids
  • Collective excitation of the electron gas (plasmons and magnons)
  • Second quantization for Bosons
  • Bogoliubov description of sound in superfluids
  •  Phonons and magnons in solids as examples of Bosons
  • Bloch's theorem - topological insulators
  • Electron-phonon interaction
  •  Phonon mediated electron attraction
  • BCS theory of superconductivity
  • Ginzburg-Landau theory
  • Boltzmann transport in metals

 

 

 

 

Required Resources

Course website: elms.umd.edu

Text book: A Quantum approach to Condensed Matter Physics, Taylor and Heinonen, 1st edition, Cambridge University Press 2002.

 

Dr. Jay D. Sau

jaydsau@umd.edu

Class Meets

Tuesdays & Thursdays

11:00 am – 12:15 pm

PHY/Toll #1204

Office Hours

PHY/Toll #2330

by appointment

 

Grader

Amit Nag (Toll #2111)

anag@umd.edu

Suggested Prerequisites

Undergraduate quantum mechanics (PHYS 401/402 or equivalent)

Undergraduate statistical mechanics (Phys 404 or equivalent)

Course Communication

All updates and information regarding the course will be made using the announcements on ELMS – please make sure your ELMS settings do not delay announcements. I may or may not repeat in class.

Please send any questions or notifications of absences that you need to inform me preferably by email (see above).  

 

 

Campus Policies

It is our shared responsibility to know and abide by the University of Maryland’s policies that relate to all courses, which include topics like:

  • Academic integrity
  • Student and instructor conduct
  • Accessibility and accommodations
  • Attendance and excused absences
  • Grades and appeals
  • Copyright and intellectual property

Please visit www.ugst.umd.edu/courserelatedpolicies.html for the Office of Undergraduate Studies’ full list of campus-wide policies and follow up with me if you have questions.

 

Activities, Learning Assessments, & Expectations for Students

Lectures: Class time will be occupied by lectures that follow a set of notes that closely follow sections in the textbook. In a few cases I will follow a different textbook, which I will point out. I will post my notes online in this case. In addition to explaning the physical intuition behind concepts I will provide mathematical derivation of some of the more important results where the derivation is instructive. A firm grasp of quantum mechanics at approximately the advanced undergraduate level will be needed to follow parts of the lectures as well do some of the homeworks. The thorough use of quantum mechanics is what distinguishes the graduate solid state course from the undergraduate one.

Participation: The lectures assume that you are keeping track of the material of the previous lecture. This will enhance your learning and participation in the class, which is crucial to the classes success. To ensure a minimal level of participation, I will keep track of your participation through questions you ask or answer. You get full credit for participation if you ask or answer 6 questions in the semester related to the material presented in the lectures. Participation points of 1.67/lecture will be added to your grades within 24 hours of the lecture you participated in (i.e. asked/answered a relevant question/clarification).  I might forget to credit you for this. IT IS YOUR RESPONSIBILITY TO EMAIL ME IF I FORGET TO ADD THIS WITHIN TWO DAYS.  Late (by more than a few days) may or maynot be credited depending on whether I remember.

Homework : Problem sets will be posted as assignments on ELMS. The problems can also be downloaded from the assignments folder. Homework submission should be preferably by paper in class or at instructor office. Email submission to TA is allowed but should not be hand written. Homework will be assigned roughly once a week, and is to be turned in at the beginning of class on the due date. Homework will typically be posted on Friday and due the Thursday two weeks later (i.e. about 11 days). 20% will be marked off on homework turned in after the end of class. Homeworks turned in after the solutions are posted will not be graded. If you cannot attend class, please get your homework to me before class starts.  New assignments will be posted on the course website, along with the homework solutions. Homework problems are carefully chosen to highlight some of the important topics covered in lecture, complete some of the important steps, as well as important applications of the ideas. It is important that you carefully complete and make sure you understand all of the homework. You are encouraged to work with others on homework, however, it is forbidden to blindly copy another person’s work. There are 9 homework sets and one will be dropped. 

 

Grades

Grades are not given, but earned.  Your grade is determined by your performance on exams, homeworks and participation in the course and is assigned based on your score according to a curve. Typically I follow a curve scheme where the median score would be graded at B+. The lowest grade would be B- (very few). The top grades will be A+ and As. The number in each category would be roughly equal depends on appropriate breaks in the score distribution. 

Of course, all this being said this rule is subject to change depending on the performance of the class. If some students do extremely poorly (e.g. score well below 40%) I might consider going below B- for the lowest grade.  On the other hand, if everyone does well (i.e. above 90%) I have no hesitation giving the entire class an A. Also, if someone scores above 80 that is a B or better independent of whether the average is above 80.

If earning a particular grade is important to you, please speak with me at the beginning of the semester so that I can offer some helpful suggestions for achieving your goal.

All assessment scores will be posted on the course ELMS page.  If you would like to review any of your grades (including the exams), or have questions about how something was scored, please email me to schedule a time for us to meet in my office.

Late work (as explained in the instruction) will not be accepted for course credit so please plan to have it submitted well before the scheduled deadline.  I am happy to discuss any of your grades with you, and if I have made a mistake I will immediately correct it.  Any formal grade disputes must be submitted in writing and within one week of receiving the grade.

Learning Assessments

 #

Category Weight

Participation points

6

10%

Homework (out of 10 assignments)

9

90%

 

Course Schedule

 

Week 1

Thursday, January 25

  • Semiclassical phonons (1.2)

Week 2

Tuesday, January 30

  • Semiclassical solitons, plasmons (1.3, 1.5)

Thursday, February 1

  • Magnons (1.4), Semiclassical interacting fermi gases (1.6) 

Week 3

Tuesday, February 6

  • Collective modes of Fermi liquids (1.6, Landau-Lifshitz v9)
  • Measurement of collective modes (role of conservation - & symmetry)

Thursday, February 8

  • Second quantization for electrons (2.1-2.3)

Week 4

Tuesday, February 13

  • Anti-ferromagnetism
  • Hartree-Fock for electron gas (2.4)

Thursday, February 15

  • Hartree-Fock for electron gas  contd (2.4)
  • Ferromagnetism

Week 5

Tuesday, February 20

  • Perturbation theory for electrons ( 2.5 )
  • Density operator, screening, spin-waves ( 2.6-2.8 )

Thursday, February 22

  • Plasmons and Thomas Fermi from Lindhard dielectric
  • Bloch's theorem: (Chapter 4)

Week 6

Tuesday, February 27

  • example hexagonal lattice/graphene (Chapter 4)

Thursday, March 1

  • Band-gap, effective mass and Dirac points in Graphene

Week 7

Tuesday, March 6

  • Symmetry in band structure (Chapter 4)

Thursday, March 8

  • Bernevig-Hughes-Zhang model for quantum spin-Hall  ( Chapter 4 )

Week 8

Tuesday, March 13

  • Electric fields - transport, Block oscillations (Chapter 4)

Thursday, March 15

  • Magnetic fields and quantum oscillations (Chapter 4)

Week 9

Tuesday, March 27

  • Quantum Harmonic oscillators, quantization for Bosons (3.1 - 3.3 )

Thursday, March 29

  • Bogoliubov excitations in superfluids (3.4)

Week 10

Tuesday, April 3

  • Quantization of phonons, acoustic, optical, DOS ( 3.5-3.8 )

Thursday, April 5

  • Magnets and Quantizing Magnons (Holstein-Primakoff) ( 3.10, 3.11)

Week 11

Tuesday, April 10

  • Electron phonon interaction ( Chapter 6 )

Thursday, April 12

  • Kohn-anomaly (Chapter 6)

Week 12

Tuesday, April 17

  • Peierls instabilities (chapter 6)

Thursday, April 19

  • Phonon-induced electron pairing ( Chapter 6 )

Week 13

Tuesday, April 24

  • Phenomenology of superconductivity: transport and gap ( Chapter 7 )

Thursday, April 26

  • Phenomenology of superconductivity: coherence ( Chapter 7 )

Week 14

Tuesday, May 1

  • Cooper pairing and the BCS Hamiltonian ( Chapter 7 )

Thursday, May 3

 

  • BCS ground state wavefunction and quasiparticle gap ( Chapter 7 )

Week 15

Tuesday, May 8

  • BCS gap equation and transition temperature ( Chapter 7 )

Thursday, May 10

  • Josephson effect and Landau-Ginzburg theory ( Chapter 7 )

 

Note: This is a tentative schedule, and subject to change as necessary – monitor the course ELMS page for current deadlines.  In the unlikely event of a prolonged university closing, or an extended absence from the university, adjustments to the course schedule, deadlines, and assignments will be made based on the duration of the closing and the specific dates missed.

Course Summary:

Date Details Due