Physics 471: Solid State Physics

Professor Micky HolcombOffice: 437 White Hall

mikel.holcomb@mail.wvu.eduhttp://community.wvu.edu/~mbh039/

Today: Introduction to me, you, class structure and topic

About Your Professor

• Went to school at Vanderbilt and Berkeley• Did graduate work at a national lab• Did internship at IBM on quantum computing• Toyed with a non-scientific internet startup• Decided I liked teaching, so I’m here now

Business and Pleasure

My Work: Surface & Interface Physics

Gas Adsorption on Surfaces

Exchange Bias

Topological Insulators

Magnetic Dead Layers

MultiferroicMultiferroic

FerroelectricFerroelectricFerromagneticFerromagnetic

Definition of a Multiferroic

Spontaneous magnetization whose direction can be changed with an

applied magnetic field

Spontaneous polarization whose direction can be changed with an

applied electric field (voltage)

Before field After field

field

Electric Control of Magnetism

http://www.helmholtz-berlin.de/forschung/magma/m-dynamik/forschungsbereiche/multiferroicity_en.html

Coupling at interfaces is not well understood

Review paper, Holcomb et al., IJMPB (2012)

INDIRECT COUPLING

Measurement TechniquesWVU: Nonlinear Optics

Focused on Second Harmonic Generation and MOKE

Provides information on symmetry and interfacial time

dynamics

Synchrotron Techniques At National Labs:

X-ray Absorption Spectroscopy

Photoemission Electron Microscopy (PEEM)

San Francisco

Beyond the standard techniques (XRD, TEM, etc.), we focus on unique interfacial measurement techniques.

As we are about to spend a lot of time together,

please introduce yourself.

- Name and Year

-Planned research or interest

-Planned career path (or possibilities, if debating)

-Why are you taking this course?

Important Class Issues

• Prerequisites: PHYS 314 and Math 251 is required.

• Text: Solid State Physics, by Ashcroft(in stock on Amazon, $20 - 300) Others

• Lecture PPTs will be available online shortly after class. (bonus material, not tested)

• I expect you to do the reading before coming to class so that we can focus on details.

How Do We Learn?

Through Repetition: the more times (and more ways) we repeat something, the more important our brains think it is,

and the more likely we are to remember it

Another good reason to read multiple books

How Do We Learn?Amygdala:

Fight or Flight

Hippocampus:

Memory

Prefrontal Cortex:

Executive Function

http://prezi.com/zzcsda6jbs6n/brain-based-teaching-and-learning-journal/

Why Cramming Doesn’t Work

My Goal

Learning Assessment

• There are many different physics skills (problem solving, written and oral communication, etc). My assignments reflect this variety.

• Late assignments arriving in my hands will be counted 20% for each day late.

• Feel free to work together on HW, but do not copy.

Topic Presentation and Paper

• The ability to find, evaluate, and synthesize critical information relating to a topic

• These skills are absolutely vital to a successful scientific career!

Oral Communication of Science

Is one of the more difficult skills to master and grade. Your skill will be evaluated in 2 ways:

•In class discussion (with both a partner and to the entire class) on in-class problems•A 10 minute talk on a selected topic

Discussion Questions

• Some of these questions will be easy to make sure you have important background. If everyone thinks it’s easy, we’ll move through these fast. Otherwise, vital to cover.

• Some of the questions will be harder. My goal is to coach you through these problems, not just do them for you. You learn more this way.

Course GradingCourse Grade: Homework 25%, Exam 1 25%, Final

25%, In-class Discussion 5%, Presentation 10%, Paper 10%

Grading scale: A (>90), B (80 - 89), C (70 - 79), D (60 - 69), F (<59)

Teaching: A student receiving an A on their talk will at

least 1) make and share organized powerpoint slides, 2) make eye contact with classmates, 3) discuss applications of physics, 4) motivate why topic is interesting, 5) identify key points and 6) stay close to the allotted time.

My Teaching Philosophy Regarding Slides

•If you become a professor, you will be instructed to (regarding teaching) “beg, borrow and steal.” Preparing a good lecture is hard! So, if someone manages to, then reuse it!

• Therefore, many of my slides are adaptations. I pick what I deem to be the most instructive slides.

• I find this to work out pretty well, yet there is a problem with it. Many different notations for the same things are used. (e.g. lattice vectors)

• In reality, papers use different notation, so maybe good practice? Feel free to ask if confused.

Physics 471: Solid State Physics (SSP)

Professor Micky HolcombOffice: 437 White Hall

Office hour: Wednesday 2-3PM or by apptmikel.holcomb@mail.wvu.edu

http://community.wvu.edu/~mbh039/

Today’s Plan:Take ungraded pre-test. When finished, read over

syllabus. If time remains, I will introduce SSP.

• Solid state physics (SSP) explains the properties of solid materials which follow from Schrödinger’s equation for a collection of atomic nuclei and electrons interacting with electrostatic forces.

• SSP, also known as condensed matter physics, is the study of the behavior of atoms when they are placed in close proximity to one another. Many of the concepts relevant to liquids too.

What is solid state physics?

What is the point?

• Understanding the electrical properties of solids is right at the heart of modern society and technology.

• The entire computer and electronics industry relies on tuning of a special class of material, the semiconductor, which lies right at the metal-insulator boundary. Solid state physics provide a background to understand what goes on in semiconductors.

New technology for the future will involve developing and understanding new classes of materials. By the end of this course we will see why this is a non-trivial task.

Electrical resistivity of three states of solid matter

They are all just carbon!

How can this be? After all, they each contain a system of atoms and especially electrons of similar density. Graphite is a metal, diamond is an insulator and buckminster-fullerene is a superconductor.

With the remaining time today:

Let’s remind ourselves of how we’ve dealt with individual atoms through quantum mechanics

In the remainder of the semester we’ll focus on the effects of bringing lots of atoms together

Multielectron Atoms• Because electrostatic forces between electrons are strong, we need to take

them into account in multielectron atoms (i.e., atoms other than hydrogen)

• We approximate this by treating the force on each electron independently, which includes force from nucleus + force from all other electrons

• In this case, inner electrons can shield the nuclear charge, called “screening”

We write the effective potential energy felt by an electron as

rke

rZrU eff

2

)()(

Zeff is the effective charge that the electron feels and depends on r. Note that

ZZeff

1effZ

when r is inside all other electrons

when r is outside all other electrons

+Ze

electron

Screening electron

cloud

r

Reminder: k=1/4o

Energy Levels• As in the hydrogen atom, quantum states of electrons in multielectron

atoms are specified by the quantum numbers n, l, m, mS

• In hydrogen atom, all states of a given n are degenerate (in zero magnetic field and neglecting the fine structure)

• In multielectron atoms the dependence of the potential energy on r due to screening lifts the degeneracy between these states:

In hydrogen, all n orbital (ns,np,nd) states have the same energy

Electron distribution• For a multielectron atom, how are the electrons distributed

among the different energy levels and orbitals?

• Electrons would all crowd the ground state (lowest energy) if it wasn’t for the:

Pauli Exclusion Principle: No two electrons (fermions) in a quantum system can occupy the

same state (i.e., have the same quantum numbers)

Helium ground state Helium excited stateLithium ground state

Would ground state helium or lithium be easier to ionize (remove an electron)?

The Periodic Table

How does quantum mechanics determine the electronic configuration

and properties of the elements?

Properties of HeliumUse notation ZE: e.g. 1H, 2He

2He: • Ground state: two electrons in 1s state (spin up and

spin down)• Screening of each electron by the other• This results on a relatively large ionization energy

(energy to remove an electron from a neutral atom) of 24.6 eV; excitation energy (E2s-E1s) = 19.8 eV vs. 10.2 eV for H

• Chemically inactive as a result of the large excitation and ionization energies – will not solidify unless low temperatures (4.2 K) and high pressures are used

• Chemically inert gases are called noble or inert

Helium excited state

Helium ground state

In groups, consider (for ~3 minutes):

Compare ionization energies and effective radius of the elements Z=3 Lithium & Z=4 Beryllium

Draw the ground state and excited states

Properties of Lithium3Li: • Ground state: two electrons in 1s state + one electron in

2s state (due to Pauli exclusion principle)• Ionization energy significantly smaller than He: expect Zeff

~1 with n=2, resulting in 5.4 eV• Large effective radius due to occupancy of n=2 level • Reactive as a result of the small ionization energy – can

form compounds such as LiF

Properties of First Ten Elements4Be: • Ground state: two electrons in 1s state + two electrons in 2s state• Larger Z means larger ionization energy than Li (9.3 eV vs. 5.4 eV) • Excitation energy to 2p state is relatively low (2.7 eV) which makes Be

chemically active and allows it to bond to other atoms (forms a solid)• Smaller effective radius due to larger Z than Li

Lowest excited state for Be:

Properties of First Ten ElementsOther elements • Increasing Z causes electrons to be more tightly bound (causing greater

ionization energies), however, higher energy states are occupied, meaning they are less tightly bound (causing lower ionization energies)

• For Z=5 (B) electron goes to 2p state, slightly higher in energy (due to screening) causing binding energy to drop slightly (8.3 eV vs. 9.3 eV for Be). Very pure isolated boron is produced with difficulty, as boron tends to form refractory materials containing small amounts of carbon or other elements.

• For Z=6 (Be) to Z=10 (Ne) electrons go into 2p state causing steady increase in ionization energy and decrease in radius due to increase in Z (all electrons go into n=2 level)

• In going from Z=10 (Ne) (full n=2 shell) to Z=11 (Na, one electron in 3s) level ionization energy suddenly drops due to large increase in occupation energy of n=3 state (Zeff ~1, similar to Li)

Other Properties

Closed-shell elements: noble gases

Closed-shell –plus one (alkali) elements: reactive due to loosely-bound outer electron in s-shell

Closed-shell–minus-one elements (halogens): elements with high electron affinity A (energy gained when an additional electron is added to a neutral atom); will easily form negative ions (take additional electron) in remaining p-shell state due to large nuclear charge; these elements are very reactive (e.g., F- with e.a.=3.4 eV)

Organization of Periodic Table

Columns: groups with similar shells, similar propertiesRows: periods with elements with increasingly-full shells

Dmitri Mandeleev

Metallic/insulating properties can be understood by how loose (i.e. low ionization energy) outer electrons are.

So, on which side of the table are the metals?

Other ElementsAfter 3s23p6 shell (Ar) one would expect (naively) that 3d shell would fill, but in fact the 4s shell fills first due to screening by 3s and 3p electrons which increases energy of 3d shell:

Dynamic periodic tablehttp://www.dayah.com/periodic/

• Transition metals have similar properties• they are metallic due to relatively – loosely bound 4s

electrons• unpaired d-electrons tend to make them magnetic (net

spin)• Inner transition elements (rare earths) result from filling of f-

shells (4f after 6s and 5f after 7s)• f-electrons relatively isolated – result in strong magnetic

properties

In Groups: Rank the Ionization EnergiesFor each of the following sets of atoms, decide

which has the highest and lowest ionization energies and why.

a. Mg, Si, S b. Mg, Ca, Bac. F, Cl, Br d. Ba, Cu, Ne

e. Si, P, N