This is the course blog for Semester 1, 2011 at the University of Queensland

## 4/26/11

### Semimetal and Semiconductor

At T = 0, a pure semimetal behaves as good conductor, as there are some partialy filled electrons and holes band.

At T = 0, a pure semiconductor behaves as insulator, as the carriers are either due to thermal excitation or presence of impurities.

### Fermi Surface

### Reading for next week

Key concepts include:

The many-body Schrodinger equation

Hartree approximation and the self-consistent field

Hartree-Fock approximation and the exchange interaction

Screening

Fermi liquid theory

Singlet-Triplet splitting

## 4/24/11

### How are predictions derived from fermisurface ?

### Fermi surfaces

### Landau Levels

### Necessary condition for observing the quantum oscillation

## 4/22/11

### use of superconductor in train

Ever since the discovery of superconductors, there has been great interest in their use in electronics. It turns out that the magnetic properties of superconductors has been more useful in a larger variety of applications than the lack of resistance.

Maglev trains use superconductors to levitate the train above magnetic rails. This enables them to operate without friction, and therefore acheive unheard of speeds. The maglev train below is being installed at the Old Dominion University in Hampton, Virginia. It is the first to be installed in the US. Unfortunately, due to the short track it is on, it can only reach speeds of 40 miles per hour. Maglevs, with sufficient track, can reach speeds over 300 mph. A new Maglev train in Shanghai recently broke the 500 Km/h barrier (310 mph). These trains are also more efficient because there less energy loss to friction between the train and the track. |

## 4/20/11

### Visualising Landau level filling and the IQHE

## 4/19/11

### de Haas van Alphen Effect

This is a nice little collection of info on the de Haas van Alphen effect I found (might be where Ross pinched some pictures from).

For an example of how you can actually apply the effect to construct the Fermi surface, have a look through this paper:

http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-pub-14075.pdf

If you don't want to get into the gritty details at least check out fig. 2 to look at the relations between measurement and theory.

### Lecture on determination of the Fermi surface

## 4/18/11

### Notes on semi-classical transport theory

## 4/17/11

### New Organic Conductor for Electronic Devices

Now just as fast as silicon plus much cheaper, this inexpensive organic conductor could be used in areas where silicon struggles to compete, eventually slashing the cost of transistors, PDA’s, flat panel screens and bringing electronic paper into common use.

### The Development of Organic Conductors

Metals, Superconductors and Semiconductors. Lecture 2A. Introduction and Synthesis of Important. Conjugated Polymers. Lecture 2B. Solid State Polymerization

Lecture 3. Fullerene Chemistry. Lecture 3B. Molecular Engineering. www.lios.at/VirtualAcademy/.../Organic_Conductors_Intro_Lecture.pdf - Similar

### Filled bands are inert.

### Huckel assumption

### Huckel Method

http://ocw.kyushu-u.ac.jp/3063/0002/lecture/QC_AH3_LM2.pdf

## 4/16/11

### Practice Mid-Semester Question

Has anyone had success with question 2 iv) of the practice mid-semester? I know that:

h^2/2m* = d^2E/dk^2

and have tried a few other methods, but I can't quite seem to get the answer. Any suggestions? I'm figuring I'm probably not taking the approximation near the boundary correctly.

## 4/15/11

### Delocalisation of electrons

## 4/14/11

### Molecular Orbital Theory

### Advantages of organic electronics

One of the main advantages of organic electronics is the possibility of manufacturing components and circuits over large areas, while silicon chips are restricted to the area of circular pads of limited sizes.

Most of these advantages, however, is certainly the fact that organic electronics can be fabricated on plastic substrates, thin and flexible.

Only the flash memory transistor, the silicon component found in the pen-drives in digital cameras and MP3 players, continued to resist the benefits of plastic.

Now, Physicists built the first organic transistor Flash memory plastic.

## 4/13/11

### Huckle Method.

### Reading for next week

The semi-classical theory of conduction in metals

Important equations are

13.11, 13.19

13.22-25

13.44-46

13.58, 13.61

### Magnetoresistance for Open Orbits

For the open orbit case we discussed in the lecture the form of the current:

j = sigma(0)n(n.E) + sigma(1).E

Where n unit vector in the direction of the open orbit. It was argued that the component sigma(1) vanishes in the high-field limit, whereas the sigma(0) contribution does not. This means that unlike the closed-orbit case the magneto-resistance will not approach a constant.

To see this last assertion it is useful to examine a simple case where in the high-field limit the current flow is directed in a direction =/ n, say n'. From our statement above this means that the projection of the electric field, E.n = 0.

Following the working in Ashcroft and Mermin, this gives a particular form for the electric field which I will not write here. Suffice to say, defining the magneto-resistance rho as;

rho = E.j/|j|

One can arrive at the expression:

rho = (n'.j)^2/(n'.sigma(1).n')

Now as we have previously argued that sigma(1) vanishes in the high-field limit we clearly see that the magneto-resistance must diverge, i.e. it grows with increasing magnetic field.

### Lecture notes

## 4/12/11

### Magnetoresistance in orbits

### Semiclassical Electron Dynamics

The semi-classical model looks at the effect on the electron dynamics of external electric or magnetic fields that are approximately uniform over the scale of one such wave-packet. The periodic potential considered in the Bloch model is responsible for the important distinction between the classical and semi-classical models (because the free electron approximation is no longer valid). This potential changes on a scale far smaller than that of the wave-packet, requiring a quantum mechanical treatment.

### Hall Effect

### Revised schedule for this week

Ross McKenzie lectures on transport in the Bloch model

Wednesday noon

Ross gives tutorial looking at old mid-semester exam questions

Wednesday 2pm

Paul Shaw lectures on the relationship between tight-binding and the Huckel model in chemistry.

## 4/11/11

### Assignment 4: due Tuesday May 3

### Slides for electron transport in the Bloch model

They need to be read in parallel with chapter 12 of Ashcroft and Mermin.

## 4/10/11

### A good clip to watch for the introduction to quasicrystal

### Types of Quasicrystals

**quasiperiodic in two dimensions **(polygonal or dihedral quasicrystals)

*There is one periodic direction perpendicular to the quasiperodic layers.*

- octagonal quasicrystals with local 8-fold symmetry [primitive & body-centered lattices]
- decagonal quasicrystals with local 10-fold symmetry [primitive lattice]
- dodecagonal quasicrystals with local 12-fold symmetry [primitive lattice]

**quasiperiodic in three dimensions, no periodic direction**

- icosahedral quasicrystals (axes:12x5-fold, 20x3-fold, 30x2-fold) [primitive, body-centered & face-centered lattices]

**new type** (reported in Nature, Nov.2000)

- "icosahedral" quasicrystal with broken symmetry (stable binary Cd
_{5.7}Yb)

### Types of Quasicrystal

* octagonal quasicrystals with local 8-fold symmetry [primitive & body-centered lattices]

* decagonal quasicrystals with local 10-fold symmetry [primitive lattice]

* dodecagonal quasicrystals with local 12-fold symmetry [primitive lattice]

- In three dimensions (no periodic direction), there is only one type:

* icosahedral quasicrystals (axes:12x5-fold, 20x3-fold, 30x2-fold) [primitive, body-centered & face-centered lattices]

- Interestingly, there is a New type that was reported in Nature, Nov.2000). it is "icosahedral" quasicrystal with broken symmetry (stable binary Cd5.7Yb).

### The reciprocal lattice and first Brillouin zone

### A site showing 2D reciprocal vectors

http://www.matter.org.uk/diffraction/geometry/2D_reciprocal_lattices.htm

This should be helpful for anyone who hasn't figured this out yet.

It's not a perfect site though :P

## 4/9/11

### General form of reciprocal basis vectors

_{i}, is

b_{i} ·a_{j} = 2πδ_{ij}

Where a

_{j}is the real-space basis.

### Why 5 fold symmetry is a problem?

### The definition of quasicrysta

### Penrose and Aperiodic Tiling

http://en.wikipedia.org/wiki/File:Penrose_Tiling_(P1).svg

The symmetry and other properties are completely equivalent between the three styles, and is an example of of substitution. This is where one can break the original shapes into smaller variations, and use these to reconstruct the the tiling.

Due to this possible substitution the tiling shares some features with fractals, in that it may be inflated or deflated, yet present the same image and symmetry.

A list of other forms of aperiodic tiling in various geometries can be found here:

http://en.wikipedia.org/wiki/List_of_aperiodic_sets_of_tiles

## 4/8/11

### Mid-semester exam

The exam is worth 20% of the summative assessment.

We will look at some of the sample questions at next wednesday's tutorial.

### Two helpful websites

**how to generate the reciprocal lattice and to construct Brillouin Zones**.

http://www.doitpoms.ac.uk/tlplib/brillouin_zones/aims.php

Self study material in Solid State Electronics using Multimedia: A great website that

**shows lots of plots for the Crystal structure, Brillouin zones, energy bands and energy surface...**

http://people.seas.harvard.edu/~jones/ap216/lectures/ls_2/ls2_u7/sse_tut_1/solid1.html

## 4/7/11

### The advantage of Bloch model over Sommerfeld model

## 4/6/11

### Next tuesdays lecture

### Reading and some notes for next week

Chapter 12

Take particular note of

Table 12.1

Equations 12.6

subsection: Filled bands are inert

subsection: Holes

Here are some preliminary notes.

### Tight-Binding Model

For anyone interested this collection of slides is a useful discussion of the basics of tight-binding theory. It goes through the same mathematical derivation of the energy eigenvalues, but also gives a good graphical example in k-space.

## 4/5/11

### Wednesday's Tutorial

- A laptop with the software installed
- A copy of the "Bloch" chapter from "Simulations for Solid State Physics". You can download it here if you haven't already done so.

### Schedule for wednesday April 6

noon - Paul will give the tutorial

2pm - Ross will give the lecture

### Tomorrows lecture on quasi-crystals

### Nearly free Electron Metal

## 4/4/11

## 4/3/11

### Bragg plane

### The nth Brillouin Zone

"The nth Brillouin zone is the set of k-space points reached from k=0 by crossing exactly n-1 zone boundaries in the outward direction."

### two ways to proof the Bragg's law

### Bragg and Van Laue diffraction

**n**, where a is the angle between the incident ray and lattice plane. So we reach the Bragg condition which is 2dsina=n* wavelength of incident ray.

### Ewald's sphere

## 4/2/11

### Fermi surface

### Cleavage (crystal)

Cleavage is an important mechanism in examining the structure of solids and also in some industries. Some crystals have the probability to split along certain crystal planes. And because of the repeated structure these distinct and week planes repeat and become visible even to the naked eye.

Pic. ref.: ( http://www.doitpoms.ac.uk/tlplib/atomic-scale-structure/single2.php?printable=1)