Research Projects

Guidelines

The idea of a Research Project is to tackle a topic borrowed from research frontiers (such as from recently published in journal articles) while spending more time on researching literature, doing computation, and compiling a report than it is usually required for simple homework problems. When you have enough results to tell a coherent story, you should end the Research Project by writing (in a clear writing style, obeying the rules of grammar and spelling) and submitting a Report. The Report should be understandable to a person who has not done the assignment.

Format of the report for the midterm project

The midterm project should be finalized as a paper similar to research articles dealing with Mesoscale and Nanoscale Physics posted every day on arxiv.org. The format of the paper mimicking this is:

• Title, Name of the person and affiliation, Abstract, Introduction, Methods, Results, Dicussion, Conclusion, and References.

• Paper should be typed in two column style. For this you can use:
  • LaTeX in the form of RevTeX style for Physical Review journals, as implemented by PHYS 824 template and the embedded EPS figure for this example. You can also find more examples of typing mathematical formulas in Math into LaTeX: How to Beautify Equations (and the embedded EPS figure).
  • Open Office version of Microsoft Word (Word itself is not advisable since you need additional programs, such as MathType, on the top of it to be able to type equations).

Format of the report for the final project

The final project will be reported through a Poster Session, during the final exam time, and it will also include peer reviewing. To make a poster, you can use this PowerPoint Template. Poster printing is available in Smith Hall and its cost will be covered by the Department.

Midterm Research Project

The project explores recently discovered graphene nanoribbons (GNRs) by computing their electronic structure as equilibrium property using simple tight-binding method and more involved density functional codes:

a) Using the nearest-neighbor tight-binding Hamiltonian with single $p_{z}$ orbital per carbon atom, compute the subband structure of three armchair GNRs whose width is $N_{a}=4,5,30$. The expected result is shown in Lecture 9.

b) Using the nearest-neighbor ($t_{1}=2.7$ eV) tight-binding Hamiltonian with single $p_{z}$ orbital per carbon atom, compute the subband structure of three armchair GNRs whose width is $N_{z}=4,5,30$. The expected result is shown in Lecture 9. Plot the amplitude squared of the transverse part of the eigenfunction (i.e., conducting channels) close to the Dirac point $E=10^{-3}\gamma$ for $N_{z}=30$. This plot should show that probability to find electron peaks around the nanoribbons edges.

c) Repeat subband structure calculations for $N_{a}=5$ AGNR and $N_{z}=5$ ZGNR using the tight-binding Hamiltonian which includes up to third-nearest neighbour hoppings whose values are: $t_{1}=2.7$ eV, $t2=0.20$ eV, and $t3=0.18$ eV.

d)

e) Using DFT code SIESTA (installed of fermi), compute subband structure for $N_{a}=5$ AGNR and $N_{z}=5$ ZGNR and compare this with your result in c).

MAIN REFERENCE: A. Cresti, N. Nemec, B. Biel, G. Niebler, F. Triozon, G. Cuniberti, and S. Roche, Charge transport in disordered graphene-based low-dimensional materials, Nano Research 1, 361 (2008). [PDF].