This website uses cookies to ensure you have the best experience. Learn more

Project In Graphene And Silicene Essay

5111 words - 21 pages

PHYS3531 Physics Project

Multi-valley monolayer materials

Fok Hong Ting

Under the supervision of
Dr. Wang Yao

Acknowledgement 4

Introduction 5
Motivation 5
Project outline 5

Chapter I Tight binding model 6
Basics 6
The secular equation 8
Conclusion 9

Chapter II Graphene 11
Formulation 11
π energy band of graphene 15
σ energy bands of graphene 17
Conclusion 18

Chapter III Silicene 19
Tight Binding Hamiltonian of silicene without SOC 20
Constructing orthogonal basis 21
...view middle of the document...

Project outline
In this project, we try to investigate the band properties of graphene and silicene with tight binding method. The principal of tight binding method is discussed in Chapter I.
In Chapter II, we will formulate a tight binding Hamiltonian for graphene and calculate its energy band structure.
In Chapter III, we will include SOC effect in the calculation of silicene energy bands and look for an analytical solution.
Finally, in Chapter IV, we focus on investigating the edge states of both graphene and silicene.

Chapter I Tight Binding Method

In this section we explain the tight binding method. In our model, we assume the material is a perfect lattice. It has no defects and can be produced by choosing a suitable unit cell.

Because of the translational symmetry of the unit cells in the direction of the lattice vectors, ai (i = 1,2,3,) , any wave function of the lattice should satisfy Bloch's theorem:
TaiΨ=eik∙aΨ ,(i=1,2,3)
where Tai is a translational operation along the lattice vector ai, and k is the wave vector.

There are many possible functional forms of Ψ which satisfy this equation and the most commonly used form for Ψ is a linear combination of plane waves.

Plane waves are used because of the following reasons:
1. The integration of the plane wave wavefunction is easy and can be done analytically,
2. The numerical accuracy only depends on the number of the plane waves used.

However, the plane wave method also has limitations:
1. The scale of the computation is large,
2. It is difficult to relate the plane wave wavefunction to the atomic orbitals in the solid.

Another functional form which satisfies the above equation is based on the jth atomic orbital in a unit cell. This is a tight binding, Bloch function:
Фjk,r=1NRNeik∙Rρj(r-R), (j=1,2,…n)
Where R is the position of the atom and ρj denotes the atomic wavefunction in state j.

The number of atomic wavefunctions in the unit cell is denoted by n, and we have n Bloch functions in the solid for a given k. The ρj in the N unit cells are weighted by the phase factor eik∙R and are then summed over the lattice vectors of the whole crystal.

The advantages of using orbitals in Bloch functions are as follows:
1. The number of basis functions can be small compared with the number of plane waves.
2. The formula for many physical properties can be easily derived.

The eigenfunctions in the solid Ψj are expressed by a linear combination of Bloch functions Фj' as follows:
Ψjk,r=j'=1nCjj'(k)Фj' (k, r)
where Cjj' are coefficients to be determined.

Then, the j-th eigenvalue as a function of k is given by:
Here Hjj'(k) is the transfer integral matrices and Sjj'(k) is the overlap integral matrices, respectively.

The secular equation
For a given k value, Cij is optimized so that Ej is minimized.

Other Papers Like Project in Graphene and Silicene

Analysis Project: Kudler Fine Foods Outsourcing and in-House Photography

1155 words - 5 pages Analysis Project: Kudler Fine Foods Outsourcing and In-House Photography IT/235 Brook Dennen May 09, 2014 Kudler Fine Foods: Outsourcing and In-House Photography Deciding on whether to outsource your photography to a professional photographer or keep them in-house depends on many factors. There are numerous benefits to outsourcing and using a professional photographer. But, as a business, Kudler Fine Foods must review both the

Mba in Project and Construction Mnagement

818 words - 4 pages The Reinforcement Theory of Motivation includes 4 aspects: Positive, Negative, Punishment, Extinction.           Positive reinforcement – When the employees work hard, have done work well, and bring some interests for the organization, the organization will give some rewards to motivate them.           For example: In a company, the employees’ work exploits will be showed in the notice board every month. The best employee should be given some

The Effect Of Different Level Of Npk 15:15:15 Fertilizer On The Vegetative Growth And Yield Of Tomato (Lycopersicon Esculentum) In Yandev. Area Of Benue State A Project Research Work Submitted To...

5426 words - 22 pages height at 4th WAP iii) Plant height at 6th WAP iv) Number of flower at 10th WAP v) Number of fruit at 14th WAP vi) Weight of fresh fruit Kg/plot at harvest 3.11 Statistical Tool and Data Analysis In order to obtain the needed result of the project, the researcher employed the use of tables, percentage and mean. Statistical model design to determine whether the four treatment as represented by their means are significant different

Advanced Materials. Global Industry Analysis

1904 words - 8 pages in advanced materials are global drivers of other connected industries and companies which are operating and leading in each specific industry are always looking for new inventions in this sphere. One of the industries which are most interesting now for scientists is nanotechnology. It will definitely develop our future and will lead us to revolutionary inventions. For instance new material “Graphene ” was created in 2004 and has great potential

The Market Aspect of Ito

1862 words - 8 pages transparency, tunability across a wide range of optical wavelengths, and excellent mechanical flexibility make graphene a very promising candidate for flexible transparent conductors. Conclusion: To conclude we can say that ITO is a material used in a lot of domains. IT’s used for his consistency and reproducibility, ability to produce large displays, mature technology, for his optically transparency, and for his electrically conductivity

Chemistry in 2050

3060 words - 13 pages Biopackaging has numerous uses for packaging food, water, cosmetics and medicines and is being used in many different countries around the world. It is better for people’s health, the environment and Our Future Planet. Bio-plastic technology is an important step on the road to a more sustainable society. Mahendra Kalra,K.V.No 1 Kota 2. Nanotechnology & Picotechnology using Graphene as material in 2050. Graphene is a transparent single layer


2032 words - 9 pages tend to shows different properties and have a different application in different fields. Diamond is a common allotrope of carbon that exhibits hardness and has a high ability to disperse light. Diamond is the hardest discovered mineral and industries find it useful in cutting and drilling of other elements. It is also used to manufacture jewelry. Graphite is another common allotrope of carbon. Graphite is formed in a single layer by graphene that


1347 words - 6 pages to the graphene surface. This could result in a higher amount of storage and a lighter fuel tank. Another major field that uses nanotechnology and will benefit from it greatly is in the field of medicine. Professor Johannes Heitz from the University of Linz, Austria said, “About 10 years ago, scientists discovered the important influence that nano-structures had on the way a line of cells would develop. It was the beginning of an entire new

Supercapacitors Market: Global Industry Analysis and Forecast 2016 - 2022

1345 words - 6 pages in the near future. The leading players in the industry includes Advanced Capacitor Technologies, Inc., Axion Power International, Inc., CAP-XX Ltd., EEStor Corporation, ELTON, Inc., FastCAP Systems, Inc., Graphene Energy, Inc., Maxwell Technologies, Inc., and Nesscap Energy, Inc. Request TOC (table of content), Figures and Tables of the Report: The report covers exhaustive analysis on

Carbon Nanotubes

1201 words - 5 pages graphene sheets into a seamless cylindrical shape with open ends. Then cylinders spliced into many small fragments with diameter ranging from 1 to 100 nm and couple micrometer in length. Since raw CNTs are not soluble, rendering these molecules with functional organic groups were strictly essential for biomedical applications. Due to the uniquely large surface area, CNTs are capable of absorbing and conjugating with a variety of therapeutic

Project Plan

1201 words - 5 pages What is a Project Plan? The Project Plan is the central document by which the project is formally managed. A Project Plan is a document which lists the activities, tasks and resources required to complete the project and realise the business benefits outlined in the Project Business Case. A typical Project Plan includes: • A description of the major phases undertaken to complete the project • A schedule of the activities, tasks, durations

Related Essays

Project And Program In A Organization

621 words - 3 pages Question 1: A. What is the deference between a Project and Program in a organization with example and justification Answer: Definition of a Project A project is a temporary entity established to deliver specific (often tangible) outputs in line with predefined time, cost and quality constraints. A project should always be defined and executed and evaluated relative to an (Executive) approved business case which balances the costs

Ppp And Project Financing In Logistics Infrastructure

2337 words - 10 pages Project Finance and Private Public Partnership in financing logistics infrastructure. Introduction Finance scholars acknowledge a clear-cut distinction between corporate finance and project finance. The two techniques are considered as basically different approaches to the problem of raising debt to fund capital investments. In corporate finance lenders assess the creditworthy of a whole company, evaluating the going concern, the full range of

Project Management And Success In Academic Research Essay

3103 words - 13 pages PROJECT MANAGEMENT AND SUCCESS IN ACADEMIC RESEARCH Lori Criss Powers   Dr. Gillian Kerr May 21, 2009 Abstract: Conventional project management approaches do not seem to work well in academic research. In our experience, problems include resistance to basic project management processes like milestone development, extended delays caused by researchers not responding to emails or phone calls, a consistent lack of clarity regarding project

Discipline, Profession, And Growth Of Project Management In An Organisation

753 words - 4 pages Projects have ‘being undertaken in a rudimentary form back beyond the Romans to early civilizations,’(Walker and Dart, 2011, p.4-16) from building the ‘Great Wall of China’, to ‘The Great Pyramid of Giza’ (Haughey, 2013) and notable architectural buildings that are still in existence today. Project management tools such as program evaluation review technique (PERT) and critical path method (CPM) came into effect between 1956 to 1958 (Azzopardi