2009.02.25-ECE659-L19-notes

2009.02.25-ECE659-L1 - ECE 659 Quantum Transport Atom Atom to Transistor Lecture 19 Self Energy Supriyo Datta Spring 2009 Notes prepared by Samiran

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ECE 659 Quantum Transport: Atom Atom to Transistor Lecture 19: Self Energy Supriyo Datta Spring 2009 Notes prepared by Samiran Ganguly Σs Γ j = i Σ j − Σ Σin = Γ j f j j + j Σ1 Σ2 µ1 H [ EI − H − Σ]ψ = s G n = 2πψψ + Σin = 2π ss + When reservoir and channel are disconnected µ2 2t t [ EI − H ]ψ = 0 [ EI R − H R ] Φ R = 0 To connect a battery to the reservoir: ( E + iη ) I R − H R Φ R = sR HR H η allows an electron to go out of the reservoir χ = GRτ +ψ HR where H GR = ( E + iη ) I R − H R now −1 ( EI − H ) − τχ = τ Φ R EI − H −τ + −τ ψ 0 = E + iη ) I R − H R Φ R sR ( gives [ EI − H − Σ]ψ = s Σ = τ GRτ + s = τ ΦR −τ gives the coupling between reservoir and channel Φ R is changed due to that EI − H −τ + −τ ψ 0 = E + iη ) I R − H R Φ R + χ sR ( R R R Γ = i Σ − Σ+ Γ = iτ GR − GR + τ + = τ ARτ + Σin ∼ τ Φ R Φ +τ + → τ ARτ + f → Γf R ( ( E + iη ) I − H ) Φ + ( ( E + iη ) I − H ) χ R R −τ +ψ = sR τ 2t For 1 column: τ −t 2t −t τ β α α β * H = α β αβ * β α ⋱ ⋱ ⋱ τ g1 = ( E + iη ) I − α For 2 columns: −1 β g 2 = ( E + iη ) I − α − β g1β + g n +1 = ( E + iη ) I − α − β g n β + −1 −1 We need top 3x3 elements of: ( E + iη ) I R − H R −1 In general: This can be solved recursively till gn+1 and gn converge In 1-D wire: 1 Σ = −teika = t 2 − eika t with α = 2t β = −t Gives the same result with τ GRτ + ...
View Full Document

This note was uploaded on 01/30/2011 for the course ECE 659 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

Page1 / 5

2009.02.25-ECE659-L1 - ECE 659 Quantum Transport Atom Atom to Transistor Lecture 19 Self Energy Supriyo Datta Spring 2009 Notes prepared by Samiran

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online