Computational Solid State Physics 計算物性学特論第１０回 10. Transport properties II: Ballistic transport.

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Presentation transcript:

Computational Solid State Physics 計算物性学特論第１０回 10. Transport properties II: Ballistic transport

Electron transport properties l e : electronic mean free path l φ : phase coherence length λ F : Fermi wavelength

Tunneling transport I L

Current in one-dimension T(k): transmission coefficient

Total current in one-dimension

Low bias limit : conductance at low temperatures

Landauer ’ s formula ： transmission coefficient ： Conductance ： Quantum conductance ： Quantum resistance I: current, V: bias

Two- and four- terminal measurements

Tow- and four- terminal measurement 2-terminal measurement 4-terminal measurement

Conductance of a quantum point contact

Only one channel (n=1) is open. for n=1 Conductance of a quantum point contact Quantization of transverse motion

Nanowire of Au

Mechanically Controllable Break Junction

Histogram of conductance of a relay junction

Conductance through a quantum dot

:Lorentzian broadening of resonant tunneling through quantized energy E N of a dot :Thermal broadening Tunneling current via quantum dot

A bound state and a resonant state

Transmission coefficient for resonant tunneling If T L =T R

Transmission coefficient of a resonant-tunneling structure

Characteristics of resonant tunneling diode

Resonant tunneling current :wave function :energy

Large bias and low temperature limit Total resonant tunneling current

Transmission coefficient for resonant tunneling If T L =T R

Profile through a three-dimensional resonant-tunnelling diode. The bias increases from (a) to (d), giving rise to the I(V) characteristic shown in (e). The shaded areas on the left and right are the Fermi seas of electrons. Profile through a three-dimensional resonant tunneling diode

Problems 10 Calculate the density of states for free electrons in one, two and three dimensions. Calculate the ballistic current in two dimensions. Calculate the transmission coefficient for a square barrier potential. Calculate the transmission coefficient for a double square barrier potential.