Advanced Solid State Physics

12 Electron-electron interactions, Quantum electronics 12.1 Electron Screening For a single electron in vacuum Gauss’s law is ∇· ...

Figure 84: Unscreened and screened potential. So the resulting potential is V = −exp (−k|r−r′|) 4 πε|r−r′| . (182) Fig. 84 shows ...

Figure 85: STM picture of GaAs doped with Si at Ga-sites. 12.2 Single electron effects 12.2.1 Tunnel Junctions A tunnel junction ...

tunnel through the barrier because below all the states on the right side are filled and above there are no electron states occu ...

12.2.2 Single Electron Transistor Figure 87: Single electron transistor. In fig. 87 you can see a single electron transistor wit ...

suppressed or at its maximum. Figure 89 shows the set up and its circuit. island gate 2 gate 1 source drain V 1 Vg1 Vg2 V 2 Cg1 ...

and from the island on the second electrode or from the second electrode on the island. The relating change in energy is as foll ...

Figure 91: Experimental data: current as a function ofVbandVG. Figure 92: Coulomb staircase. Figure 92 shows the so-called Coulo ...

Now we have a look at the charging time of the capacitance which isRCΣ. If this charging time is much faster than a quantum fluc ...

Figure 93: Uniform tunnel barrier; Random tunnel barriers, some with resistance above the resistance quantum. make a transition ...

Figure 94: Semiconductor at low temperature: P in Si. and become one big crystal and the conductivity gets better. If they are w ...

Figure 95: Small crystals as a model to describe a Mott insulator. R T critical Resistance insulator metal Figure 96: T vs. R; s ...

Figure 98: Periodic distortion of a one dimensional lattice with lattice constant 2 a. bands), if there is an odd number of atom ...

Figure 100: Plot of the band gap atk = 2 πa One example for a Peierls transition is shown in fig. 101. Due to two different type ...

I V Figure 102: Current flow ofNbSe 3. If an electric field affects on the material the current increases and the charge density ...

13 Optical Processes In chapter 10.1 (Linear Response Thoery) we derived the Kramers-Kronig relations. The Kramers- Kronig relat ...

HerePrepresents thePrinciple part, which is important because at a particular pointω′ = ωthe integral gets undefined (singularit ...

Figure 103: Response of a mass spring system with ω 0 = √ k m Fig. 103 shows an expected response of a mass spring system. At lo ...

Figure 104: Dielectric response of an insulator. The dotted line represents the real part, the solid line the imaginary part. fr ...

Figure 105: Example of a quantum calculation with two harmonic oscillators Figure 106: Infrared absorption of a thin material ...