NOTE: This is an old course page. Information about current courses can be found from here

Kyl-0.108 NANOPHYSICS

Nanophysics is one of the most fascinating fields of modern-day physics. It combines both the fundamental research and the aim for useful applications. In nanoelectronic circuits quantum phenomena characteristic for microscopic systems show up in easily measurable quantities such as currents and voltages. This course gives the students an overview of the basic phenomena taking place in nanoelectronic circuits at low temperatures, including single-electron and phase-coherent effects, noise and dissipation, and discusses some of their applications ranging from nanoscale transistors to quantum computing.

This course will be lectured during the Fall term 2005. The first lecture is on 22.9.

The course amounts to 3 credit points (according to the old system).

Lecturer: Dr Tero Heikkilä

Assistant: Pauli Virtanen

Lectures: Thursdays 15.30-17.15 Hall F3 (Note the time!)

Exercises: Mondays 12-14 Hall F2 (starting Sep 26th)

The course will also contain an excursion to the experimental nanoelectronics research groups (nano and pico) at the Low Temperature Laboratory

Language: English if the number of non-Finnish speakers is non-vanishing. The lecture notes will be in English.

Passing: Whole-term exam + points from the exercises

The course is recommended for interested undergraduate and graduate students with basic knowledge on quantum mechanics and solid state physics (for example, have passed courses Tfy-44.126 and Tfy-3.362).

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Results

• Exercise points
• Total points

Note that the first exams take place on Thursday the 15th December at 9-12 in the Hall F1.
This was different in an earlier exam schedule.

Lecture notes:

• PDF (Updated Dec 9th - now corrected the typos and errors found in the last lecture)

Low Temperature laboratory excursion was held on Thursday 13th October, at 10 am.
Dr Juha Vartiainen was your guide.

Exercises:

• Exercise 1. PDF (On Mon Sep 26th)
  Problems 1, 2, 3, 4, and 5 from Chapter 1 in the lecture notes.
• Exercise 2. PDF (On Mon Oct 3th)
  Problems 1, 2, 3, and 4 from Chapter 2 in the lecture notes.
• Exercise 3. PDF (On Mon Oct 10th)
  Problems 1, 2, 3, and 4 from Chapter 3 in the lecture notes.
• Exercise 4. PDF (On Mon Oct 17th)
  Problems 1, 2, and 3 from Chapter 4 in the lecture notes.
• Exercise 5. PDF (On Mon Oct 31th. Note that there are no exercises on Mon Oct 24th, due to the exam week.)
  Problems 1, 2, 3, and 4 from Chapter 5 in the lecture notes.
• Exercise 6. PDF (On Mon Nov 7th)
  Problems 5-7 from Chapter 5. Note that in the second problem (problem 5.6), you should assume T=0. This was not stated in the previous exercise sheet.
• Exercise 7. PDF (On Mon Nov 14th)
  Problems 1, 2, and 3 from Chapter 6 and problem 1 from Chapter 7 in the lecture notes.
• Exercise 8. PDF (On Mon Nov 21st)
  Problems 2-5 from Chapter 7 in the lecture notes.
• Exercise 9. PDF (On Mon Nov 28th)
  Problems 1-4 from Chapter 8 in the lecture notes.
• Exercise 10. PDF (On Mon Dec 5th)
  Problems 5 and 8 from Chapter 8 and 2 from Chapter 9 in the lecture notes.

Solutions:

• PDF (Dec 15th, fixed mistake in 5.3.)
  Solutions to problems in exercises.

Tentative schedule:

1. General concepts
   Studied systems
   Energy, time and length scales
   When is Ohm's law valid and when it is not, how is it broken?

2. Scattering theory of quantum transport
   Reservoirs, leads and scattering states
   Scattering matrix
   Landauer formula
   Resistance of a ballistic low-dimensional contact
   Connection to the Drude formula

3. Interference effects in quantum wires
   Weak and strong localization
   Aharonov-Bohm effect
   Universal conductance fluctuations
   Dephasing

4. Semiclassical Boltzmann equation
   Distribution function and its kinetic equation
   Different forms of scattering
   Diffusive limit and Drude formula
   Thermoelectric effects

5. Single-electron tunneling and Coulomb blockade
   Tunnel Hamiltonian and Anderson model
   Sequential tunneling
   Quantum dots
   Single-electron transistor SET
   Dynamical Coulomb blockade, effect of environment
   Higher-order effects: cotunneling, Kondo effect
   Applications: transistor, thermometer

6. Introduction to superconductivity
   Basic concepts: dissipationless transport, pairing, energy gap
   Josephson effect
   Tunnel structures: quasiparticle current and supercurrent
   Andreev reflection and proximity effect

7. Small Josephson junctions and open quantum systems
   RCSJ model
   Hamiltonian of a Josephson junction
   Superconducting SET
   Dissipation in quantum systems: Caldera-Leggett -model

8. Noise I
   Fluctuation-dissipation theorem
   Thermal and quantum noise
   Shot noise: effective charge
   Noise in electric circuits
   Symmetrization and frequency dependence

9. Noise II
   Effect of noise in small systems
   Cross correlations
   Full counting statistics

10. Linear response theory (if time allows)
    Hamiltonian
    Response functions
    Derivation of the fluctuation-dissipation theorem
    Connection to the measurement theory

11. Advanced topics (if time allows)

Literature

Datta: Electron Transport in Mesoscopic Systems

T. Dittrich, P. Hänggi, G.-L. Ingold, B. Kramer, G. Schön, and W. Zwerger: Quantum Transport and Dissipation

Ya. A. Blanter and M. Büttiker: “Shot Noise in Mesoscopic Conductors”, Physics Reports 336, 1 (2000)

F. Giazotto, T. T. Heikkilä, A. Luukanen, A. M. Savin, and J. P. Pekola: “Electronic refrigeration: Physics and Applications”