Nanoelectronics course

The properties of the world's smallest refrigerator can be studied with the methods introduced in this course. For more information, see



Tfy-3.4801: Low Temperature Physics: Nanoelectronics (L, 6 cr)

Time: Fall 2009

Lectures (Doc. Tero Heikkilä) on Tuesdays at 10-12 in Nanotalo room 228. First lecture on the 8th of September.

Exercises (Janne Viljas): on Thursdays at 14-16 in Nanotalo room 228. First session on the 10th of September

Previous exam on 15.12. 2009 at 9-12 in K216 (department of mechanical engineering building). Results are available here!

Next exam on 9.2. 2010 at 16-19 in K215 (department of mechanical engineering building)

Information on the exam: The chapters included in the exam are those discussed in the lectures, i.e., Ch. 1-7 and 10-13, including the separate notes on molecular electronics, excluding the sections marked with the stars from both notes. You can take the lecture notes with you to the exam.

Problem solving sessions

The students get points from each exercise that they have solved and marked in the list at the problem solving sessions. The exercise points are added to the points of the exam such that full exercise points lead to approximately one grade increase to the grade of the exam.

  1. Problems for the first session: problems 1.1-1.4 from the lecture notes.
  2. Problems for the second session: problems 1.5-1.7 and 2.4 from the lecture notes.
  3. Problems for the third session on 24th Sep: problems 2.1-2.3 and 2.6 from the lecture notes. Hint for problem 2.6: expand the 3D density of states (see Eq. (1.5)) to the first order in energy and use this in the Mott relation.
  4. Problems for the fourth session on 1st Oct: problems 3.1-3.3 and 3.7 from the lecture notes. Due to the cancellation of the lecture, these will be on the same week as the lecture about the third chapter. Those who want to solve the problems already beforehand can use the present version of the notes, which will not change much before Tuesday's lecture.
  5. Problems for the fifth session on 8th Oct: problems 3.3, 3.5, 3.6 and 3.8 from the new set of lecture notes. Note that problem 3.3 was added in the most recent version!
  6. Problems for the sixth session on 15th Oct: problems 4.1-4.3 (note that the newest versions of the lecture notes contain only those three problems in Ch. 4) and problem 5.1. Additional hint for 4.3: think what happens to the conductance of a 2d conductor as both its width and length are increased.
  7. Problems for the seventh session on 22nd Oct: problems 5.2, 5.3, 5.5 and 5.11. There were some minor typos in the exercises - you can download the latest version of the lecture notes to find them out. Note that exercise 5.11 was a bit ill-defined. You can use the new version that can be found from the new lecture notes!
  8. Problems for the eight session on 5th Nov: problems 5.4, 5.6, 5.7 and 5.10. Use the latest version of the lecture notes.
  9. Problems for the ninth session on 12th Nov: problems 6.1, 6.4, 6.8 and 6.10. Note: use the latest version of the lecture notes (there was a sign error in 6.1 in the old version). Note 2: There is no exercise session on Thursday Nov 12th. You should return your solutions on paper by noon, Friday 13th to LTL room 177.
  10. Problems for the tenth session on 19th Nov: problems 6.2, 6.9, 7.3 and 7.4.
  11. Problems for the eleventh session on 26th Nov: problems 2, 3, and 5 from the molecular electronics lecture notes. As the fourth problem you can choose either problem 1 or 9. Please use the most recent version of the notes! Small modifications have been made in several places.
  12. Problems for the twelfth session on 3rd Dec: problems 11.1, 11.2, 11.3 and 11.4. Note: use the latest version of the lecture notes (there was a serious sign error in Eq. (11.3) and a few other typos). If the general problem is too hard, in 11.2 and 11.4 you can also assume a limit of dominating tension/force.
  13. Problems for the last session on 10th Dec: problems 10.1-10.4. Use the latest version of the lecture notes.

Topical issues

  • Please give feedback on the course using this link. Note that there was a problem with the previous version of the web address - now it should work. It should work within the tkk/hut domain. If it does not, please email Tero at Tero.Heikkila at tkk.
  • Lecture notes for molecular electronics are available here. (Updated 26.11.2009: list of references was extended.)
  • No exercise session on Thursday Nov 12th! See above.
  • Note that there are no lectures or problem solving sessions during the exam week starting 26th October
  • The extra lecture took place on Thursday 5.11. at 12-14. The excursion to the Low Temperature Laboratory will be held on Wednesday 11.11. at 10-12.
  • The rest of the lecture notes have now been updated. Download them here. (Updated 8.12.2009).
  • I ran out of candies already during the third lecture! Well done! Or perhaps the candy bags are nowadays smaller than they used to be...

Lecture notes

The lecture notes will be updated by the beginning of each lecture. You can download the 2009 version from here. To report errors, typos or poorly explained sections, please use this form. Note that the lecture notes are password protected - you can get the password from Tero Heikkilä. If you only wish to see the contents of the course, you can get them from here.

The lecture notes for molecular electronics may be found here.

Course description

Nanoelectronics is one of today’s big fields of physics research. It enables the study of many fundamental topics, such as the transition from the quantum-mechanical microscopic world to the macroscopic everyday scales or quantum engineering where phenomena familiar from atomic physics are studied in up to micron-size structures with highly tunable physical parameters. At the same time, a thorough understanding of the transport phenomena is of a paramount importance when designing ever smaller electronic devices. This course details the most relevant phenomena encountered in nanoelectronic circuits, e.g., Coulomb blockade, interference effects and noise, and discusses some of their uses in novel electronic applications. It also introduces the theoretical models that are usually applied to study these phenomena, such as the scattering theory, Boltzmann transport equation and the master equations.

The course is aimed for advanced undergraduate or for graduate students and it assumes basic knowledge of quantum mechanics and solid state physics.

Tentative contents of the course:

  1. Introduction to basic notions and the most relevant systems including metallic or semiconducting systems, carbon nanotubes and graphene
  2. Semiclassical Boltzmann theory
  3. Scattering approach
  4. Interference effects
  5. Fluctuations and correlations
  6. Single-electron tunneling and Coulomb blockade
  7. Quantum dots
  8. Molecular electronics (lectured by Janne Viljas)
  9. Mesoscopic effects in graphene
  10. Dissipation in quantum mechanics
  11. Nanoelectromechanical systems

Properties of superconducting junctions have been removed as there is another course dedicated to them. However, in case of strong desire to include them I may reconsider.


In the course, we mainly follow the lecture notes, but many of the topics have obviously been published in different books or review articles. For such references, see

  1. Basic mesoscopic physics: Y. Imry, Introduction to Mesoscopic Physics, 2nd edition, Oxford University Press, 2002. A more advanced book, covering most of the topics in this course, is Yu. V. Nazarov and Ya. M. Blanter: "Quantum Transport - Introduction to Nanoscience", Cambridge University Press, 2009.
  2. Semiclassical Boltzmann theory: H. Smith and H. H. Jensen, Transport Phenomena, Oxford University Press, 1989; F. Giazotto, et al., "Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications", Rev. Mod. Phys. 78, 217 (2006).
  3. Scattering approach: S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, 1995.
  4. Interference effects: above Datta's book, Ch. 1 in T. Dittrich, et al., Quantum Transport and Dissipation, Wiley-VCH, 1998, and the book M. Janssen: "Fluctuations and Localization in Mesoscopic Electron Systems", World Scientific, 2001.
  5. Noise: General properties of noise can be found in the book by Kogan: Electronic noise and fluctuations in solids (Cambridge, 1996). Linear response theory and the associated fluctuation-dissipation theorem is found in many advanced statistical physics texts, such as Ch. 10 in M. Plischke and Birger Bergersen: Equilibrium Statistical Physics (2nd Ed., World Scientific, 1994). An exhaustive review of shot noise is Ya. Blanter and M. Büttiker: Shot noise in mesoscopic conductors, Phys. Rep. 336, 1 (2000) and can be also found at arXiv:cond-mat/9910158.
  6. Single-electron tunneling and Coulomb blockade: Ch. 3 in the book by T. Dittrich, et al.
  7. Transport through Quantum Dots: Ch. 8-10 in the book H. Bruus and K. Flensberg, Many-Body Quantum Theory in Condensed-Matter Theory: An Introduction (Oxford University Press, 2004); on Kondo effect: Leo Kouwenhoven and Leonid Glazman: Revival of the Kondo effect, Physics World 14, 33 (2001).
  8. Superconductivity: M. Tinkham: Introduction to Superconductivity (McGraw-Hill 1996).
  9. Superconducting junctions: also the book by Tinkham, and the review by F. Giazotto, et al. (see chapter 2 above).