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Quantum Materials Summer School
May 25-28, 2009

Stephen Julian (Toronto)

Talk 1: Theory of Quantum Oscillation Measurements
In this seminar I will outline the basic, semi-classical, theory of quantum oscillations: orbit quantization, extremal areas, oscillation frequency (the Onsager relation), effect of impurity scattering (Dingle effect) and the temperature dependence of  oscillations (Lifshitz-Kosevich relation and beyond).

The appearance of oscillations in various physical quantities will be discussed, including magnetic susceptibility oscillations (the de Haas van Alphen effect), resistivity (Shubnikov-de Haas effect), Hall voltage, sample volume, specific heat, etc..

The talk will be illustrated by classic measurements of Fermi surfaces and quasiparticle properties.

Talk 2: Quantum Oscillation Studies of Strongly Correlated Electron Systems
This seminar will present recent measurements in cuprates, heavy fermion systems, organics, etc., discussing both the measurement techniques used and the interpretation of results.  Recent advances such as the use of pulsed magnets reaching up to 70 T will be emphasized.

References
There are no recent reviews, and the textbooks are out of print, but available in most libraries.

  1. D. Shoenberg, Magnetic Oscillations in Metals, Cambridge University Press (Cambridge, 1984)
  2. A.B. Pippard, Magnetoresistance in Metals, Cambridge University Press (Cambridge 1989)
  3. A.V. Gold, in Solid State Physics, Electrons in Metals, vol. 1,
    ed. J F Cochran and R R Haering (New York, Gordon and Breach, 1968)
  4. A. McCollam et al., Physica B, vol 403, pp 717-720. "de Haas van Alphen in heavy fermion compounds -- effective mass and non-Fermi-liquid behaviour"
  5. N. Doiron-Leyraud et al., Nature vol. 447, pp 565-568, and citations thereof. "Quantum oscillations and the Fermi surface of an underdoped high-Tc superconductor"
  6. B. Vignolle et al., Nature vol. 455, pp. 952-955, "Quantum oscillations in an overdoped high-Tc superconductor."

Igor Herbut (SFU)

Emerging Relativity in Graphene
About four years ago the single two-dimensional layer of graphite, the so-called graphene, has been successfully isolated. In spite of its utter simplicity, thousands of research papers, and numerous reviews in essentially all popular science magazines have been devoted to it ever since. Why? From the physicist's point of view the reason is that the electronic excitations in graphene behave like quasi-relativistic massless particles with a velocity of about 1/300 of the speed of light. In this pedagogical talk I will explain how this feature emerges from the honeycomb structure of the graphene's crystal lattice, and then discuss some manifestations of this novel two-dimensional "relativistic" physics in presence of magnetic fields, electron-electron interactions, and wrinkling of the graphene sheet.  

Useful literature

  1. A. H. Castro Neto, F. Guinea, and N. M. Peres, Physics World vol. 19, No. 11, 33 (2006), for a popular account.
  2. A. K. Geim and K. S. Novoselov, Nature Materials vol. 6, 183 (2007), for a review by graphene's discoverers themselves.

Marcel Franz (UBC)

Lecture 1: Exact Quantization in Solids
Certain physical observables in certain solids are precisely quantized despite the fact that the solid may contain imperfections. Two best known examples of this phenomenon are the flux quantization in a superconductor and the Hall conductance quantization in a quantum Hall liquid. Modern understanding of this exact quantization involves the concept of topological order. In this lecture I will review the basic relevant facts and discuss topological order in some detail.

Lecture 2: Intro to Topological Insulators
Over the past 3 years a new type of topological order has been discovered, first theoretically and then (!) experimentally, in ordinary band insulators that respect the time-reversal symmetry (i.e. non-magnetic insulators). The precisely quantized physical observable here is the number of robust gapless states associated with the material's surface, modulo 2. In this lecture I will attempt to convey the essence of this new topological order and explain what makes topological insulators special and worthy of future studies.

Suggested reading

  1. R.B. Laughlin, "Nobel Lecture: Fractional quantization", Rev. Mod. Phys. 71, 863 (1999)
  2. C.L. Kane, "An insulator with a twist", Nature Physics 4, 348 (2008)
  3. S.C. Zhang, "Topological States of Quantum Matter", Physics 1, 6 (2008)

Claude Bourbonnais (Sherbrooke)

Lectures 1 & 2: Introduction to the Physics of Low Dimensional Organic Conductors and Superconductors
In these lectures, I shall highlight some of the basic aspects that define the physics of low-dimensional conductors and superconductors. From an historical perspective, we first introduce the pioneering efforts that yielded the synthesis of the first stable quasi-one-dimensional organic metals in the seventies and which then pave the way to the synthesis of the first series of organic superconductors (TMTSF)2X (X= PF6, AsF6, ClO4, ...), christened as  the Bechgaard salts series. These salts and their cousin materials, the Fabre salts series (TMTTF)2X, constitute a remarkable, if not a unique ensemble of compounds superimposing on their own a large part of concepts condensed matter physics.

References

  1. "Physics of Organic Superconductors and Conductors", edited by A. G. Lebed, Vol. 110, Springer Series in Materials Science (Springer, Heidelberg, 2008). P. 357-412"
  2. Lecture Notes given for a series of lectures at the Boulder Summer School last year.

Adrian del Maestro (UBC)

Lectures 1 & 2: Introduction to Quantum Phase Transitions
A quantum phase transition occurs between two states of a system at identically zero temperature.  Such a transition lies outside our experience with classical phase transitions (like melting), where a diverging length scale is driven by thermal fluctuations.  At T = 0 K, the transition must necessarily be driven by quantum fluctuations, and we discover that unlike the classical case, the dynamic and static critical behavior are inexorably intertwined.  There is strong coupling between thermodynamics and dynamics at all length scales resulting in fascinating and non-trivial consequences throughout the finite temperature phase diagram.  In these lectures I will attempt to present the basic ingredients needed to understand a field theoretic description of quantum critical points and their resulting finite temperature crossovers.

References

  1. J.A. Hertz, Phys. Rev. B 14, 1165 (1976).
  2. S. Sachdev, Quantum Phase Transitions (Cambridge University Press, New York, 1999).
  3. S.L. Sondhi, S.M. Girvin, J.P. Carini and D. Sharhar, Rev. Mod. Phys. 69, 315 (1997).

Martin Zwierlein (MIT)

Lecture 1: The BEC-BCS Crossover in Ultracold Fermi Gases
This lecture will cover the basic theoretical tools to understand fermionic superfluidity in the BEC-BCS crossover regime and present its experimental realization in ultracold atomic gases. Topics include: The many-body wavefunction of pair condensates, from Bose-Einstein condensates of tightly bound molecules to long-range Cooper pairs, single-particle and collective excitations, pair binding energy via Radio-Frequency spectroscopy, demonstration of superfluid flow via the observation of vortex lattices.

Lecture 2: Fermionic Superfluidity with Imbalanced Spin Populations
In this lecture we will discuss imbalanced Fermi mixtures. Here, not every fermion can find a partner to form a pair, and too large an imbalance will cause a breakdown of superfluidity, at the so-called Clogston-Chandrasekhar limit of imbalance. Several ground states for the imbalanced regime have been proposed, for example the Fulde-Ferell-Larkin-Ovchinnikov (FFLO) state where Cooper pairs have finite momentum, a phase separated state where a balanced superfluid and an imbalanced normal Fermi mixture phase separate. In the limit of large imbalance, the few minority atoms interacting with the majority environment form dressed quasiparticles, the Fermi polarons. The state can then be described as a Landau Fermi liquid of these quasiparticles with renormalized masses and energies.

References

  1. Theory of ultracold Fermi gases 
    Stefano Giorgini
    Lev P. PitaevskiiSandro Stringari
    Rev. Mod. Phys. 80, 1215 (2008)
     
  2. Making, probing and understanding ultracold Fermi gases 
    Wolfgang Ketterle, Martin W. Zwierlein
    in: Ultracold Fermi Gases, Proceedings of the International School of Physics "Enrico Fermi", Course CLXIV, Varenna, 20 - 30 June 2006, edited by M. Inguscio, W. Ketterle, and C. Salomon (IOS Press, Amsterdam) (2008)
  3. Many-Body Physics with Ultracold Gases 
    Immanuel BlochJean DalibardWilhelm Zwerger
    Rev. Mod. Phys. 80, 885 (2008)
  4. Making, probing and understanding Bose-Einstein condensates 
    W. Ketterle, D.S. Durfee, D.M. Stamper-Kurn
    in: In Bose-Einstein condensation in atomic gases, Proceedings of the International School of Physics "Enrico Fermi", Course CXL, edited by M. Inguscio, S. Stringari and C.E. Wieman (IOS Press, Amsterdam, 1999) pp. 67-176