交叉學科理論研究中心PhysicsCUHK課件

1、Einstein and quantum theory of solidsYu LuInstitute of Theor. Phys. & InterdisciplinaryCenter of Theor. Studies, CAS第1頁，共38頁。Einsteins paper in March 1905Planck proposed the radiation distribution，while Einstein suggested that the radiation consists of a gas of “l(fā)ight energy quanta” (Lichtenergiequa

2、nten), or simply “l(fā)ight quanta” (Lichtquanten), each with energy proportional to frequency.第2頁，共38頁。第3頁，共38頁。Among the 1905 papers Einstein only consideredthis paper “revolutionary”Planck derived this relation“Experiments are in unsolvable contradiction with classicalmechanics and classical electrod

3、ynamics”第4頁，共38頁。Using Boltzmanns entropyWiens radiation law, for“high energy quanta”Analogy of radiation with ideal gas-“gas of light quanta”Einsteins heuristic derivation第5頁，共38頁。Not accepted by contemporaries， strong objection by Planck himself，Nobel prize only in 1922.Proved in 1906 and 1907 pap

4、ers：Quantization of “l(fā)ight quanta” Plancklaw1905 paper： Quantization of interaction energy of radiation with matterStokes rule, photo-ionization, photo-effect第6頁，共38頁。Dulong-Petits empirical law ：it should be a constantMany solids, in particular insulators, SH much smaller, Strongly temperature depe

5、ndentSpecific heat (SH) puzzle for solidsBoltzmanna derivation in 1876 ：c=3Rn=5.94n cal/molegrad第7頁，共38頁。Boltzmann: motion of atoms constrained in solids, not as simple as he imaginedLord Kelvin: doubt on Boltzmanns derivationLord Rayleigh: Both theory and experiments are right，genuine contradiction

6、, new “insight” is needed!Einsteins quantum theory of specific heat for solidsWhat is the reason?第8頁，共38頁。1907 paper: “Plancks theory of radiation and theory of specific heat” Annalen der Physik 22 (1907) 180-190第9頁，共38頁。1907 paper assumes quantization of energy of atom vibration,with the same frequ

7、ency, the same average energyEinstein founded the quantum theory of solids! derivation of typical frequency fromcompressibility and density第10頁，共38頁。1910 Nenrst measured the temperature dependence for more solidsComparison of theory with diamonds SH in 1905s paperThe earliest confirmation of quantum

8、 theorycame from solidsMillikans 1914 photoeffect experimentsOnly after Compton scattering experiment in 1923，the concept of “l(fā)ight quanta” was accepted by physicists第11頁，共38頁。1911 Debye modelcontinuum model1911 Born- von Karman molecular chainlattice1924 Heisenberg quantum mechanical calculationsBo

9、rn-Huang lattice dynamics theory第12頁，共38頁。Drude-Lorentz free electron theory of metalsElectrons in metals are “free”, can conduct electricity, heat，with some “mean free path”Wiedemann-Franz lawLorentz gave rigorous proof using Maxwell- Boltzmann distributionDifficulties:1）Why some solids are metals？

10、 2）Why SH of metals is not z times bigger？第13頁，共38頁。Pauli-Sommerfeld free electron theory of metals Identity principle Bose-Einstein and Fermi-Dirac statisticsPauli with “great regret” gave up the Bose character assumption of electrons derived Pauli paramagnetismSommerfeld systematically applied Fer

11、mi-Dirac statisticsFor most metals FT, “l(fā)ow temperature phenomena”Electron SH T, rediscovered Wiedemann-Franz lawWhat is the difference between metals and insulators?第14頁，共38頁。Energy band theory of solidsBloch theoremMetalpartially filled bands；Insulator（semiconductor）fully filled bands第15頁，共38頁。Two

12、 opposite views on the Nature Reductionism: Everything is reduced to its constituents, governed by the most fundamental laws. “Ultimate Goal”To establish THE THEORY OF EVERYTHING Emergence: There are different levels of the real world, and there are fundamental laws at each level.Our mission is to s

13、tart with the basic experimental facts, to unveil these fundamental laws and to understand “ How qualitatively new phenomena areEMERGING.”第16頁，共38頁。Philip W. Anderson: More is different (1972)at each new level of complexity, entirely new properties appear, and the understanding of this behavior requ

14、ires research as fundamental in its nature as any other.第17頁，共38頁。Theory of EverythingR B Laughlin & D Pinesjka b第18頁，共38頁。Achievements: atoms, molecules, solids Nk Approximate methods：crystal structure, phonon spectrum, even Tc under el-ph model of SCDFT1998 Nobel Prize in ChemistryWalter KohnQuant

15、um Molecular DynamicsCar-Parrinello methodDynamic Quantum Mean Field Theory （DMFT）第19頁，共38頁。LDA DMFTPhonon spectra of plutonium，theoretical predictions (red circles)（X. Dai et al., Science 300, 953 (2003); Neutron scattering results (black squares) (Science 301,1078 (2003)第20頁，共38頁。Failures：Supercon

16、ductivity, superfluidity, QHE Josephson effect High Tc not talking about protein functions understanding of conscience.We can decompose complex systems into the simplestconstituents and understand the behavior of these constituents, as ancient Greeks dreamed, but we knownothing about the complex sys

17、tems themselves!第21頁，共38頁。Lattice vibration and phonons If ground state stable:low energy excitations harmonic oscillations. Quantization of these oscillations- phonons “Like” ordinary particles，dispersion (p) No restrictions on generation: bosons They do not survive, while leaving crystals:quasipar

18、ticles Not sensitive to microscopic details，which cannot be recovered from the phonons This was initiated by Einstein ！第22頁，共38頁。Landau Fermi Liquid Theory Low energy excitations of interacting Fermi systems（like electrons in metals）can be mapped onto weakly interacting Fermi gas These quasipariticl

19、es follow Fermi statistics，with dispersion (p)，with the same Fermi volume as free fermions (Luttinger theorem). They cease to exist if taken away from the matrix (metal) Their properties not sensitive to microscopic interactions，which cannot be derived from these properties From the RG point of view

20、, interacting and free fermion systems are controlled by the same fixed point第23頁，共38頁。Superconductivity1911 Kamerlingh Onnes discovered zero resistanceEarly 30s Meissner effect was discovered，complete diamagnetism more fundamentalWave function “rigidity” ansatz (London brothers)London equations第24頁

21、，共38頁。1950 Ginzburg-Landau equation，introducing macroscopic wave function Bardeen realized：gap in spectrum leads to “rigidity” SuperconductivityCooper pairing：arbitrarily weak attraction gives rise to boundstates at the Fermi surfacepairing energy is the gap第25頁，共38頁。Is SC Bose-Einstein condensation

22、 of Cooper pairs?- a bit more complicated! BCS wave function：Problem solved！Nobel prize was delayed by 15 years！Particle number not conserved，change from one Hilbert space to another one symmetry breakingconceptual breakthrough第26頁，共38頁。Goldstone mode: collective excitations, recovering the symmetry

23、 like spin wavesWhen external (gauge) field coupled, becomes massive- Meissner effectAnderson-Higgs mechnismUnified weak-electromagnetic interactions 1979 Nobel prize in physics第27頁，共38頁。Josephson effect：visualization of the phaseMost profound demonstration of emergence! Bardeens objectionUsing two

24、Josephson junctions- SQUID第28頁，共38頁。Discovery of the integer quantum Hall effect 1985 Nobel prize in physicsT 1 KB 8 T第29頁，共38頁。QHE as an emergent phenomenon Precision：10-9 Self-organization： 10111012 /cm2 particles synchronized Universality“robustness”not sensitive to impurities, details of microsc

25、opic interactions, etc.第30頁，共38頁。What guarantees “exactness” of quantization? Disorder caused localizationElectron interactions can be “adiabatically” switched off“pumping” integer number of electrons-emergence第31頁，共38頁。Fractional QHE- 1998 Physics Nobel Daniel C. Tsui Horst L. Strmer Robert Laughlin 第32頁，共38頁。Comparison of fractional and integer QHECommon features： exact Hall plateauconstante2/h Zero longitudinal conductivity and resistance Thermal activation，gap，described by Mott VRHDifferences：constant -integer or fractional？“adiabatically” derivable from non