Lecture 1 Introduction and Overvie · Rare Earth 5f. Actinide. 3d. Transition metal....

Lecture 1 Introduction and Overview

D. L. Feng

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Outline

1. The importance of a framework or paradigm2. Scales, renormalization, emergent phenomena3. Simplicity vs. complexity4. History5. Main conceptual lines , paradigm

凝聚态物理学——封东来

A FRAMEWORK OF KNOWLEDGE IS THE BASE FOR RESEARCH !

Point #1

凝聚态物理学——封东来 3

学科框架的重要性

大多数人都是整理进步

华罗庚：读书有个从薄到厚，再从厚到薄的过程

量变质变

只有建立理论的框架，全局观和概念体系，才能融会贯通，以“不变”应“万变”，才能慧眼识“珠”（前沿的问题）

凝聚态物理纷繁复杂，往往入门很难

要多读多想，建立自己的概念体系，学科框架

冯端、金国钧《凝聚态物理》是这方面的一个尝试，非常适用于“实战”

达到这一步并不难，因为精髓其实很薄。


SCALES, RENORMALIZATION, EMERGENT PHENOMENA

Point #2


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What’s condensed matter physics?

For a condensed matter system, 1. All important elementary particles are known

2. All interactions are known

3. The basic Hamiltonians are known

“Solid state physics is the physics of dirt.”

As always, Pauli was wrong again.



0.1.1 物质结构的不同层次


0.1.2 物理学的分支学科与研究对象的尺寸

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Philip W. Anderson: More is different (1972)

…at each new level of complexity, entirely new properties appear, and the understanding of this behavior requires research as fundamental in its nature as any other.

0.1.3 层展现象


Emergent Physics

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Hierarchy: particle, atoms, molecules, solids, condensed matter, biology, …, cosmology

“Emergent’’ physics:Every level is fundamental

Then

Now


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Condensed Matter : another fundamental vacuumParticle Physics Condensed Matter Physics

Ground state vacuum, nothing T = 0 K, particles in their lowest quantum state

Vacuum fluctuations

Generation of particles T > 0 K, thermal excitations

Elemental excitations

Electron, positron, mesons, neutron, photon ……

Phonon, magnon, exciton, polariton, plasmon, … …

Highly excited state

The first several seconds of the universe; CERN, SLAC …

T >>0 K, a quantum soup, cheap and easy to achieve

External probe

Particle collisions Scattering processes, transport ……

Description language

Quantum field theory, QCD, string theory etc

Many body physics, quantum field theory

Complexity Few body problem Many body problem, self organization, strong interactions

More fundamental physics beyond the simple analogy!凝聚态物理学——封东来

SIMPLICITY, COMPLEXITY AND MANY BODY PROBLEM

Point #3


Exact Hamiltonian

is not solvable for N large, however, we need to understand only low energy excursions from ground state

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Diversity, a broad spectrum of materials

Applications: wide diversity of (tunable physical and chemical properties), e.g., small class of TM oxides (3d) Metals: CrO2 [Cr4+, d1], Fe3O4 (T>120K) Insulator: Cr2O3[Cr3+,d3], V2O5, CoO, Co3O4

Semiconductor Metal: VO2, V2O3 [keep coming back],Ti4O7

Superconductor: La2-xBaxCuO4,LiTi2O4

Piezo-ferroelectric: BaTiO3, CuCl Ferromagnets: CrO2

Antiferromagnets: MnO Ferrimagnets: γ−Fe2O3, Ferrites Tunable TN, Tcomp, anisotropy Catalyst: Fe oxides, Co oxides, Ni Oxides TM-Nitrite and more

Basic researchWe do not understand them, and we are continuously surprised!


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what’s the challenge ?

The MANY BODY PROBLEM

Understand the Complexity !


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Three levels of complexity

•small scale, few electrons; quantum mechanics • Nano physics• Mesoscopic physics

•many-electron quantum systems• Semiconductor (electron gas)• Metal (electron liquid)• BCS superconductor: metal + Cooper pairing

•strongly correlated electron systems • Quantum Hall effect • High-Tc cuprate superconductor• Kondo system• Quantum Criticality


Non-Interacting Interacting

Essence of many body problem: Interaction

Many-body effects are due to the interactions between the electrons, or with other excitations inside the crystal :

1) A “many-body” problem : intrinsically hard to calculate and understand

2) Responsible for many surprising phenomena :Superconductivity, Magnetism, Density Waves, ....


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Some important parameters to determine the electronic phases of matter

Structure/Topology +

Phases of Matter Electronic Parameters

Simple Metals -> large tBCS Superconductors -> t vs λMott Insulators -> t vs UCDW, SDW etc -> λ & UHigh Tc, CMR, Stripes, NDO, etc. - - - - - - - - - - - -

Organization of Correlated Electrons in Matter :

+ Other factors(Chemistry)

An “Love triangles” illustration of the complexity

tt(Hopping)(Hopping)

UU(Coulomb)(Coulomb)

λλ(Lattice)(Lattice)


HISTORYPoint #4


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History (1) solid state physics time 1929-1931

Bloch and Wilson theory of solids Band theory explain metals, band insulators, and semiconductors

1937 de Boer & Verwey [NiO, CoO are large band gap insulators] Peierls [due to d-d electron-electron interaction]

1949 Mott: Metal-Insulator transition

1950 Jonker, van Santen: Mn perovskites Zener: double exchange theory

1957 Bardeen, Cooper, & Schrieffer: BCS theory of superconductivity

1959 P.W. Anderson: Super-exchange theory starting from localized d electrons

(d-d interaction U) 1964

Hubbard: A model to describe correlation Hohenberg-Kohn: Density functional theory (DFT) C. Herring: Stay at home principle J. Goodenough: Transition-Metal compounds

1965 J. Wilson: metal, non-metal

1976 B.H. Brandow: Mott insulators

Bloch, Heisenberg, Peierls, Weisskopf


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• Quasi-particles, Landau Fermi Liquid Theory, Adiabaticity• Field-Theoretical Methods – Green’s Functions• Broken Symmetry: Phase Transitions & Critical Phenomena• Scaling – Renormalization Group, Kondo Effect

Philip W. Anderson Lev D. Landau Kenneth K. Wilson

Condensed Matter Physics starts in the 50s - 70s


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• Effect discovered in the 30s• 1964 Kondo’s explanation of resistance minimum• 1971 Anderson scaling theory• 1974 Wilson renormalization group, Nozieres FL interpretation

Kondo Effect in Alloys


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History (2) CMP matures from 1980’s 1984

J. Zaanen, G.A. Sawatzky, A. Fujimori: Charge transfer insulator

Integer and fractional Quantum Hall effects 1986

Bednortz & Muller: High-TC superconductors 1993, ZX Shen and others: d-wave gap 2002, The Bell labs scandal

2008 iron based superconductivity

History of Superconductivity spin glass etc. Slater, Van vleck, Kondo, Friedel, Rice, Gunarsson, Laughlin David Pines


Many-Body Physics for the last two decades

Strong Correlations Disorders

Exotic States

Novel Concepts

Localization

Mesoscopic

Nanoscience,Quantum Information

Spin Glasses

ComputationalComplexity,Random Graphs,Optimization,Error correctingCoding….

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1. Quantum Hall Effect, Integer & Fractional (1985, 1998 Nobel Prizes in Physics)

2. Heavy Electron Physics3. High Temperature Superconductivity

(1987 Nobel Prize in Physics)4. Quantum Criticality5. Colossal Magnetoresistance6. Cold atom many body physics7. Topological insulator……

New Exotic States


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John Hertz (1976), Andrews Millis, Subir Sachdev

• State as a function of a control parameter ghas a singularity at gc

• At the quantum critical point noquasiparticles

• No intrinsic energy scale (e.g. gap), only scale |g-gc|

S. Sachdev

Quantum Phase Transitions


Novel Concepts

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1. Breakdown of Fermi Liquid Theory2. Fractionalization of Quantum Numbers3. Quantum (Berry, et al.) Phases4. Strong Coulomb Repulsion, Constraints5. Spin-Charge Separation6. “Gauge Forces”7. Composite Fermions8. ………


MAIN CONCEPTUAL LINES , PARADIGM

Point #5


固体物理的范式

范式的特点

周期结构和波

德布罗意波

晶格（Born,黄昆) 电子 (Brillouin, Bloch） Anderson localization 无公度相，准晶

化学键和能带

过去相对独立的发展

• 量子化学、原子分子物理

• 固体物理

新现象和新问题的出现

• 纳米结构

• 关联体系

• 磁性体系

• Kondo效应重费米子体系量子相变和临界现象


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R/d Model

d R

Valence electrons/electronic structure of molecules/solids properties; two extreme situations for open shell valence orbital

R >> d, large overlapHave lost atomic identity

Broad bands, Weak e-e interaction (U <<W)

Low energy scale charge fluctuationNon-magnetic

independent electron models, p states, Na, Al, Mg, Zn …..

R << d, little overlapRemain atomic, multiplets

Narrow bands, Large e-e interaction (U>>W)

Low energy scale spin fluctuationMagnetic, Hund’s Rule

Tight binding model3d, 4f states


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What’s in between? : d - f open shell materials

Increasing localization

4f Rare Earth

5f Actinide

3d Transition metal


Interesting systems exist in between these two extreme:Coexistence of these two types of states (p and d electrons) + hybridization Kondo, Mott-Hubbard, Heavy Fermion, local moments, HTSC, Spin electronics

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Controlparameters

Bandwidth (U/W)Band filling

Dimensionality

Degrees offreedom

Charge / SpinOrbital Lattice

d - fopen shells

materials

U<<WCharge fluct.

U>>WSpin fluct.

• Kondo• Mott-Hubbard• Heavy Fermions• Unconventional SC• Spin-charge order• Colossal MR

Nd2-xCexCuO4 La2-xSrxCuO4

0.3 0.2 0.10

100

200

300

SC

AFTem

pera

ture

(K)

Dopant Concentration x0.0 0.1 0.2 0.3

SC

AF

Pseudogap

'Normal'Metal

Tc

I II IIIb IVb Vb VIb VIIb VIIIb Ib IIb III IV V VI VII 0H HeLi Be B C N O F NeNa Mg Al Si P S Cl Ar

Rb Sr Y Zr Nb Mo Rh Pd Ag Cd In Sn Sb Te I XeCs Ba La* Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At RnFr Ra Ac** Rf Db Sg Bh Hs Mt

Lanthanides*Actinides** Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

K Ca Sc Ti V Cr Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

MnRu

Ca2-xSrxRuO4

Strongly Correlated Electron Systems


凝聚态物理的范式

主要表现在

新的概念体系，新的视角 (朗道、P.W.Anderson）• Broken symmetry, Phase transition, order parameter，广义刚度，拓扑缺陷

• Elementary excitations 新的体系

• 液晶、玻璃态、高分子体系、生命体系、冷原子

• 强相互作用区的强关联体系

• 非平衡体系，协同现象、非线性、自组织、耗散结构、时空结构、湍流


Donglai Feng “Electronic Structure of Strongly Correlated Systems” 33Sachdev


0.3.1 与对称破缺有关的多粒子系统的能态示意图

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Future ?! New problem (surprise keep emerging !)

Subtle balance Sensitivity to environment Nano strongly correlated systems (new material, surprise)

New kinds of co-operative material.(things like MgB2), nano+ strongly correlated systems

Strong demand for engineered quantum coherence: Moore's law. Quantum cryptography. Quantum computers. Spintronics, TMO based electronics, photonics, orbitronics

Between "life" and "high temperature superconductivity", it would be naïve not to expect a profusion of new discoveries of a fundamental nature. Polymer biological systems

Old problem but new techniques (a lot to be done) Quantum critical point High Tc Superconductors EELS, RIXS, 2PPES, ARPES+MBE


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We used to think that if we knew one, we knew two, because one and one are two. We are finding that we must learn a great deal more about "and" .

Sir Arthur Eddington.

Elements Tertiary QuaternarySimplest moleculesof Life ?

1 2 3 4 10

104100

Nb U Be13

CePdSi YBCO

106 108

Unfinished frontier


At the frontier of CMP


Many simple models – emphasizing physical intuition

Handwaving argumentsGuided by a lot of experiments

Resistivity//Hall effect//Thermopower//Nernst effect // Optical conductivity //Neutron scattering // NMR, NQR //ARPES //Tunneling/ /STM //Specific heat…….

Lecture 1 Introduction and Overvie · Rare Earth 5f. Actinide. 3d. Transition metal....

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Transcript of Lecture 1 Introduction and Overvie · Rare Earth 5f. Actinide. 3d. Transition metal....