PowerPoint

Department of ElectronicsNanoelectronics14Atsufumi Hirohata

10:00 Tuesday, 3/March/2015 (B/B 103)1Quick Review over the Last LectureFermi-Dirac distributionBose-Einstein distributionFunctionEnergy dependence

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Contents of Nanoelectonics

I. Introduction to Nanoelectronics (01) 01 Micro- or nano-electronics ?II. Electromagnetism (02 & 03) 02 Maxwell equations 03 Scholar and vector potentialsIII. Basics of quantum mechanics (04 ~ 06) 04 History of quantum mechanics 1 05 History of quantum mechanics 2 06 Schrdinger equationIV. Applications of quantum mechanics (07, 10, 11, 13 & 14) 07 Quantum well 10 Harmonic oscillator 11 Magnetic spin 13 Quantum statistics 1 14 Quantum statistics 2V. Nanodevices (08, 09, 12, 15 ~ 18) 08 Tunnelling nanodevices 09 Nanomeasurements 12 Spintronic nanodevices314 Quantum Statistics 2 BosonFermionBose-Einstein condensationFermi degeneracyFermi liquidIdeal quantum gas4

Fermions / BosonsIn particle physics,Fermions : 1 fermion occupies 1 quantum state (Fermi-Dirac statistics)Particles, which consist of materials; e.g., protons, neutrons and electronsIf electrons were bosons...If protons / neutrons were bosons...Bosons : Several bosons occupy 1 quantum state (Bose-Einstein statistics)Particles, which transfer particle-interactions; e.g., photons and gluons

* http://www.wikipedia.org/

If photons were fermions...

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Fermions / Bosons (Cont'd)* http://www.sci.osaka-cu.ac.jp/phys/ult/invitation/helium/helium.htmlParticles consisting of even numbers of fermions : bosonse.g., He 4Particles consisting of odd numbers of fermions : fermionse.g., He 3

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Low-Temperature GenerationBy using 3-He and 4-He, a dilution refrigerator is realised (< 100 mK) :

* http://www.sci.osaka-cu.ac.jp/phys/ult/invitation/cryo/dr.html

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Dilution RefrigeratorOxford Instruments SM4000-8 with Heliox TL :

Temperature : < 350 mK

Magnetic field : 8 T8

Bose-Einstein Condensation - He 3 superfluidIn boson systems, all bosons fall into the lowest energy state at very low temperature. Bose-Einstein condensation* http://photos.aip.org/e.g., superfluid of He 4 (1938 Fritz W. London)

e.g., superfluid of He 3 (1972 Douglas D. Osheroff, Robert C. Richardsonand David M. Lee)

2 He-3 fermions form a Cooper pair quasi-particle superconducting state9

Bose-Einstein Condensation - Rb atomIn 1995, B-E condensation observed in Rb atom by Eric A. Cornell and Carl E. Wieman :*** R. Baierlein, Thermal Physics (Cambridge University Press, Cambridge, 1999).

Reduced speed by photon-momentum absorption

** http://jila.colorado.edu/content/bec-transporter

* http://www.wikipedia.org/

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Bose-Einstein Condensation - Na atomIn 1995, Wolfgang Ketterle also observed B-E condensation in Na atom :** http://cua.mit.edu/ketterle_group/Projects_1997/Interference/Interference_BEC.htm

* http://www.wikipedia.org/

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Bose-Einstein Condensation - SuperconductorCooper pair in a superconductor :** http://hyperphysics.phy-astr.gsu.edu/Hbase/solids/coop.html* http://www.phys.shimane-u.ac.jp/mutou_lab/

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Superconductor and Heavy-Electron SystemCooper pair in a superconductor :** http://www.lorentz.leidenuniv.nl/~pjhdent/* http://www.lanl.gov/news/index.php/fuseaction/1663.article/d/20075/id/10392Heavy-electron system :

Lattice deformation Quadra-pole rigid lattice Dipole Cooper pair Mott insulator13

Magnetic Quantum Critical PointPhase diagram :* http://physicsworld.com/cws/article/print/3504/1/pw1501092Fermi liquid :

Frustrated spin system :*** http://www.jst.go.jp/kisoken/presto/complete/soshiki/theme/first_r/07nantoh/link011.htm** http://kotai2.scphys.kyoto-u.ac.jp/index.php?Research

Mott insulator Conventional metals14

Fermi LiquidIn 2D and 3D, Landau proposed electron behaviour as liquid :

Electron states can be defined by the competition among Kinetic energy Liquid Coulomb interaction Solid crystal Potential randomness Amorphous glassAt very low temperature,Coulomb interaction becomes negligible. Fermi liquid15

Fermi DegeneracyFermi-Dirac distribution :ET = 0T 0Pauli exclusion principleEF Fermi degeneracy Free electrons in a metal at room temperature Higher energy states are occupied. Heat capacity becomes smaller than expected from the classical model. Magnetic susceptibility becomes smaller (Pauli paramagnetism). Star cores even at 10 9 K Very high density degeneracy pressure After nuclear fusion, white dwarf stars by electron degeneracy pressure neutron stars by electron degeneracy pressure black holes16

Ideal Quantum GasEquation of states for ideal gas :

where P : gas pressure, V : volume, N : number of particles, kB : Boltzman constant and T : temperatureEnergy E satisfies :

TE

FermionsBosonsFermions :Compared with the classical modelE increases / P increases(classical model)= Repulsive force between particles Pauli exclusion lawBosons :Compared with the classical modelE decreases / P decreases= Attractive force between particles17