高溫超導體研究及熱物理教學(High Tc superconductivity

and Thermal physics)--30 年之研究及教學心得

古煥球 (H. C. Ku) 清華大學物理系 (NTHU)

NCHU 5/7/2010

(original talk title)

Anisotropic x-ray absorption near edge spectrum (XANES) for FeAs-based (1111)

aligned superconducting powder

H. C. Ku, B. C. Chang, T. J. Shiu, M. F. Tai National Tsing Hua U., Hsinchu, Taiwan

Y. Y. HsuNational Taiwan Normal U., Taipei, Taiwan

L. Y. Jang, J. F. LeeNational Synchrotron Radiation Research C., Hsinchu, Taiwan

K. Q. Ruan, X. G. LiU. of Science and Technology of China, Hefei, China

Introduction

Fe-based superconductors

Sc2Fe3Si5 Tc = 5 K (1980)Braun et al. Phys. Lett. 75A (1980)

RFeAs(O1-xFx) (R = La - Sm,0 x < 0.4) Tc > 50 K (2008)

-- ZrCuAsSi-type (1111) tetragonal layer structure (P4/nmm)-- LaFeAs(O0.95F0.05)

Tc(max) = 26 K Kamihara et al. JACS 130, 3296 (2008) -- high pressure (3 GPa) Tc(max) = 43 K Takahashi et al. Nature 453, 376 (2008)

Introduction

Undergraduate Thermal Physics lecture*

(2009-2010) on

-- Superconductivity ( 超導性 ) -- Cryogenics ( 低溫學 )-- Superfluid ( 超流性 ) and BEC (Bose-Einstein

凝結 )

*some from Introduction to Solis Sate Physics

(Magnetic work and superconductors)( 磁功和超導體 )

Magnetic work: work performed by apply the magnetic field Ba ( 外磁場 ) to the system U = U(T,V,N,Ba) dWm = -m.dBa (m = MV total magnetic moment 總磁矩 ) (Ba ≡ H or simply B)Apply magnetic field Ba to a superconductor

(ex) Electric resistance R(T) of mercury metal Hg shows an electronic phase transition ( 電子相轉變 )from normal metal ( 正常金屬 ) to superconductor( 超導體 ) at critical temperature Tc = 4.2 K (1911) Perfect conductor: electrical resistivity ( 電阻率 ) = 0 (or R = 0) in the superconducting state ( 超導態 )

(ex) maximum transition temperature in high temperature superconductor (HTSC 高溫超導體 ) Hg2Ba2Ca2Cu3O8 (Tc = 134 K at 1 atm, ~160 K under high pressure) Heika Kamerlingh Onnes (1853-1926) 1913 Nobel physics prize “for his investigations on the properties of matter at low temperatures which led, (8-17) inter alia, to the production of liquid helium”

(Helium liquefier)( 氦液化機 ) Onnes use Claude cycle to liquefy helium in 1908, discover

superconductivity in 1911

Heika Kamerlingh Onnes (1853-1926) 1913 Nobel physics prize “for his investigations…which led to the production of liquid helium”

(ex) Linde Cryogenics L1610 helium liquefiera Collins machine using modified Claude cycle( 克勞德循環 ) with two gas piston expanders (similar to Koch 1410 liquefier in NTHU)(2012) 20 liters LHe per hour without LN2 precooling49 liters LHe per hour with LN2 precooling (at 4.4 K)

(12-8)

(Linde cycle)( 林迪循環 )Linde cycle: the combination of Joule-Thomson expansion valve with a counterflow heat exchanger in a gas liquefier (W = 0, constant enthalpy)

let one mole of gas enter, with fraction l liquefied Hin = l.Hliq + (1 - l)Hout

where Hliq is the enthalpy per mole of liquid at boiling point Tb under pressure ~output pressure pout

liquefaction coefficient ( 液化係數 ) l = (Hout – Hin)/(Hout – Hliq)liquefaction (l > 0) takes places when Hout(Tout~Tin, pout~1 atm) > Hin(Tin, pin)

(ex 1) for air liquefier ( 空氣液化機 ) Tinv = 893 K for O2 (LO2 Tb = 90.19 K)(blue)Tinv = 621 K for N2 (LN2 Tb = 77.36 K)

Carl von Linde use such a cycle in 1895 to liquefy air starting from Tin = 300 K (12-6)

Flow diagram of KOCH 1410 helium liquefier (National Tsing Hua University 1985)

(Claude cycle with LN2 pre-cool, expansion engines, heat exchangers and JT valve)

(12-9)

Meissner effect ( 邁斯納效應 )perfect diamagnet ( 完美抗磁體 ) (1933)total magnetic field B = 0 inside for lowapplied magnetic field Ba

magnetic susceptibility ( 磁化率 ) = 0M/Ba < 0 for T < Tc

due to induced screening supercurrent ( 表面感應屏障超導電流 ) on surface T > Tc T < Tc

(ex) For a long superconductor sample with constant applied field Ba parallel to long axis

uniformly magnetized with magnetization ( 磁化強度 ) M (M = m/V magnetic moments

per unit volume), magnetic field induced by M Bind = (1 - N)0M (SI, 0 = 4 x 10-7 T.m/A) total magnetic field B inside the long sample (demagnetization factor 去磁因素

N = 0) B = Ba + 0M (B in tesla, 1 T = 104 G, M in A/m) = 0 (T < Tc, B = 0 due to screening supercurrent) = 0M/Ba (volume susceptibility is dimensionless) = -1 < 0 (perfect diamagnetism)

(note) magnetic field B will penetrates on surface, penetration depth ( 滲透深度 ) ~ 102 nm

(8-18) (magnet levitation by HTSC at 77 K)

(Type I superconductor)( 第一類超導體 )

Destruction by magnetic field forBa Bac (critical magnetic field, 臨界場 ): superconducting state (S)Ba > Bac (≡ Hc): normal conductor state (N) magnetic work density ( 磁功密度 ) in an isothermal process (T = constant) dWm/V = dF = -M.dBa (M = m/V) For a type-I long superconductor with Ba Bc parallel to long axis at T <

Tc

1. superconducting Helmholtz free energy density dFS = -M.dBa = (Ba/0)dBa FS(Ba) – FS(0) = Ba

2/20

2. normal state free energy density is almost independent of Ba since magnetization M is very small if nonmagnetic (M ~ 0) FN(Ba) ~ FN(0)3. since at critical field Bac(T), FN(T,Bac) = FS(T,Bac) stabilization energy density (for type I and II) F(T,Ba=0) = FN(T) – FS(T) = Bac(T)2/20

(8-19)

Secondary thermometer ( 次溫度計 ): thermometers whose X(T) must be calibrated

empirically with another already calibrated thermometer

(ex 1) Thermocouple thermometer ( 熱偶溫度計 ) thermoelectric voltage Vtc(T)used as an interpolating instrument in ITStemperature range: 400-1400 K

(ex 2) Pt resistance thermometer ( 白金電阻溫度計 ) R(T)used as an interpolating instrument in ITS (see next page)temperature range: 14-1200 K

(ex 3) 4He vapor pressure thermometer ( 氦四蒸氣壓溫度計 ) p(T) (Chap 7,10,12) temperature range: 1-5.2 K (vaporization curve of p-T phase diagram)

(ex 4) 3He vapor pressure thermometer ( 氦三蒸氣壓溫度計 ) p(T) (Chap 7,12) temperature range: 0.3-3.3 K

(2-12)

(I-V characteristics of a p-n junction diode)(p-n 接面二極體 I-V 特徵 ) forward-biased ( 前向偏壓 ) Vf: voltage V applied with p-side at positive voltage, drives conduction electrons from n-side to p-side, dives holes from p-side to n-side

I-V curve for a p-n junction diode

(note) Si diode (see figure) and (Ga,Al)As diode are good wide-range temperature sensors, use forward voltage Vf(T) at constant current I (10 mA)temperature range: 1.4 K – 500 K

(13-21)

(Evaporation cooling)( 蒸發冷卻 ) Evaporation cooling of liquid helium by pumping away the helium vapor,

the latent heat of vaporization of liquid ( 液體蒸發潛熱 ) is extracted along with the

vapor

(ex) liquid helium L4He evaporation coolingpump 4He vapor along the vaporization curvep = 760 torr 4.222 K (1 atm = 760 torr) 100 torr 2.64 K ( point = 2.172 K) 10 torr 1.74 K (0.013 atm) 1 torr 1.27 K 10-1 torr 0.98 K 10-2 torr 0.79 K 10-3 torr 0.66 K 10-4 torr 0.56 K

(12-10)

Superconducting transition temperature Tc in element crystals ( 元素晶體 )

Nb: Tc = 9.25 K (maximum at 1 atm) Cu: normal good conductor, no Tc

Li: Tc = 20 K (at 50 GPa)(2002) C: insulator (Tc = 15 K? in nanotube)

Rh: Tc = 35 K (minimum at 1 atm) Fe: ferromagnet (Tc = 2 K at 21 GPa)

Si: semiconductor (Tc = 8.5 K at 12 GPa) Eu: Tc = 1.8 K (under pressure/2009)

(8-20)

(note) Diamond anvil cell (DAC 鑽石砧具 )A high pressure device to compress a small piece (size < 1 mm) of material to extreme pressure (p > 300 GPa)

1. force-generating deviceuniaxial force ( 單軸力 ) is applied to the bases oftwo anvils

2. two-opposing diamond anvils ( 對頂鑽石砧 ): mm size (very hard and virtually incompressible) p = F/A

3. metal gasket ( 金屬密封墊 )

4. pressure-transmitting media ( 壓力傳輸介質 )uniaxial pressure ( 單軸壓力 ) supplied by DAC maybe be transformed into hydrostatic pressure ( 流體靜壓 ) using a pressure transmitting media such as helium (He), argon (Ar) or paraffin oil ( 石蠟油 )pressure standard: ruby fluorescence ( 紅寶石螢光 )

(9-9)

reciprocal lattice vector G = ha* + kb* a* = (2/3a)x + (2/a)y b* = -(2/3a)x +(2/a)yFirst Brillouin zone: hexagonal by six planes that are perpendicular bisectors of a*, b*, (a*-b*)For energy near the Fermi energy F and wavevector near K = (/a)kx 2D band structure can be approximated as (k) ~ ħvFlk - Kl = ħvFlklconical dispersion of energy with eF at K point (Fermi or Dirac point) where vF = 8 x 105 m/s

Consider a carbon nanotube rolled up along the x-axis with circumference of na: (n,0)/zig zagapplying the periodic boundary conditions along the roll-up x-directionthe dispersion of 1D subbands e(k) near K point can be foundIf n is divisible by 3, the nanotube is a metal If n is not divisible by 3, the nanotube is a band semiconductor (with an energy gap Eg)

(18-6)(ISSP)

(Helium dilution refrigerator)( 氦稀釋致冷機 )

T ~ 0.3 K: limit of classical refrigeration principle3He-4He dilution refrigerator: Tmin ~ 2 mK3He: fermion; 4He: boson (superfluid below 2.17 K)3He-4He binary phase diagram (Chap 11)T > 0.87 K: homogeneous solutionT < 0.87 K: solubility gap, phase separationas T 0 K (mK range)3He-rich phase: ~pure 3He4He-rich phase: dilute 6% 3He (behaves like gas)+ 94% 4He (superfluid, almost all atoms condensed into ground orbital, behaved like a vacuum)

In the mixing chamber ( 混合器 ) of adilution refrigerator, T ~ 5-10 mK rangelighter 3He liquid is in equilibrium with the heavier dilute 3He-4He mixture

when 4He is added to the dilute mixture3He “evaporates” from pure 3He liquid and absorbs heat in the process

(12-13)

(Operation principle of 3He-4He dilution refrigerator)

3He gas pump loop: (10 torr)Pumped L4He bath: 1 K (0.1 torr)Condenser ( 凝結器 ) with constriction(flow impedance 流抗 ): 1 K L3He condensationStill ( 靜止器 ) with heater: 0.6-0.7 K only ~ 3He gas is pumped awayvapor pressure of 3He > 1 torrvapor pressure of 4He < 10-2 torr pre-cool L3He (0.6 K)Heat exchanger ( 熱交換器 ) further pre-cool L3He (0.1 K)Mixing chamber ( 混合器 ): 5-10 mK L3He virtual-evaporation ( 虛蒸發 )

(note) low temperature thermometersGe resistance RTD (range: 50 mK-100 K)RuO resistance RTD (range: 10 mK-40 K)

(ex) Oxford Kelvinox MX dilution refrigerator(12-14) base temperature ~ 10-25 mK

(Isentropic demagnetization)( 等熵 ( 亂度 ) 去磁 )

For temperature below 10 mK, dominant cooling process is isentropic (adiabatic)

demagnetization ( 等熵 ( 亂度 )/ 絕熱去磁 )of an electronic paramagnetic system ( 電子順磁系統 ) (~ 1 mK) or a nuclear paramagnetic system ( 核子順磁系統 )(~ 1 K)

For a weakly-interacting paramagnetic system with magnetic moment m and a small internal effective field B 1. apply a magnetic field H = Ba at constant initial temperature Ti ( 等溫加磁 ) spin excess Ba/Ti (M mBa/kTi)2. magnetic field is removed (Ba = 0) at constant entropy ( 等熵 ( 亂度 ) 去磁 )same spin excess B/T(spin) = Ba/Ti

final temperature for spin system T(spin) T(spin) < Ti if B < Ba

(12-15)

(Nuclear demagnetization)( 核子絕熱去磁 ) First nuclear cooling experiment (1959)use 63Cu nuclei in Cu metal 63Cu (69%), I = 3/2, m = 2.22 mp

small effective internal field for weak 63Cu nuclear moment m, B ~ 3.1 G T2(nuclei) = T1(3.1/B)for T1 = 12 mK (electronic demagnetization) Ba = 3 T = 30 kG T2(nuclei) ~ 1.2 K = 1.2 x 10-6 K

(note) use metal rather than insulator is thatconduction electrons ensure rapid thermalcontact between lattice and nuclei at T1

(ex ) A one stage cell for L3He experiment1. pre-cool stage: mixing chamber of the dilution refrigerator (5 mK)2. heat switch ( 熱開關 ): superconducting Al 3. nuclear stage: Cu nuclear cooling stage(Cu plates coated with Ag sinter) (12-18)

Lowest temperature reached (1993)1. pre-cool by 3He-4He dilution refrigerator 2. use multi-stage nuclear demagnetization (103Rh (100%), I = ½, m = 0.088 mp)3. single-shot experiment (non-cyclic) Tmin(nuclei) = 300 pK = 3 x 10-10 K

(ex) A two stage nuclear demagnetization refrigerator ( 二段式核子去磁致冷機 ) for neutron scattering experiment on Ag

1. pre-cool stage: dilution refrigerator (5 mK)(60Co NQR thermometer) 2. first stage: Cu nuclear cooling stagerefrigerant magnet B = 9 T (50 K)(Pt NMR thermometer)3. second stage: 109Ag nuclear cooling stagepolarization magnet B = 7 T(Tf = 80-350 K, T(nuclei) < 700 pK)

(12-19)

Heat capacity C(T) shows a second-order phase transition ( 第二階相轉變 ) at Tc

discontinuity in C ≠ 0 and no latent heat ( 無潛熱 ) L = 0 CS(T) = C(Ba = 0), superconducting state entropy SS(T) = dQ/T =

(CS/T)dTCN(T) = C(Ba > Bac), normal state entropy SN(T) = (CN/T)dT SN(T) > SS(T) for T < Tc, superconductor is an ordered state ( 有序態 )but SN(Tc) = SS(Tc) at Tc for second order transition (no latent heat)

(ex) molar heat capacity C(T) = Cp ~ CV of Ga with Tc = 1.09 K, Bac(0 K) = 51 G

discontinuity C ~ 1 mJ/(mol.K2)CS = C(0 G) ~ CeS + AT3 (T << D = 320 K)CN = C(200 G > Bac) ~ T + AT3

electronic contribution in superconducting stateCeS/Tc = 7.46 exp(-1.39Tc/T)

there is an activation energy Eac = 1.39 kTc = Eg/2with energy gap ( 能隙 ) Eg = 2.78 kTc

(8-21)

(Type II superconductor )( 第二類超導體 )

Ba Bac1 (Hc1 lower critical field 下臨界場 ): superconducting Meissner state ( 邁斯納態 )(S)Bac1 < Ba < Bac2 (Hc2 upper critical field 上臨界場 ): vortex state ( 漩渦態 )(S + N) Bac2 < Ba: normal state ( 正常態 )(N)

(ex) Nb0.6Ti0.4 binary alloy ( 二元合金 ) Tc = 10 K, Hc2(4.2 K) ~ 11 T (Bac2 Hc2)

(ex) Nb3Sn compound (A15 structure) Tc = 18 K, Hc2(4.2 K) ~ 24 T (1957 Matthias)

(note) large Hc2 and critical current density Jc ( 臨界電流密度 ) needed for superconducting magnet ( 超導磁鐵 )

(8-22) Bernt T. Matthias (1918-

80)

(ex) 1.5 GeV Taiwan Light Source (TLS 台灣光源 ) in the National Synchrotron

Radiation Research Center (NSRRC 國家同步輻射研究中心 )with superconducting wavelength shifter ( 超導增頻磁鐵 ), superconducting

wiggler ( 超導聚頻磁鐵 ) and superconducting RF cavity ( 超導高頻共振腔 ) (Nb-Ti

wire)(note) a new 3 GeV Taiwan Photon Source (TPS) is under construction

(2009-)

(8-23)

Normal metal behaves like a weakly interacting Fermi gas (Fermi liquid) In the superconducting state, two electrons form a loosely Cooper pair

(total spin S = 0, singlet boson) with coherence length ( 相干長度 ) (~1-10 nm)

much larger than the average interatomic spacing d (~0.1 nm)orbital angular momentum L = 0 (s-wave pairing)(note) for p-wave pairing (L = 1, S = 1), d-wave pairing (L = 2, S = 0)

BCS theory: Cooper pair are mediated by phonon-assisted attractionfermionic condensation ( 費米子凝結 ): BCS pairing + BEC macroscopic

quantum stateJ. Bardeen, L. N. Cooper, J. R. Schrieffer: 1972 Nobel physics prize“for their development of a theory of superconductivity” (BCS theory)(s-

wave)

J. G. Bednorz, K. A. Muller: 1987 Nobel physics prize“for their important break-through in the discovery of superconductivity

in ceramic materials” (high temperature superconductors HTSC 高溫超導體 )(d-

wave)

A. A. Abrikosov, V. L. Ginzburg: 2003 Nobel physics prize“for pioneering contribution to the theory of superconductors” (phenomenology 現象學 )

(8-24)

(Liquid 4He)( 液氦四 )

Heat capacity C = Cp ~ CV of liquid 4He showsa liquid phase transition from normal liquid ( 正常液體 ) (liquid He I) to superfluid phase ( 超流體 ) (liquid He II) at 2.17 K ( point) -line separates LHe I and LHe II triple point ( point) at 2.17 K where LHe I, LHe II and vapor coexistsanother triple point at 1.74 K where solid (bcc) is in equilibrium with LHe I and LHe II

liquid 4He behaves like is a weakly interacting Bose gas with large quantum zero-point motion1. large molar volume ( 大摩爾體積 ) Vm(observed) = NA/n = 27.6 cm3/mol > Vm(calculated) ~ 9 cm3/mol2. low critical point ( 低臨界點 ) Tc = 5.20 K (low binding energy) 3. stable liquid phase from 4.22 K to 0 K at 1 atm ( 穩定液相 ), solid phase only for p > 25 atm (see Chap 12 cryogenics)

(7-15)

Fountain effect ( 噴泉效應 ) (1938)thermo-mechanical effect ( 熱機效應 )when radiation warms a superfluid, expansion push up the free surface of liquid forming a fountain manifestation of two-fluid model of LHe II

Creeping effect ( 爬行效應 )LHe II will creep up the side of open container to form a layer, 30 nm thick liquid film (Rollin film) on surface (will creep out of a open container and forming a drop below)

P. L. Kapitsa (1894-1984) (discovery of superfluid in 1937) 1978 Nobel physics prize, “for his

basic inventions and discoveries in the area of low temperature physics”(7-17)

(Superfluidity in liquid 3He)( 液氦三超流性 )

3He is a fermion with nuclear spin I = ½

3He remains liquid for pressure less than~34 atm (~3.4 MPa)(note) 1 Pa = 1 N/m2 = 9.87 x 10-6 atm1 atm = 1.01 MPa

L3He shows a phase transition from normal liquid to superfluid phase (liquid A or liquid B) for T < 2.5 mK (1971) (note)to liquid B at 1.9 mK (1 atm) (see Chap 12 Cryogenics for low temperature cooling method)

Normal liquid 3He behaves like a weakly interacting Fermi gas

(7-20)

In the superfluid phase, two 3He fermions form a loosely boson pair (Cooper pair,

mediated by spin fluctuation) with radius much larger than the average interatomic

spacing (pair radius r >> d)nuclear spin I = 1, 2I + 1 = 3, mI = 0, ±1orbital angular momentum L = 1 (p-wave pairing)

phase A: mixture of mI = 1 and -1 (in applied magnetic field Ba, the phase divides into two components of opposite nuclear magnetic moments, A and A1) phase B: mixture of mI = 0, 1, -1

Fermionic condensation ( 費米子凝結 ): BCS-like pairing + BEC(Bardeen-Cooper-Schrieffer theory on electron pairing in superconductors)

D. M. Lee, D. D. Osheroff, R. C. Richardson 1996 Nobel physics prize “for the discovery of superfluidity in helium-3” A. J. Leggett2003 Noble physics prize, “for the theory of superfluids”

(7-21)

(Bose-Einstein condensation of dilute gas of alkali atoms)( 鹼金屬原子稀釋氣體之玻色 - 愛因思坦凝結 )

Bose-Einstein condensation (BEC) of adilute boson gas (vapor) of 2000 87Rb atoms (e + p + n = even, boson)cooled by combination of laser cooling and magnetic evaporation cooling

particle velocity distribution shows asharp peak centered around zero speed v = 0 (condensate atoms inthe ground state) below Einstein condensation temperature TE ~ 170 nK (left: T ~ 400 nK > TE, center: T ~ 200 nK ~ TE, right: T ~ 50 nK < TE) (in

3D)

for the dilute gas at T, room-mean-square velocity vrms = (3kT/M)1/2 (see Chap 14)

particle concentration n = N/V ~ 1010 cm-3 due to small trapped volume V n ~ nQ quantum boson gas at ultra-low temperature

E. A. Cornell, W. Ketterle, C. E. Wieman, 2001 Nobel physics prize“for the achievement of Bose-Einstein condensation in dilute gases of alkali

atoms”

(7-22)

(Laser cooling)( 雷射冷卻 )

Dilute gas (vapor) of atoms can be cooled by combination of laser Doppler cooling

and magnetic evaporation cooling

Magneto-optical trap ( 磁光陷阱 ) 1. three pairs of two circularly-polarizedcounter-propagating laser beams from laser diodes with a red-detuned frequencyhf < E ( 紅調變頻率圓偏振雷射 ) 2. two solenoid magnets with currents inopposite directions (anti-Helmholtz configuration), generate a spherical quadrupole magnetic field B ( 球四極磁場 )

Dilute atom vapor is cooled and trapped in a very small volume

Steven Chu ( 朱棣文 ), C. Cohen-Tannoudji, W. D. Philips1997 Nobel physics prize, “for development the methods to cool and trap atoms with laser light”

(12-20)

3. High-Temperature Superconductors ( 高溫超導體 )

Exotic superconductors ( 奇特超導體 )- new physical properties are exhibited- existing theoretical models are challenged- superconducting pairing mechanism is not well established High-temperature superconductors ( 高溫超導體 )(1986)(La,Ba)2CuO4 (214) cuprate (copper oxide, 銅氧化合物 )Tc ~ 30 K (> Tc = 23 K of Nb3Ge)(J. G. Bednorz & K. A. Muller, 1987 Nobel Physics Prize/for theirimportant breakthrough in the discovery of superconductivityin ceramic materials )

YBa2Cu3O7 (123) Tc = 95 K (> LN2 77 K)Bi2Sr2CaCu2O8 (2212) Tc = 110 KQuasi-2D electronic system, CuO2 layers dominatesthe superconducting properties Pairing: anisotropic d-wave pairing (s = 0, l = 2)singlet with anisotropic energy gap (k) lcoskxa - coskyal Superconducting mechanism ( 超導機制 ):BCS theory based on Fermi-liquid theory not applied?

(10-21)(ISSP)

1900 1920 1940 1960 1980 20000

20

40

60

80

100

120

140

160

180?

Hg2Ba

2Ca

2Cu

3O

10

Bi2Sr

2CaCu

2O

8

Hg2223 (pressure)

La1.85

Ba0.15

CuO4

Nb3Ge

Nb3SnNbN

Tl2Ba

2Ca

2Cu

3O

10

YBa2Cu

3O

7

NbPbHg

LN2

LHe

Tc (

K)

Year

(ex) typical high-temperature superconductorsystem La2-xSrxCuO4 (0 x 0.4) with maximum Tc ~ 38 K for optimum-doped La1.85Sr0.15CuO4 1. Crystal structure: tetragonal-orthorhombic structural transition ( 四角 - 正方結構轉變 ) due to CuO6 octahedron distortion2. Electronic properties: metal-insulator transition ( 金屬 - 絕緣體轉變 ) from antiferromagnetic (AF) insulator ( 反鐵磁絕緣體 ) to superconducting (SC) metal due to strongly-correlated electrons ( 強關聯電子 ) in CuO2 layers. 3. Superconducting properties related to the formation of pseudogap ( 虛能隙 ) in the normal state?

(Exercise 10) Final report (due day: 1/12/2007)Describe as much as you can on the propertiesLa2-xSrxCuO4 (0 x 0.4) system Specify:1. Crystal structure2. Normal state electronic properties 3. Superconducting properties

(10-22)(ISSP)

Phase diagram: LaFeAs(O1-xFx)Luetknes et al. Nature Mater. 8, 305 (2009) Hess et al. submitted (2009)

Conclusions

I hope you enjoy my talk