FIRST YR JAPANESE 2
FIRST YR JAPANESE 2 JAPAN 2
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This 23 page Class Notes was uploaded by Zoe Rogahn on Thursday October 22, 2015. The Class Notes belongs to JAPAN 2 at University of California Santa Barbara taught by Staff in Fall. Since its upload, it has received 28 views. For similar materials see /class/226846/japan-2-university-of-california-santa-barbara in Japanese at University of California Santa Barbara.
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Date Created: 10/22/15
JFJ OT T T RA H r L7 1 zit OXIDE INTERFACE GROUP MEETING What is a Mott insulator Mott transitions as quantum phase transitions Physics near the Mott transition 1 ll 39 39 gilrcc rrt i3 r 2 Wt 6 lg SEE f a 5 39 a A I n 71 in n p a l s L 7 x x 4 quotit EJ l l i l l l 1 has 11 l X W x it x 391 M W y l l Xi rswijnfk quotI A l 9772 i 5 f V N N l x aquot 7 f l AV f39i 3 i K2 3 39 5 n ltZVAXA J ukhtrr 1quot t 3953 r w 7 J M r X l xkxi Iy KC 394 a 392 kaknyyquot 1 iii H 7quot 39r nD RagaJ Us vn QVUWW J lt d gt O O O O O Q Q Q Mott RMP OOOQQ 9 hole FIG 1 A crystalline array of monovalent atoms 04 as Imagine varying the lattice spacing of a solid s1 74va When the spacing is large compared to the Bohr radius it should be an insulator 2A Eion Eaff all4 as When spacing is reduced orbitals overlap and bands form leading to a metallic state FIG 1 A crystalline array of monovalent atoms gtgtlltltlt Usually we require a Mott Insulator to have an odd number of electrons per unit cell gtgtXltlt Then the atomic states are degenerate r314 Usually there is magnetic or occasionally more complex order at low temperature gt3KltltA complication the low T state usually has an enlarged unit cell with an even number of electrons in it that could be interpreted as a hand insulator Physically a Mott Insulator is one which is insulating due to interaction induced localization not due to band physics 3 This is a question of energy scales 3 Deep in the Mott state Magnetic paramagnetic insulator insulator I USE UBBARD H 7220ch UZmTnu 17gt 139 9 Two dimensionless parameters F Uz t Coulomb energyBandwidth CF ling n ltni nip 1 for MI 15 More generally have 9 mul ple hopping parameters 9 more orbitals more interac ons l J W f f y 3 xl U x r l l J K l 4f is 5K i V K la is ww 4 K VQLJ VX rl L39g 1 fix x p 1 If a f N T i l Er i l l r A quot l M L i39 kiwy y 00000 hole FIG 1 A crystalline array of monovalent atoms When doped away from halffilling the Mott insulator becomes a bad conductor particlesholes can hop Without additional sv 71R energy cost w as many complex thlngs can occur phase separation stripes localization MOTT TRANSHTMON Mott state UW S39mgle particle gap VI Mott Insulator 0 insulating 0 local moments lingconnl j n Metal 1 G Fermi surface M6 tal G conducting G Pauli paramagnetism bandwidth comm QUANTUM PHASE TRANSMTHQNS Any phase transition at T0 is a quantum phase transition QPT 3 Quantum because at T0 there is perfect phase coherence 4 At Tgt0 there is always some nite dephasing length beyond which the physics is effectively classical The Mott transition at T0 is a QPT TYPES Qt 3 First order transition 9 nLevel crossingquot 3 Two phases are unrelated 9 Observables jump at QPT QPT 9 Second order transition 3 Phases smoothly transform into one another 9 Diverging correlation length 0 nQuantum criticalityquot BAN DWIDTH CONTROLLED MOTT TRANSITION 92K Mott originally argued for E b 1 39 t re ictions a first order trans1tlon 215fg jiggeg ef m gtgtIlt But he Changed his mind V M 1 d later V as If it is a line of first order transitions must exist at TgtO insulator metal 92K this is often seen in p experiment FIRST ORDER MOTT T RA N S I T I O N S Vanadates from Mott s RMP I quot Cr VIHXMX203 004 002 0 002 004 006 5OOIIIIIIIIIII I CRITICAL POINT I I 400 I I I I I 39 Iaim 3 INSULATOR I METAL 0 300 I PRESSURE EXP J x a V 0 g a 3 lt IE I quot 0 00380139 I E I o 0030 Ti 2 I It 200 I I I I I I 100 I C ANTIFERROMAGNETIC INSULATOR I I i u I 0 I I I I I I I I If INCREASING PRESSURE a 4 kbarDIVISION ZERO PRESSURE POINT MOVES WITH TOP SCALE Il 210 Nickelates perovskites Rare 0th Ionic Radius angstroms O 20 we 0 d I I I 1 t 0 M09 E r 400 P AA Damazeau e raI 5m ELI Lacorre eI aI Q PresenI work 300 INSULATOR 200 100 TransIIion Temperature K 0 086 088 090 092 Tolerance FacIor IO TiO O V203 TIZO3 1 V0 conoucrwm ohmquot cmquot 6 IO 0 2 4 6 8 IO 12 1000 TEMPERATURE KI FIG 7 Conductivities of oxides Morin36 I I I I 104 Nd I A P 403K 8 r 8 I c 201 K 2 I 393 1039s 135K 0 a La RNI03 a 106 IL I I Jr Sm 1005 lt gt Nd Pr b 0995 I I I I 9 1 lP 5 I m Pr I Nd II E E f Eu Eu H Sm 0 49 0 c T O J I I I 0 100 200 300 400 500 Tempera rure K FIRST ORDER MOTT TRANSITIONS K ET2CuNCN2Cl 93 Seen in several organic quasi2d c 0 n du ctor s 200 100 dRdTm 7 A yaM T const K39 Mottinsulator QQFFR A1 I 10 8 quot a Spin liquid 22 Tc Mew Fermi liquid Superconductgr 1 i i i i 2 3 4 5 6 Pressure 10391GPa Eco N D R D E R M OTT T RA N IT 1 o N s but they do exist 921 eg magnon BEC transitions edges of magnetization plateaus 3 o T15K l 4 j o T50 mK HC157 T 39 339 3 39 E 5 39 b 3939 2 FIG 2 Di erent predictions 3 2 l 0 about the way the activation 11 3 CT 39 C o o energy changes at the trans1 C 39 tion LU 1 1d O I I I I I I I I I I I I I I I I I I I I I I I I O 2 4 6 8 1O 12 14 Field H T I But I do not know of any experimentally clear examples of continuous Mott transitions ZQNTHNUQUS MQTT TRANSlTEQNS Theoretically this is an active suggestion lVlight occur in frustrated situations Even if it doesn39t the most interesting situation is When the transition is only weakly rst order 1 In this case the material combines features of metals and insulators and exhibits strong uctuations near the transition SOME PHYSICAL FEATURES FEATURES OF THE MOTT TRANSITION On the metallic side 4 formation of band at the Fermi energy 4 mass enhancement anomalous scattering On the insulating side 4 magne c order 4 quasipar cle gap 1 High energy scale picture deep in the Mott state Zaanen Sawatzky Allen scheme AND EVOLUTIQN EF Fermi level a a E MENU interacliwn u U charge gap p band a MonHubbard Insulator charge gap drband 7 e e SF Farmi level a a 2 E merammn u u A phand b Charge Transfer Insulator THET3FEFaTV 1 253 4 1 gtMl 39 551iy U A AN VV I 69 5 6 l Giif 5 3 gll 5 amp L35 v 6 ggg39Q d0 d1 d2 d3 d4 d5 d6 d7 d8 8 8 f 1 5g E gt Ti3d LH 8 8 5 Optical conductivity 2 lcm391 Energy CV FILLING CONTROL quot La2XSrXCuO4 ltagt o BIS 1 Spectral welght transfer 3 Mott Hubbard 5 5 4 U gt N E N I PES 4 EF gt PES 1 Enoergy r1eativ2e to 153FeV4 5 11 u b N4 N1 W I x AM EF I Hole doping x m 2X 1x Sawatzky Undoped Insulator 1 m LHB n1 UHB CT gap 15 eV Energy MASS ENHANCEMENT OUU 30 l I I 700 0 MAAAAAAA LoNiO3 O Q AAAM Mam 2000 0 MAMW 500 600 22aeas AA 00000000 0 A A 00 09 0 o k 13 500 A oomm 400 1500 92 g N E 3 400 E a 300 2 9v 3 1000 g 300 lt1 N B 200 200 500 V 100 o x 100 1 1 a 1 3 Y Yband M to L i 0 I I I I q 0 o 20 4o 60 80 I00 0 100 200 300 400 500 T2K2 TK V w 2y 3 80 Inf K N X 60 O E l quotD 40 I E quot NJ I P I I 20 I I I I I nmamow I X