FROM THE BCS EQUATIONS TO THE ANISOTROPIC SUPERCONDUCTIVITY EQUATIONS. Luis A. PérezP. Chumin Wang

Size: px

Start display at page:

Download "FROM THE BCS EQUATIONS TO THE ANISOTROPIC SUPERCONDUCTIVITY EQUATIONS. Luis A. PérezP. Chumin Wang"

Morris Stafford
5 years ago
Views:

1 FROM THE BCS EQUATIONS TO THE ANISOTROPIC SUPERCONDUCTIVITY EQUATIONS J. Samuel Mllá Faulad de Igeería Uversdad Auóoma del Carme Méxo. M Lus A. PérezP Isuo de Físa F UNAM MéxoM xo. Chum Wag Isuo de Ivesgaoes e Maerales UNAM Méxo. M

2 Oule MOTIVATION. THE GENERALIZED HUBBARD MODEL. TWO PARTICLES. THE BCS GENERALIZED EQUATIONS. THE p AND d COUPLED EQUATIONS. SUPERCONDUCTING PROPERTIES. CONCLUSIONS.

3 D Superodug Gap Smmer Exeded s* Smmer gs* os xa os g s* s s* s* a d x - Smmer gd os xa os g d d d a p Smmer g p 3 p s xa s g p p a

4 The Par Smmer Sgle : Φ S where Ψ Ψ S r S r r r Ψ S r α β β α r wh α β. Trple 3 : α α ΦT ΨT r r β β where Ψ r r Ψ r r. T T [ α β β α ]

5 The Crsal Sruure Ru-O O plaes Cu-O O plaes Smlar Sruure for Sr-Ru ad La-Ba BaSr ssems

6 The Dsoro of he Square Lae Y 3 Y 3 δ δ 3 δ δ 3 X X The hoppg o frs ad seods eghbors are he same boh dreos ' ' 0 ' 3 3 δ δ The hoppg o seods eghbors are dffere XY XY dreos 3

7 The Expermeal Evdee for a Dsoro o he Surfae Image of he surfae for Sr RuO 4 seeg from up of Ru-O plaes where we a see a dsoro of he oahedros formed b oxges. Mazdorf e al. See

8 The The Hubbard Model Hubbard Model Real Spae Real Spae l l l V U H ˆ > >< >>< << > < > < >> << > < l v r' rd d vl R r R r r' r' r' r' r R r R r * * ϕ ϕ ϕ ϕ ev v ev v ev v V ev v U The egrals The egrals of of erao erao bewee bewee wo wo eleros eleros are: are: * 3 u m r d h R r r R r ϕ ϕ h where where

9 Mapg Mehod o Spae of Saes β β β β x mp 0 0 ' os K os K os a / a / [ K K a / ] ' os K K 3 parg odo: x x [ a / ] x E E > 0 A proeed square lae for 74 wo parles saes wh rple sp orrespodg o spae of saes for hperube of dmeso four. S Mllá e al. Phsa C

10 The Phase Dagram wo parles a Two eleros b Two holes boh wh U6 0 V0 D0.5 0 D

11 The Elero Levels a d p s a p s d b d p s p b p s p d Two eleros Two holes

12 The The Geeralzed Hubbard Model Geeralzed Hubbard Model l l l V U H ˆ > > < >> < << > < > < >> << > < ξ ' ' ' ' ' ' ' ' ˆ W N V N H s s [ ] [ ] [ ] ' ' ' ' ' 3 3 ' ς γ β β β β β V U V ' ' ' 3 3 ' ς γ β V W [ ] [ ] [ ] a a ' a ' a a a ' a ' a a a x x x x x os os os os os os ' ' ' ' ς γ β Real Real Spae Spae: Reproal Spae Reproal Spae: Poeal Ierao wh Aparallel Sp Poeal Ierao wh Aparallel Sp: Poeal Ierao wh Parallel Sp Poeal Ierao wh Parallel Sp: where where [ ] µ ε ξ 0

13 BCS Geeralzed Theor ˆ - - H ε 0 µ V ' ' ' ' ' ' For he sgle ase he spaal par of he eerge gap s ' ' ' f η ' V e ξ η gη [ where η s s* d gs* s / s* os xa os a g os a os a whle he rple ase d 3 p V ' o ' ' wh η p g [ s a s a ] η ] [ ] [ ] x x ξ ' f η g ' η ' ' ' 3 p ' Mlla e al. Phss Leers A

14 p-smmer where d-smmer where The Coupled Equao for p ad d Smmer V 4δ 3 s xa s as x Ns E p E p ε0 µ p s xa s a N a [ ] [ ] V 4 3 Ns E d µ he Chemal Poeal µ for he Superoduor Sae sasfed 0 s ε µ Eη ah E T η os a os os x a E ah ad wh he mea feld aproxmao: U ε 4V 0 x 3 x 3 E p T [ ] ' ' os a os a os os 0 x x [ ε ] [ os a os ] 0 d x a B d µ B a E ah d T B D ε dε

15 T vs for d ad p Smmeres B T / B T / / Ssems wh UV δ I. Maz e al. Phs. Rev. Le δ squares rle rles up ragl gles s 0. 0 dow ragl gles rhomb ombus. Ise:0.6 bla 0.5 gra

16 The Ferm Surfae Iegrad /E p ploed over he frs Brllou zoe for UVδ δ p µ p

17 The Superoduor Phase Dagram The superoduor groud sae phase dagram he spae of elero des ad δ 3. Ise: Dfferee of groud sae eerges W p -W d vs W [ ] η E V η η ε η µ 4Λ V U 4

18 The Jump of he Spef Hea a Cral emperaure vs for a ssem wh arbrar U Vδ δ The se show DOS vs E for 0.09 gre le ad 0.6 bla le. b The ump for d squares ad p rles smmeres as a fuo of.

19 Elero Spef Hea vs T I low emperaures he spef hea s ver sesve o he odal les d squares ad p rles smmeres

20 The Cral Temperaure for he Asorop Superoduv 0 - * s-wave B T / If U grows s* drop d-wave L.A. Pérez P e al. Phsa B p-wave Vδ δ ad U8 0.

21 The Elero Spef Hea C α /C T α T/ α T/T α s 0.5 α p α d J.S. Mlla e al. Proeedgs of AIP T/T Vδ δ p ad.4 d. The s smmer wh U

22 Comparso of Theor ad Experme.0 C p /TC T J.S. Mlla e al. Proeedgs of AIP S.Nshza Nshza e al. J. Phs. So. Jp T/T Adus for p smmer wh Vδ δ ad wh he expermeal daa sold ragles of Sr RuO 4.

23 Comparso of Theor ad Experme T CeT/TCeT x0.4 x0.0 x eV eV La -x Sr x CuO 4 T. Masuza N. Momoo M. Oda ad M. Ido J. Phs. So. Jp dw-wavewave for UVδ δ T

24 The Sgle Parle Exao Eerg Gap / x The double of he mmal eerge erg order o brea a Cooper par r 0 as a fuo o of polar agle θa - / x for dw-wave wave wh UV Vδ δ ad he orrespodg Ferm Surfae.

25 CONCLUSIONS. The researh of sgle ad rple superoduv suggess he posbl of a ufed heor abou he Asorop Superoduv for p ad d smmeres a square lae.. The p- ad d-wave superoduv are respevel ehae he low ad hgh elero des regme. 3. We a fd approprae se of Hamloa parameers order o fd he elero spef hea ha mahes ver well wh expermeal daa. 4. The we have ow he possbl o assoae heor ad expermes of some maerals.

Quantum Mechanics II Lecture 11 Time-dependent perturbation theory. Time-dependent perturbation theory (degenerate or non-degenerate starting state)

Quantum Mechanics II Lecture 11 Time-dependent perturbation theory. Time-dependent perturbation theory (degenerate or non-degenerate starting state) Pro. O. B. Wrgh, Auum Quaum Mechacs II Lecure Tme-depede perurbao heory Tme-depede perurbao heory (degeerae or o-degeerae sarg sae) Cosder a sgle parcle whch, s uperurbed codo wh Hamloa H, ca exs a superposo