Two Dimensional Triangular Mott Hubbard Insulators in Real Life: - - PowerPoint PPT Presentation

▶
two dimensional triangular mott hubbard insulators in
SMART_READER_LITE
LIVE PREVIEW

Two Dimensional Triangular Mott Hubbard Insulators in Real Life: - - PowerPoint PPT Presentation

Jan 09, 2024 46 likes •851 views

Two Dimensional Triangular Mott Hubbard Insulators in Real Life: Sn/Si(111), Sn/Ge(111) and Si/SiC(0001)surfaces G. Profeta (L'Aquila, Italy) S. Modesti E.Tosatti (Trieste, Italy) Phys. Rev Letters 98, 086401 (2007) Hvar, 28 September

slide-1
SLIDE 1

Two Dimensional Triangular Mott Hubbard Insulators in Real Life: Sn/Si(111), Sn/Ge(111) and Si/SiC(0001)surfaces

  • G. Profeta (L'Aquila, Italy)

E.Tosatti (Trieste, Italy)

  • Phys. Rev Letters 98, 086401 (2007)

Hvar, 28 September 2008

  • S. Modesti
slide-2
SLIDE 2
  • G. FRANCO BASSANI

1929- 2008

slide-3
SLIDE 3

STRONG CORRELATIONS IN 2D

slide-4
SLIDE 4
slide-5
SLIDE 5

Sn1/3/Ge(111) Si1/3/SiC(0001) Sn1/3/Si(111)

Carpinelli, et al (96) Johansson, et al (96) Uhrberg, et al(2000) Modesti, et al (2007) Figure from Plummer et al

slide-6
SLIDE 6

Sn/Ge(111)

W ~ 0.35 eV

slide-7
SLIDE 7

SURFACE STATE “WANNIER FUNCTION” SUGGESTS STRONG CORRELATIONS

Sn Sn Sn

7.35 A

Ueff ~ 0.5 eV V<~ 0.25 eV W~ 0.35 eV !

slide-8
SLIDE 8

2D TRIANGULAR LATTICE, HALF FILLING

  • - NARROW BANDS
  • - EL-PH COUPLING
  • - STRONG EL-EL INTERACTIONS
  • - CDWs, BAND JT, MIXED VALENCE,

2D SUPERCONDUCTIVITY?

  • - MAGNETISM, SDWs?
  • - 2D MOTT HUBBARD AFM INSULATOR?

( OR RVB SPIN LIQUID STATE)

slide-9
SLIDE 9

U>Uc: MOTT INSULATOR U t MOTT TRANSITION: HUBBARD MODEL U < Uc: METAL

slide-10
SLIDE 10
slide-11
SLIDE 11

LATTICE MODEL

  • - NARROW 2D BAND, W~0.35 eV,

DEGENERACY d =1

  • - ON-SITE COULOMB REPULSION U~2W
  • - SOME N. N. REPULSION V < W
  • - EL.-PHONON COUPLING g

SANTORO et al PRB 59, 1891(1999)

slide-12
SLIDE 12
slide-13
SLIDE 13

LANDAU THEORY

3x3 DENSITY MOD 3x3 MAGNETIZ. MOD UNIFORM MAGNETIZ.

slide-14
SLIDE 14

HARTREE FOCK PHASE DIAG. COLLINEAR A: ρK=m=0, SK#0, Mott insulator. D: ρK#0, m=SK= 0, CDW metal 77K SANTORO et al PRB 59, 1891(1999) undist. metal

slide-15
SLIDE 15

300 K 100 K

Sn/Ge(111)

E.W. PLUMMER et al, (1996,++) “CDW”

slide-16
SLIDE 16
slide-17
SLIDE 17

M.C. ASENSIO et al

  • S. MODESTI et al

R.G. UHRBERG et al .......................

slide-18
SLIDE 18

PEREZ+ al (1999): LDA GROUND STATE IS 3x3 UP_DOWN DISTORTED (-10 meV) TEMPERATURE: CAUSES ORDER-DISORDER TRANSITION (“dynam. fluctuation” model) STRONG CORRELATIONS IRRELEVANT (!!!???)

Sn/Ge(111): LDA .

UP DOWN

slide-19
SLIDE 19

HARTREE FOCK PHASE DIAG. COLLINEAR D: ρK#0, m=SK= 0, CDW metal 77K 300K undist. metal SANTORO et al PRB 59, 1891(1999)

Sn/Ge(111) T-DEPENDENCE: PHASE TRANSITION

slide-20
SLIDE 20

Si/SiC(0001)

L.I. JOHANSSON et al (96)

  • M. SABISCH et al (97)

J.E. NORTHRUP,

  • J. NEIGEBAUER (98)

G.E.SANTORO et al (98,99)

  • V. ANISIMOV et al (2000)

OSTENDORF et al

LDA

slide-21
SLIDE 21

MOTT INSULATING

L.I. JOHANSSON et al (96)

slide-22
SLIDE 22

Si-SiC(0001)

MOTT-HUBBARD INSULATOR!

slide-23
SLIDE 23

HARTREE FOCK PHASE DIAG. COLLINEAR A: ρK=m=0, SK#0, Mott insulator. SANTORO et al PRB 59, 1891(1999)

Si/SiC(0001)

slide-24
SLIDE 24

Sn/Si(111)

W ~ 0.45 eV

slide-25
SLIDE 25

UHRBERG et al (2000)

Sn/Si(111)

UNDISTORTED 2D METAL...

slide-26
SLIDE 26

Sn/Si(111) DFT : UNDISTORTED 2D METAL (BUT CLOSE TO 3x3 DISTORTION)

PEREZ et al (2001)

slide-27
SLIDE 27

HARTREE FOCK PHASE DIAG. COLLINEAR undist. metal SANTORO et al PRB 59, 1891(1999)

Sn/Si(111)

slide-28
SLIDE 28

HARTREE FOCK PHASE DIAG. COLLINEAR A: ρK=m=0, SK#0, undistorted Mott insulator. D: ρK#0, m=SK= 0, “CDW” distorted metal undistorted metal SANTORO et al PRB 59, 1891(1999)

Si/SiC(0001) Sn/Ge(111) Sn/Si(111)

slide-29
SLIDE 29

S n / S i AT LOW T, SOME EVIDENCE OF 3X3 BAND FOLDING! UHRBERG et al (2000)

Sn/Si(111) BUT....

slide-30
SLIDE 30
slide-31
SLIDE 31
slide-32
SLIDE 32

“ab initio” L(S)DA +U CALCULATIONS H = H0+ U Σi niσni-σ

  • <UΣi niσni-σ>

= H0+ (U/2) Σiσ niσ(1 - niσ )

ANISIMOV et al, 1990's (LMTO)

  • M. COCOCCIONI, S. DE GIRONCOLI 2002 (PWSCF)

MOTT HUBBARD INSULATOR here appears as MAGNETIC (AF) BAND INSULATOR

slide-33
SLIDE 33

U=0 U(Sn)=4 eV

∆

Sn/Ge(111)

LSDA+U:

U=4 eV

Correlations may turn Sn/Ge(111) into a MAGNETIC and UNDISTORTED NARROW GAP INSULATOR!

  • G. PROFETA, E.T.,

PRL 98, 086401 (2007) U REMOVES DISTORTION!!

slide-34
SLIDE 34
slide-35
SLIDE 35

EVOLUTION OF Sn/Ge(111) 10K 77K 300K

slide-36
SLIDE 36

Sn/Si(111) LSDA+U:

  • G. PROFETA, E.T., PRL 98,

086401 (2007) EF

MAGNETIC INSULATOR GROUND STATE NO DISTORTION ∆E ~ - 10 meV/adat

slide-37
SLIDE 37

Sn/Si Sn/Ge insulating gap Sn magn. moment Sn adatom heigth exchange splitting

slide-38
SLIDE 38

Sn/Si(111) STM/STS data

  • S. MODESTI et al

PRL (2007)

slide-39
SLIDE 39
slide-40
SLIDE 40
slide-41
SLIDE 41

EVOLUTION OF Sn/Si(111) 50K 300K

slide-42
SLIDE 42

HARTREE FOCK PHASE DIAG. COLLINEAR A: ρK=m=0, SK#0, Mott insulator. SANTORO et al PRB 59, 1891(1999)

Si/SiC(0001) Sn/Ge(111) Sn/Si(111)

slide-43
SLIDE 43
  • K. KANODA (2006)
slide-44
SLIDE 44
  • K. KANODA (2006)
slide-45
SLIDE 45
slide-46
SLIDE 46

SPINS ½ ON TRIANG. LATTICE ESTIMATE OF AF COUPLINGS

Si/SiC (0001) J ~ 30 K Sn/Si(111) J ~ 100 K Sn/Ge(111) J~ 150 K ∆EFE-FI ~ 3J

slide-47
SLIDE 47

T U PSEUDOGAP METAL (PM) MOTT INSULATOR (AF) d-WAVE SUPER COND. Sn/Si(111) SPECULATIVE PHASE DIAG.

slide-48
SLIDE 48

Sn/Si(111) t ~ 350 K T = 0.2t ~ 70 K!

slide-49
SLIDE 49

EXPERIMENTAL CHALLENGES

  • - DETECT SPIN ½ ON Si ADATOM

IN Si/SiC(0001), AND ON Sn ADATOM IN Sn/Si(111), Sn/Ge(111)

  • - UNDERSTAND SPIN ORDER
  • - MAYBE CREATE “2D Hi-Tc “

SUPERCONDUCTOR BY DOPING ANY OF THESE SURFACES AWAY FROM HALF FILLING

slide-50
SLIDE 50

CONCLUSIONS

  • - GENUINE 2D MOTT HUBBARD

INSULATORS IN SEMICONDUCTOR SURFACE STATES

  • - BAND PHYSICS (VALENCE

DISPROPORTIONATION) RESTORED BY TEMPERATURE IN Sn/Ge(111)

  • - PROBABLE T-INDUCED METALLIZATION

IN Sn/Si(111)

  • - d-WAVE SUPERCONDUCTIVITY BY DOPING?
slide-51
SLIDE 51

THE END

  • G. Profeta, E.T., Phys. Rev Letters 98, 086401 (2007)
  • S. Modesti et al, Phys. Rev Letters 98, 126401 (2007)
slide-52
SLIDE 52

SPIN ORBIT INTERACTION: WEAK ANISOTROPY

slide-53
SLIDE 53
slide-54
SLIDE 54

Si/SiC(0001) LSDA+U (3x3 FERRIMAGNETIC)

Anisimov et al,

  • Phys. Rev. B 61,

1752 (2000)

slide-55
SLIDE 55

Sn/Ge(111)

W ~ 0.35 eV

slide-56
SLIDE 56

Sn/Si(111)

  • S. MODESTI et al

n(EF )

slide-57
SLIDE 57
slide-58
SLIDE 58

“AB-INITIO” : DENSITY FUNCTIONAL CALCULATIONS

  • - ACCURATE FOR GEOMETRY, BOND

LENGTHS

  • - Sn/Ge(111) 3x3 DISTORTED, METAL
  • - Sn/Si(111) sqrt3xsqrt3 UNDISTORTED

METAL

  • - Si/SiC(0001) AF INSULATOR,

BUT GAP TOO SMALL

slide-59
SLIDE 59

(4H)-SiC(0001)

slide-60
SLIDE 60

IS B PHASE REALIZED ANYWHERE??

slide-61
SLIDE 61

C1/3/Ge(111)

C

slide-62
SLIDE 62
slide-63
SLIDE 63

The Mott-Hubbard Transition

U

±

(ONE BAND MODEL)

energy Z

slide-64
SLIDE 64

LSDA+U calculations ELDAU[nr]=ELDA[nr]EHub[nm

I]−EDC[n I]

EHub−EDC=EU=U/2∑I∑m, {nm,m

I −∑m' nm,m' I

nm' ,m

I }

  • -- Slab geometry with three Ge (Si) bilayers, 18 atoms each in 3x3 cell

3 Sn adatoms in T4 position and 9 H atoms saturating bottom surface

  • - PWSCF code (www.pwscf.org)

Plane Wave cutoff energy 12 Ry Monkhorst-Pack k-points up to 36 in IBZ, 0.002 Ry of gaussian smearing Gradient corrected LDA (PBE)

  • -- Total energy curves calculated by constrained optimization
  • G. PROFETA
slide-65
SLIDE 65

SPIN: FERROMAGNETIC STATE

Si Si

ADATOM

∆E = 9J/4

slide-66
SLIDE 66

SPIN: FERRIMAGNETIC STATE

Si Si

ADATOM

∆E = - 3J/4

slide-67
SLIDE 67

20 100-200 T (K) Mott Insul.

  • Per. Distort.

Metal Undist.(Fluct.) Metal Sn/Ge(111) ? ?

slide-68
SLIDE 68

Sn/Si(111)

EXPT.: UNDISTORTED METAL

  • TH. : UNDISTORTED METAL

(CLOSE TO 3x3 DISTORTION)

PEREZ et al (2001)

slide-69
SLIDE 69

Sn/Ge(111)

UP Sn ADATOM DOWN Sn ADATOMS PEREZ et al (1999) DE GIRONCOLI et al(2000) BALLABIO et al (2002)

LDA

∆E ~ 9 meV/adatom

“CDW” “Band JT effect” “Bond Density Wave” “Disproportionation”

slide-70
SLIDE 70
slide-71
SLIDE 71
slide-72
SLIDE 72

ON MOST SEMICONDUCTOR SURFACES: NO MOTT INSULATORS, NO CDW/SDW, NO SC STATES....

IN REALITY: WHY? CHEMICAL PASSIVATION OF “DANGLING BONDS”

slide-73
SLIDE 73

20K-100K=3x3 T>100K=root3xroot3 Si(111)7x7

slide-74
SLIDE 74

”

SEMICONDUCTOR SURFACES

“DANGLING BONDS”

slide-75
SLIDE 75

IDEAL Si SURFACES:BAND STRUCTURE

HALF FILLED SURFACE STATES (=2D METALS)

SURFACE RECONSTRUCTIONS!

EF

slide-76
SLIDE 76

NEED SURFACE DANGLING BOND STATES THAT WILL NOT SPONTANEOUSLY PASSIVATE!

slide-77
SLIDE 77

HARTREE FOCK PHASE DIAG. COLLINEAR A: ρK=m=0, SK#0, Mott insulator. D: ρK#0, m=SK= 0, CDW metal 77K 300K undist. metal SANTORO et al PRB 59, 1891(1999)

Si/SiC(0001) Sn/Ge(111) Sn/Si(111)

slide-78
SLIDE 78
slide-79
SLIDE 79

Sn/Si(111)

Expt.: metallic, does not distort down to 5 K

Si Si

slide-80
SLIDE 80