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 2008
G. FRANCO BASSANI 1929- 2008
STRONG CORRELATIONS IN 2D
Sn 1/3 /Ge(111) Carpinelli, et al (96) Si 1/3 /SiC(0001) Johansson, et al (96) Sn 1/3 /Si(111) Uhrberg, et al(2000) Modesti, et al (2007) Figure from Plummer et al
Sn/Ge(111) W ~ 0.35 eV
SURFACE STATE “WANNIER FUNCTION” W~ 0.35 eV ! SUGGESTS STRONG CORRELATIONS 7.35 A U eff ~ 0.5 eV V<~ 0.25 eV Sn Sn Sn
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)
MOTT TRANSITION: HUBBARD MODEL U t U < Uc: METAL U>Uc: MOTT INSULATOR
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)
LANDAU THEORY 3x3 DENSITY MOD 3x3 MAGNETIZ. MOD UNIFORM MAGNETIZ.
HARTREE FOCK PHASE DIAG. SANTORO et al PRB 59, COLLINEAR 1891(1999) A: ρ K =m=0, S K #0, Mott insulator. 77K D: ρ K #0, m=S K = 0, CDW metal undist. metal
Sn/Ge(111) E.W. PLUMMER et al, (1996,++) 300 K 100 K “CDW”
M.C. ASENSIO et al S. MODESTI et al R.G. UHRBERG et al .......................
Sn/Ge(111): LDA . PEREZ+ al (1999): LDA GROUND STATE IS 3x3 UP_DOWN DISTORTED (-10 meV) UP DOWN TEMPERATURE: CAUSES ORDER-DISORDER TRANSITION (“dynam. fluctuation” model) STRONG CORRELATIONS IRRELEVANT (!!!???)
HARTREE FOCK PHASE DIAG. SANTORO et al PRB 59, COLLINEAR 1891(1999) T-DEPENDENCE: PHASE TRANSITION 77K D: ρ K #0, m=S K = 0, CDW metal Sn/Ge(111) 300K undist. metal
Si/SiC(0001) LDA 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
MOTT INSULATING L.I. JOHANSSON et al (96)
MOTT-HUBBARD INSULATOR! Si-SiC(0001)
SANTORO et al PRB 59, HARTREE FOCK PHASE DIAG. COLLINEAR 1891(1999) A: ρ K =m=0, S K #0, Mott insulator. Si/SiC(0001)
Sn/Si(111) W ~ 0.45 eV
Sn/Si(111) UNDISTORTED 2D METAL... UHRBERG et al (2000)
Sn/Si(111) DFT : UNDISTORTED 2D METAL ( BUT CLOSE TO 3x3 DISTORTION) PEREZ et al (2001)
HARTREE FOCK PHASE DIAG. SANTORO et al PRB 59, COLLINEAR 1891(1999) undist. metal Sn/Si(111)
HARTREE FOCK PHASE DIAG. SANTORO et al PRB 59, COLLINEAR 1891(1999) A: ρ K =m=0, S K #0, undistorted Mott insulator. Si/SiC(0001) D: ρ K #0, m=S K = 0, “CDW” distorted metal Sn/Ge(111) undistorted metal Sn/Si(111)
BUT.... Sn/Si(111) S n / S AT LOW T, SOME i EVIDENCE OF 3X3 BAND FOLDING! UHRBERG et al (2000)
“ab initio” L(S)DA +U CALCULATIONS ANISIMOV et al, 1990's (LMTO) M. COCOCCIONI, S. DE GIRONCOLI 2002 (PWSCF) H = H 0 + U Σ i n i σ n i- σ - < U Σ i n i σ n i- σ > = H 0 + (U/2) Σ i σ n i σ (1 - n i σ ) MOTT HUBBARD INSULATOR here appears as MAGNETIC (AF) BAND INSULATOR
LSDA+U: Sn/Ge(111) G. PROFETA, E.T., PRL 98, 086401 (2007) U REMOVES DISTORTION!! ∆ U(Sn)=4 eV U=4 eV U=0 Correlations may turn Sn/Ge(111) into a MAGNETIC and UNDISTORTED NARROW GAP INSULATOR!
10K EVOLUTION OF Sn/Ge(111) 77K 300K
Sn/Si(111) LSDA+U: G. PROFETA, E.T., PRL 98, 086401 (2007) ∆ E ~ - 10 meV/adat E F MAGNETIC INSULATOR GROUND STATE NO DISTORTION
insulating gap Sn magn. moment Sn/Ge Sn/Si exchange Sn adatom heigth splitting
Sn/Si(111) STM/STS data S. MODESTI et al PRL (2007)
50K EVOLUTION OF Sn/Si(111) 300K
HARTREE FOCK PHASE DIAG. SANTORO et al PRB 59, COLLINEAR 1891(1999) A: ρ K =m=0, S K #0, Mott insulator. Si/SiC(0001) Sn/Ge(111) Sn/Si(111)
K. KANODA (2006)
K. KANODA (2006)
SPINS ½ ON TRIANG. LATTICE ESTIMATE OF AF COUPLINGS ∆ E FE-FI ~ 3J Si/SiC (0001) J ~ 30 K Sn/Si(111) J ~ 100 K Sn/Ge(111) J~ 150 K
Sn/Si(111) SPECULATIVE PHASE DIAG. T PSEUDOGAP METAL (PM) MOTT INSULATOR d-WAVE (AF) SUPER COND. U
Sn/Si(111) t ~ 350 K T = 0.2t ~ 70 K!
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
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?
THE END G. Profeta, E.T., Phys. Rev Letters 98, 086401 (2007) S. Modesti et al, Phys. Rev Letters 98, 126401 (2007)
SPIN ORBIT INTERACTION: WEAK ANISOTROPY
Si/SiC(0001) LSDA+U (3x3 FERRIMAGNETIC) Anisimov et al, Phys. Rev. B 61, 1752 (2000)
Sn/Ge(111) W ~ 0.35 eV
Sn/Si(111) S. MODESTI et al n(E F )
“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
(4H)-SiC(0001)
IS B PHASE REALIZED ANYWHERE??
C 1/3 /Ge(111) C
The Mott-Hubbard Transition (ONE BAND MODEL) U Z ± 0 energy
LSDA+U calculations G. PROFETA I ]− E DC [ n I ] E LDA U [ n r ]= E LDA [ n r ] E Hub [ n m I − ∑ m' n m,m' I } E Hub − E DC = E U = U / 2 ∑ I ∑ m, { n m,m I n m' ,m ● -- 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
SPIN: FERROMAGNETIC STATE ∆ E = 9J/4 ADATOM Si Si
SPIN: FERRIMAGNETIC STATE ∆ E = - 3J/4 ADATOM Si Si
Sn/Ge(111) ? ? Mott Per. Distort. Undist.(Fluct.) Insul. Metal Metal T (K) 100-200 20 0
Sn/Si(111) EXPT.: UNDISTORTED METAL TH. : UNDISTORTED METAL (CLOSE TO 3x3 DISTORTION) PEREZ et al (2001)
Sn/Ge(111) LDA DOWN Sn ADATOMS UP Sn ADATOM ∆ E ~ 9 meV/adatom “CDW” “Band JT effect” “Bond Density Wave” “Disproportionation” PEREZ et al (1999) DE GIRONCOLI et al(2000) BALLABIO et al (2002)
IN REALITY: ON MOST SEMICONDUCTOR SURFACES: NO MOTT INSULATORS, NO CDW/SDW, NO SC STATES.... WHY? CHEMICAL PASSIVATION OF “DANGLING BONDS”
Si(111)7x7 20K-100K=3x3 T>100K= root 3x root 3
SEMICONDUCTOR SURFACES ” “DANGLING BONDS”
IDEAL Si SURFACES:BAND STRUCTURE HALF FILLED SURFACE STATES (=2D METALS) E F SURFACE RECONSTRUCTIONS!
NEED SURFACE DANGLING BOND STATES THAT WILL NOT SPONTANEOUSLY PASSIVATE!
HARTREE FOCK PHASE DIAG. SANTORO et al PRB 59, COLLINEAR 1891(1999) A: ρ K =m=0, S K #0, Mott insulator. Si/SiC(0001) 77K D: ρ K #0, m=S K = 0, CDW metal Sn/Ge(111) 300K undist. metal Sn/Si(111)
Sn/Si(111) Expt.: metallic, does not distort down to 5 K Si Si
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