Spectroscopy of correlated electrons in nickelates and titanates

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1 Spectroscopy of correlated electrons in nickelates and titanates Metal-insulator transitions and novel 2DEGs Dept. of Physics University of CA, Santa Barbara

2 Strong Electron Correlations Materials which depart from our typical description of solids. Phenomena that cannot be described by single electron physics.

3 Starting point of Solid State Physics Atoms: Orbitals Discrete energies Energy Conduction band Valence band Core levels Momentum Solids: Bloch states Continuous energy bands Energy gaps

4 Starting point of Solid State Physics Calculate the energy bands Single particle physics within a band Band mass Conduction band Energy Valence band Core levels Momentum

5 Starting point of Solid State Physics Calculate the energy bands Single particle physics within a band Band mass Energy Conduction band E Fermi Metal Valence band Core levels Momentum

6 Starting point of Solid State Physics Calculate the energy bands Single particle physics within a band Band mass Conduction band Energy Valence band E Fermi Insulator Core levels Momentum

7 But don t the electrons interact? Accounting for e-e interactions - Density functional theory - Replace quantum interactions with average density to obtain energy bands - Then consider single electron dynamics in these bands - Confined semiconductor structures - Schrodinger-Poisson VERY SUCCESSFUL What if the motion of the electrons is inherently collective?

8 Example: The Hubbard Model e - hopping matrix element = t Energy b Consider 1 orbital at each lattice site ε W(d, t ij ) A partially filled band is metallic. Hopping Strength ~ b -3 N. F. Mott (1949, 1956, 1977, 1978), Hubbard (1964) Kamimura and Aoki The Physics of Interacting Electrons in Disordered Systems Oxford 1989

9 Example: The Hubbard Model e - hopping matrix element = t Energy Mott Insulator Metal b ε+u Upper Hubbard Band Coulomb interactions ε Lower Hubbard Band Hopping strength ~ b -3 N. F. Mott (1949, 1956, 1977, 1978), Hubbard (1964) Kamimura and Aoki The Physics of Interacting Electrons in Disordered Systems Oxford 1989

10 A Mott insulator arises from correlations

11 3d perovskite transition metal oxides Distorted Perovskites ABO 3 Ionic * A = alkaline earth or rare-earth B = 3d transition metal ion Figures adapted from S. J. May et al. Phys. Rev. B 82, (2010) e - hopping A O B Structural Distortions: Less hopping (Analogous to spacing in H crystal)

12 RTiO: a family of Mott insulators Ti 3+ : a 3d 1 system Bandwidth control Band filling control

13 RTiO: a family of Mott insulators Ti 3+ : a 3d 1 system Bandwidth control This work: GdTiO 3 Band filling control Related compound SrTiO 3 : Ti 4+, a 3d 0 band insulator

14 Thin Films of GdTiO 3 and SrTiO 3 Stemmer Group, UCSB Hybrid MBE: metal organic precursor for Ti. Insulating films GdTiO 3 is ferromagnetic Alexander Kaiser, Chuck Fadley (UC Davis)

15 The polar catastrophe and a novel 2DEG Heterostructures of GdTiO 3 and SrTiO 3 Electric Field Potential GdTiO 3 Polar SrTiO 3 Non-polar Non-zero Average E field TiO 2 (1-) GdO (1+) TiO 2 (1-) GdO (1+) TiO 2 (1-) GdO (1+) TiO 2 (1-) GdO (1+) TiO 2 (0) SrO (0) TiO 2 (0) SrO (0) TiO 2 (0) SrO (0) TiO 2 (0) SrO (0) TiO 2 (0) SrO (0) Nakagawa, Hwang, & Muller, Nature Materials 5, (2006)

16 The polar catastrophe and a novel 2DEG Heterostructures of GdTiO 3 and SrTiO 3 Electric Field TiO 2 (1-) GdO (1+) GdTiO 3 Polar ½ e - per Ti TiO 2 (1-) GdO (1+) TiO 2 (1-) GdO (1+) No macroscopic electric potential TiO 2 (1-) GdO (1+) TiO 2 (½ -) SrO (0) SrTiO 3 Non-polar TiO 2 (0) SrO (0) TiO 2 (0) SrO (0) TiO 2 (0) Extreme density 2DEG at the interface of 2 (undoped) insulators SrO (0) TiO 2 (0) SrO (0) Nakagawa, Hwang, & Muller, Nature Materials 5, (2006)

17 2DEG at the interface GdTiO 3 SrTiO 3 GdTiO 3 SrTiO 3 ½ e - per Ti ½ e - per Ti ½ e - per Ti LSAT substrate Pouya Moetakef et. al. APL (2011)

18 Where is this 2DEG? Mobility (cm 2 V -1 S -1 ) Density (10 14 cm -2 ) GdTiO 3 : 19 nm SrTiO 3 : variable LSAT substrate Temperature (K) Temperature (K) 3.0 Mobility and interface scattering suggest confinement to within a few nm of interface Temperature (K) Pouya Moetakef et. al. APL (2011), Pouya Moetakef et al. in press

19 Optical response More information from frequency dependent transport! Conductivity in the plane: Drude like? Out-of plane? Couple to intersubband transitions and plasmons?

20 Optical properties of solids Drude Model Sum Rule More general then Drude Model! Frequency dependent conductivity: Drude (free carriers), interband transitions, phonons, polarons,... Dielectric polarizability: Index of refraction and absorption coefficient

21 THz Time Domain Spectroscopy Pulse Signal (V) Empty Gap Bare LSAT GTO/STO/LSAT Femtosecond NIR pulse Picosecond broadband THz pulse Electric field versus time Fourier transform for COMPLEX spectrum Time Delay (ps) With Mark Sherwin and Chris Morris

22 Transmitted Power (A. U.) Phase (Radians) THz Time Domain Spectroscopy Amplitude and Phase Information 1E E-7 1E E-9 1E E-11 1E E E Frequency (THz) Frequency (THz)

23 Index THz Time domain spectroscopy Preliminary step: substrate properties LSAT : ( La 0.18 Sr 0.82 )(Al 0.59 Ta 0.41 )O Phase shift real refractive index 3 n 1 (295 K) n 2 (295 K) Absorption and real index absorption coefficient 2 1 n 1 (5 K) n 2 (5 K) Frequency (THz)

24 THz TDS of a 2DEG GdTiO 3 : 19 nm SrTiO 3 : 20 nm σ 2D (ω) LSAT substrate Expect phase shift < 3º Get real part of conductivity from power absorption

25 Alternate (complimentary?) hypothesis High density 2DEG Perhaps the Mott-Hubbard gap in the GdTiO 3 collapses near the interface? This was not allowed for in the self-consistent modeling!

26 MIT in rare-earth nickelates RNiO 3 (LaNiO 3, NdNiO 3 ) - MIT vs. Temperature Ni 3+, nominally d 7, e g 1 Ni O Ni Charge ordered Charge ordered J.-S. Zhou, J. B. Goodenough, B. Dabrowski, PRL (2005) Increasing orthorhombic distortion J.B. Torrence PRB 45, 8209 (1992)

27 Bandwidth control using epitaxial strain 3.7 Å LSAT 4.0 Å Pseudo-cubic lattice parameters LaNiO3 Substrates LaAlO3 DyScO3 compression tension

28 Optical reflectivity in FTIR Reflectivity Substrate matters! Optical penetration >> film thickness ε Substrate >> LaAlO 3 substrate 2 nm LaNiO 3 3 nm LaNiO 3 9 nm LaNiO 3 30 nm LaNiO 3 Direct inversion Model independent Impose Kramers- Kronig consistency Substrate artifacts remain Frequency (ev)

29 Optical conductivity of strained LaNiO 3 20 Band Theory 9 nm/laalo 3 (1.1% compressive) 1 ( cm -1 ) nm/lsat (0.6% tensile) 10 nm/dysco 3 (2.9% tensile) Free carrier (Drude) response e g e g interband transitions D. G. Ouellette et al. Phys. Rev. B (2010) In collaboration with SungBin Lee, Leon Balents, and Andy Millis (Columbia) Frequency (ev) Carrier mass is renormalized by strong correlations not included in band theory.

30 Optical Mass / Band Mass Strain control of bandwidth d dt ( cm K -1 ) A (n cm K -1 ) Optical mass, quadratic and linear contributions to resistivity show similar strain dependence LaAlO 0 3 LSAT DyScO Strain (%) 0 Tensile strain reduces hopping, i.e. bandwidth, increasing the importance of electron correlations D. G. Ouellette et al. Phys. Rev. B (2010)

31 THz TDS: 30 nm LaNiO 3 /LSAT Real Sigma ( -1 cm -1 ) K, FTIR 5K, THz TDS 298 K, FTIR 295 K, THz TDS 295 K, dc Frequency (THz) Very good agreement between reflectivity measurements in the FTIR, THz TDS transmission, and dc transport At 300 K, evidently the conductivity increases with frequency below 2 THz. Could be a phonon contribution?

32 Summary: Rare-earth nickelates Results Strong electron correlations enhance the mass ~ threefold. Bandwidth control using epitaxial strain Zero-bias tunneling anomaly: disorder or correlations? Band offsets from internal-photoemission Outlook Modulated transport and absorption to study field effect in remotely doped NdNiO 3. Improved tunneling and internal photoemission measurements.

33 Thank You! Allen Group Prof. Jim Allen Alex Kozhanov James Kally Funding: Army Research Office MURI NSF MRSEC (IRG-2) through the UCSB MRL Acknowledgments Prof. Susanne Stemmer Junwoo Son Pouya Moetakef Bharat Jalan Clayton Jackson Adam Kajdos Tyler Cain Prof. Mark Sherwin Chris Morris Ben Zacks Vinh Nguyen Prof. Chris Van-de-Walle Anderson Janotti Prof. Leon Balents SungBin Lee Prof. Andy Millis (Columbia) Everyone in the MURI collaboration