Emergent Phenomena in two-dimensional electron gases at oxide interfaces

Emergent Phenomena in two-dimensional electron gases at oxide interfaces Susanne Stemmer Materials Department, University of California, Santa Barbara Matsen Lecture University of Texas, Austin October 23, 2013

Acknowledgements Graduate students and postdocs: Clayton Jackson, Jack Zhang, Pouya Moetakef, Santosh Raghavan, Adam Kajdos, Tyler Cain, Jinwoo Hwang Collaborators: UCSB: Jim Allen, Leon Balents, Dan Ouellette, Chris Van de Walle, Anderson Janotti Stanford: David Goldhaber-Gordon, Jimmy Williams Funding: NSF, DOE, Army Research Office, DARPA National High Magnetic Field Laboratory 2

Outline Complex oxide heterostructures Oxide thin film growth Two-dimensional electron gases at complex oxide interfaces Electron correlations in extreme density quantum wells of SrTiO3 Interface-induced magnetism Summary 3

Introduction III-V Semiconductor 2D Electron Gases Complex Oxide 2D Electron Gases C. Weisbuch, B. Vinter: Quantum Semiconductor Structures Quantum-confined structures in III-V semiconductors have lead to a wealth of phenomena and new technologies Fundamentally different: Electrons in relatively narrow d-bands Occupy a significant fraction of the d-band Electron correlations, exchange...dominate transport Rich physical phenomena magnetism, superconductivity,...) Underlying physics poorly understood Exploration in its infancy High-quality films are needed

Why Complex Oxide Heterostructures? New states of matter Two-dimensionality and quantum confinement Enhance strong electron correlations Proximity effects Unique charge and magnetically ordered states External control of strongly correlated phenomena through electrostatic doping Modulation doping Electric field effect

Two-Dimensional Electron Gases High electron densities are key for strong electron correlation physics U Semiconductor 2DEGs Strongly correlated 2DEGs ~7 10 14 per atomic layer t n Short range Coulomb interactions require significant probability for two electrons to occupy the same site. Opposite of the usual correlation regime investigated in conventional semiconductor 2DEGs. 6

Complex Oxide Materials: Perovskite Titanates Mott Insulators RTiO3 where R = La... Y Band Insulators SrTiO3, BaTiO3,... d 0 SrTiO3 GdTiO 3 30 K Temp. T c T N 145 K LaTiO 3 ferrimag. antiferromag. d 1 GdTiO3 x = 0.2 Gd 1-x Sr x TiO 3 Insulator Metal La 1-x Sr x TiO 3 x = 0.05 Transition metal-oxygen octahedra: tilts and rotations Determine physical properties Modified in thin films through strain, proximity,... 7

Oxide Thin Film Deposition Techniques Regime I Regime II Regime III 0.0 0.1 1 10 100 Energy ev) MBE CVD Ion beam sputtering RF sputtering Direct ion beam Laser vaporization PLD) Ion implantation Cuomo et al., J. Appl. Phys. 70 1706 1991). Most complex oxides films are deposited by PLD or sputtering Main issues: Impurities H, C, transition metals,...) Energetic deposition creating defects Poor stoichiometry control during deposition 9

Oxide Molecular Beam Epitaxy!"1".789,3$.6 )*#2"&2$ ;<::= -+.$$* 5$6",#).2"*+#')&.+$!"#$%%&')*#+$,, <$"6$. 5"*3&,"6).#%). '"43,$#6."*'%$. High purity Low energetic deposition Stoichiometry control?! -"43,$ /012$*#3,"'4"#')&.+$ @.1) 'A.)&7 ;$'&7",#2"' "*",1>$. -&?'6."6$ 4"*3&,"6). -.#$%%&')*#+$,, :,$+6.)*#2&* %).#;<::= Without an MBE growth window, stoichiometry control requires precise flux control only possible to 0.1-1 % Corresponds to defect concentrations of 1020-1021 cm-3 10

Growth Window in III-V MBE GaAs Below this line, solid As will not precipitate excess As desorbs in the chamber Temperature C) A wide MBE growth window is largely responsible for the ease and success of III-V MBE Gas Pressure Torr) 44Ass) As4g) MBE Growth MBE Window Growth GaAss) Gal) + Asg) Window GaAss) Gal) + Asg) Above this line, As will condense on a Ga-rich GaAs surface Temperature 1000/K) C.D. Theis et al., Thin Solid Films 325, 107 1998). J. Tsao, Materials Fundamentals of Molecular Beam Epitaxy.

Growth Window in Oxide MBE SrTiO3 Below this line, solid SrO will not precipitate: SrO will desorb in the chamber* 1500 K Temperature No practical growth window in oxide MBE using solid sources Requires precise flux control only possible to 0.1-1 % Corresponds to defect concentrations of 10 20-10 21 cm -3 P SrOg) [torr] 10-6 10-9 10-12 10-15 10-18 10-21 10-24 10-27 SrOs) SrOg) MBE Growth Window SrOg) + TiO2s) SrTiO3s) 0.6 0.7 0.8 0.9 1000/T [1/K] 1.0 Above this line, SrO will condense on a TiO-rich SrTiO3 surface* C.D. Theis et al., Thin Solid Films 325, 107 1998). J. Tsao, Materials Fundamentals of Molecular Beam Epitaxy.

Oxide Molecular Beam Epitaxy C!"1".789,3$.6 )*#2"&2$ ;<::= -+.$$* 5$6",#).2"*+#')&.+$ O Ti Titanium tetra isopropoxide TTIP)!"#$%%&')*#+$,, <$"6$. 5"*3&,"6).#%). '"43,$#6."*'%$.! -"43,$ /012$*#3,"'4"#')&.+$ @.1) 'A.)&7 ;$'&7",#2"' "*",1>$. -&?'6."6$ 4"*3&,"6). -.#$%%&')*#+$,, :,$+6.)*#2&* %).#;<::= B. Jalan, R. Engel-Herbert, N. J. Wright, S. Stemmer, J. Vac. Sci. and Technol. A 27, 461 2009). B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 2009).

Oxide Molecular Beam Epitaxy after growth SrTiO3 SrTiO3 substrate Persistent RHEED oscillations indicate layer-by-layer growth mode [only been reported for a few systems: Si, Pt, AlAs] Transition to step-flow growth Streaky RHEED indicates atomically smooth film surface Surface reconstructions 2 along [110] always); 4 along [110] only for stoichiometric films after growth) Further investigations are required to understand origin of persistent RHEED oscillations. B. Jalan, R. Engel-Herbert, N. J. Wright, S. Stemmer, J. Vac. Sci. and Technol. A 27, 461 2009). B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 2009).

Oxide Molecular Beam Epitaxy MBE growth window SrTiO3 SrTiO3 Sr source oxygen plasma source TTIP B. Jalan, R. Engel- Herbert, N. J. Wright, S. Stemmer, J. Vac. Sci. and Technol. A 27, 461 2009). B. Jalan, P. Moetakef, S. Stemmer, Appl. Phys. Lett. 95, 032906 2009). TTIP desorption leads to a growth window at practical substrate temperatures and fluxes Stoichiometry is self-regulating within the growth window No need for precise flux control Shift to higher TTIP/Sr flux ratios with increasing temperatures shows that desorption of TTIP is responsible for growth window

Oxide Molecular Beam Epitaxy La:SrTiO3 SrTiO3 Single crystals MBE films PLD 2 10 18 cm -3 ) J. Son, P. Moetakef, B. Jalan, O. Bierwagen, N. J. Wright, R. Engel-Herbert, S. Stemmer, Nature Mater. 9, 482 2010); T. A. Cain, A. P. Kajdos, and S. Stemmer, Appl. Phys. Lett. 102, 182101 2013). PLD data: Y. Kozuka et al., Appl. Phys. Lett. 97, 012107 2010). 1:1 correspondence of La-concentration and free carrier concentration over several orders of magnitude Excellent control over carrier concentrations concentration of unintentional defects below doping level Higher mobility than single crystals Fewer charged impurities, such as Al, Fe..., in MBE films

2DEGs at Oxide Interfaces Polar/Non-polar Interfaces: Extreme 2D Carrier Densities Ti 3+ O 4-2 R 3+ O 2- Ti 3+ O 4-2 R 3+ O 2- -1 +1-1 +1 Mott Insulator R +3 Ti +3 O -2 3 Perovskite R = trivalent rare earth ion GdTiO3, LaTiO3,... Mobile, compensating charge density Ti 4+/3+ O 4-2 Sr 2+ O 2- Ti 4+ O 4-2 Sr 2+ O 2- Ti 4+ O 4-2 3!10 14 cm -2 Band Insulator Sr +2 Ti +4 O -2 3 Fixed charge at 001) interfaces between RTiO3 and SrTiO3 Free charge carrier density at the interface of ½ electron per interface unit cell, or ~ 3 10 14 cm -2 Order of magnitude higher charge density than what is achievable in conventional semiconductors Formally analogous to LaAlO3/SrTiO3 A. Ohtomo and H. Y. Hwang, Nature 427, 423 2004). See also early work by Harrison on Ge/GaAs W. A. Harrison et al., Phys. Rev. B 18, 4402 1978). 18

Routes to High-Density 2DEGs? Polar/Non-polar Interfaces: Extreme 2D Carrier Densities Sheet carrier density 10 13 cm -2 ) LaAlO3 SrTiO3 1 10 13 cm -2 Atomic oxygen anneal temperature C) M. Huijben, A. Brinkman, G. Koster, G. Rijnders, H. Hilgenkamp, and D. H. A. Blank, Adv. Mater. 21, 1665 2009). Well-oxidized LaAlO3/SrTiO3 interfaces show ~ 1 10 13 cm -2 carrier densities, an order of magnitude lower than predicted Significant debate in the literature as to the origin or lack thereof) of the free charge carrier density at this interface.

Two-dimensional Electron Gases at Oxide Interfaces Lack of charge at the LaAlO3/SrTiO3 interface: Origin of charge carriers: compensating charge for polar discontinuity or defect-related residual vacancies, interdiffusion,...)? If polar discontinuity is indeed compensated by a mobile charge, are the free carriers trapped or localized due strong electron localization? Carrier confinement is weak for low-density electron gases in SrTiO3 Average carrier separation from surface # layers) 5 10 15 20 0 Low density electron gases low 1!10 12 1!10 13 1!10 14 Carrier density cm -2 ) mid Guru Khalsa and A.H. MacDonald, Phys. Rev. B 86, 125121 2012) high 8.3 10 12 cm -2 At low densities, charge is spread-out Energy separation of subbands is extremely small, multiple bands are filled 1 3!! 2! $ w ~ # 4"me 2 n & " T %! 2 mw ~ 2 10!4 ev w ~ 50 unit cells 3D character

Two-dimensional Electron Gases at Oxide Interfaces GdTiO3 2DEG Ferrimagnetic Mott Insulator + Two-Dimensional Electron Gas Ti 3+ O 4-2 R 3+ O 2- Ti 3+ O 4-2 R 3+ O 2- Ti 4+/3+ O 4-2 -1 +1-1 +1 3!10 14 cm -2 Gd +3 Ti +3 O -2 3 Sm +3 Ti +3 O -2 3 + Sr 2+ O 2- Ti 4+ O 4-2 Sr +2 Ti +4 O -2 3 SrTiO3 Band insulator, superconductor Sr 2+ O 2- Ti 4+ O 4-2 LSAT New insights using alternative interfaces between two insulating oxides Charge densities close to theoretical prediction of 3 10 14 cm -2 Test of theoretical predictions Strongly confined two-dimensional electron gas Strong electron correlations in the 2DEG? Interactions between the magnetic insulator and the 2DEG? Correlation with superconductivity in the SrTiO3? Close proximity of unique properties: two-dimensionality, superconductivity and magnetism 21

MBE of GdTiO3/SrTiO3 Interfaces HAADF/STEM RHEED Superlattices SrTiO3 after growth 4x indicates cation stoichiometry) GdTiO3 on 001) LSAT after growth [100] One-unit-cell SrTiO3 quantum well embedded in GdTiO3 [110]

Properties of GdTiO3/SrTiO3 Interfaces 0 nm 0.4 nm 3.5 10 14 cm -2 1.2... 5 nm 20... 88 nm P. Moetakef, et al., Appl. Phys. Lett. 99, 232116 2011). GdTiO3 GdTiO3 is insulating p-type) vary thickness LSAT GdTiO3 SrTiO3 LSAT Remarkable drop in sheet resistance even for one unit cell of SrTiO3 Sheet resistance independent of SrTiO3 thickness for all thickness greater than 20 nm Sheet carrier density n-type) is independent of SrTiO3 thickness Conduction in a space charge layer with constant thickness Sheet charge carrier density corresponds to the theoretical expected density of ~ 3 10 14 cm -2. 23

GdTiO3/SrTiO3 Superlattices SrTiO3 GdTiO3 SrTiO3... Extrapolated from x = 1 stack x SrTiO3 GdTiO3 SrTiO3 LSAT Note: each repeat x contains two interfaces P. Moetakef, et al., Appl. Phys. Lett. 99, 232116 2011). Sheet carrier concentration scales with number of multilayer repeats interfaces) Independent of SrTiO3 or GdTiO3 thickness Each interface contributes a constant sheet charge carrier density ~ 3 10 14 cm -2. See also: J. S. Kim et al., Phys. Rev. B 82, 201407R) 2010). 24

Theory of high-density 2DEGs in SrTiO3 2DEGs in SrTiO3 at carrier densities of 0.5 electron per interface unit cell May be able to see dyz in SdH, but very large mass Energy E F d yz Many, mostly dxy-derived bands, close spacing, will be washed out in Shubnikov-de Haas experiments Large energy separation between bottom dxy band and higher-lying subbands 2D behavior d xy 160-220 mev L! X G. Khalsa and A. H. MacDonald, Phys. Rev. B 86, 125121 2012); S. Y. Park and A. J. Millis, Phys. Rev. B 87, 205145 2013); Z. S. Popovic, S. Satpathy and R. M. Martin, Phys. Rev. Lett. 101, 256801 2008); Z. Zhong, A. Tóth, and K. Held, Phys. Rev. B 87, 161102 2013); P. Delugas, et al., Phys. Rev. Lett. 106, 166807 2011); W.-J. Son, et al., Phys. Rev. B 79, 245411 2009); M. Stengel, PRL 106, 136803 2011).

Quantum oscillations from SrTiO3/GdTiO3 interfaces Moetakef et al., Appl. Phys. Lett. 101, 151604 2012). 26

Quantum oscillations from SrTiO3/GdTiO3 interfaces Oscillations in tilted fields depend only on B, consistent with a twodimensional system The product of the frequency a) of the Fourier transform of the oscillations in 1/B and cosθ is independent of θ, as expected for a two-dimensional system Moetakef et al., Appl. Phys. Lett. 101, 151604 2012). 27

Quantum oscillations from SrTiO3/GdTiO3 interfaces At low B-fields, observe two periodicities: Oscillations are due to a single, spin-split subband with an electron density of fa = nah/ e, where na = 2.8 10 13 cm -2 Consistent with oscillations due to the bottom dxy subband Density roughly agrees with theoretical predictions Landau level and and Zeeman spin splitting likely comparable in SrTiO3* Only one periodicity at high B-fields Spin splitting is B-field dependent Influence of Rashba effects? Theory lacking Moetakef et al., Appl. Phys. Lett. 101, 151604 2012). *B. Jalan, S. Stemmer, S. Mack, S. J. Allen, Phys. Rev. B 82, 081103R)2010). 28

Characteristics of the high-density 2DEG 2DEGs in SrTiO3 and carrier densities of 0.5 electron per interface unit cell Theoretical calculations for high-density 2DEGs in SrTiO3 Basic picture: Energy E F d yz Maybe able to see dyz in SdH, but very large mass Many, mostly dxy-derived bands, close spacing, will be washed out in Shubnikov-de Haas experiments d xy Large energy separation between bottom dxy band and higher-lying subbands 2D behavior 160-220 mev L! X Shubnikov-de Haas oscillations consistent with basic picture Unlikely that the other subbands will be resolved in SdH Need alternative method to probe subbands 29

Characteristics of the high-density 2DEG 2D to 2D Resonant Tunneling Barrier! dxy dxy 2DEG to 2DEG resonant tunnelling allows probing of the 2DEG subband structure Need two 2DEGs on either side of a tunnel barrier for resonant tunnelling GdTiO3 acts as the tunnel barrier between two 2DEGs in SrTiO3 Experiment: Voltage bias is applied across the two 2DEGs top and bottom) Resonant tunnelling occurs when subbands of the two 2DEGs align in energy and match conservation criteria In-plane parallel to the barrier) momentum is conserved dxy dxy) 30

Characteristics of the high-density 2DEG Raghavan et al., Appl. Phys. Lett. accepted. arxiv:1310.8168 Resonant tunnelling features are seen in the di/dv and d 2 I/dV 2 characteristics Features under a positive bias indicate tunneling from subbands in bottom 2DEG into the subbands of the top 2DEG, and vice-versa. Subband spacing of the two 2DEGs can be derived from d 2 I/dV 2 31

Characteristics of the high-density 2DEG! Resonant Tunneling Experiment Theory 0-1 mev) 1-2 mev) 2-3 mev) 3-4 mev) Millis et al. [1] 213.16 Khalsa et al. [2] 174.2 pure xy-pure xy) 136.5 pure xymixed xy) Zhong et al. [3] 219 Zhong et al. [3] ~214 Popovic et al [4] 270.96 Delugas et al [5] 160 Theory 36.84 13.8 mixed xymixed xy) 57.14 64.28 25.8 80 10.5 27.05 mixed xy - pure xy) 28.5 64.28 38.7 64 4.6 42.85 100 45.16 56 Excellent qualitative agreement between experiments and theory Subband spacing reflects the small asymmetry in carrier density between top and bottom 2DEG Larger subband spacing in experiment may be due to compressive strain from the LSAT substrate or calculations underestimating the confinement mass). Raghavan et al., Appl. Phys. Lett. accepted. arxiv:1310.8168 [1] S. Y. Park and A. J. Millis, Phys. Rev. B 87, 205145 2013). [2] G. Khalsa and A. H. MacDonald, Phys. Rev. B 86, 125121 2012). [3] Z. Zhong, A. Tóth, and K. Held, Phys. Rev. B 87, 161102 2013). [4] Z. S. Popovic, S. Satpathy and R. M. Martin, Phys. Rev. Lett. 101, 256801 2008). [5] P. Delugas, A. Filippetti, V. Fiorentini, D. I. Bilc, D. Fontaine and P. Ghosez, Phys. Rev. Lett. 106, 166807 2011).

Characteristics of the high-density 2DEG! Resonant Tunneling Experiment Theory Theory 0-1 mev) 1-2 mev) 2-3 mev) 3-4 mev) Millis et al. [1] 213.16 Khalsa et al. [2] 174.2 pure xy-pure xy) 136.5 pure xy-mixed xy) Zhong et al. [3] 219 Zhong et al. [3] ~214 Popovic et al [4] 270.96 Delugas et al [5] 160 36.84 13.8 mixed xymixed xy) 57.14 64.28 25.8 80 10.5 27.05 mixed xy - pure xy) 28.5 64.28 38.7 64 4.6 42.85 100 45.16 56 Excellent qualitative agreement between experiments and theory Subband spacing reflects the small asymmetry in carrier density between top and bottom 2DEG Larger subband spacing in experiment may be due to compressive strain from the LSAT substrate or calculations underestimating the confinement mass). Raghavan et al., Appl. Phys. Lett. accepted. arxiv:1310.8168 [1] S. Y. Park and A. J. Millis, Phys. Rev. B 87, 205145 2013). [2] G. Khalsa and A. H. MacDonald, Phys. Rev. B 86, 125121 2012). [3] Z. Zhong, A. Tóth, and K. Held, Phys. Rev. B 87, 161102 2013). [4] Z. S. Popovic, S. Satpathy and R. M. Martin, Phys. Rev. Lett. 101, 256801 2008). [5] P. Delugas, A. Filippetti, V. Fiorentini, D. I. Bilc, D. Fontaine and P. Ghosez, Phys. Rev. Lett. 106, 166807 2011).

Alternative Routes to 2DEGs: Modulation Doping R. Dingle, H. L. Stormer, A. C. Gossard, and W. Wiegmann, Appl. Phys. Lett. 33, 665 1978). Separates donors from mobile charge high mobility Controllable carrier density low density electron gases Enabled devices HEMT) and scientific discoveries fractional quantum Hall effect) Requires suitable band alignments dopants in a wide-band gap semiconductor) and controlled doping 34

2DEGs in SrTiO3 by Modulation Doping 1.9 ev E C E V R. Schafranek, et al., J. Phys. D 45, 055303 2012). SrTiO 3 SrZrO 3 SrZrO3/SrTiO3 have favorable band offsets for modulation doping Use SrTi,Zr)O3 as the analog of AlGaAs for smaller lattice mismatch and to facilitate doping Use La as the dopant in the SrTi,Zr)O3 A. P. Kajdos, D. G. Ouellette, T. A. Cain, and S. Stemmer, Appl. Phys. Lett. 103, 082120 2013). 35

2DEGs in SrTiO3 by Modulation Doping Shubnikov-de Haas oscillations provide evidence for a confined 2DEG at the La:SrTi,Zr)O3/ SrTiO3 interface Angle-dependence confirms 2D nature Interpretation of SdH underway... A. P. Kajdos, D. G. Ouellette, T. A. Cain, and S. Stemmer, Appl. Phys. Lett. 103, 082120 2013). Also see: Phys. Rev. B 88, 115304. 36

Mott/Band Insulator Interfaces 2DEGs with extreme electron densities Designing a two-dimensional electron gas with onsite Coulomb repulsion Mott physics)? SrTiO3 Electrons are located in a band insulator For electron densities approaching 1 electron/unit cell, expect transition to a Mott insulating state Two-dimensional, Artificial Mott Insulator Depends critically on the degree of the confinement of the 2DEG 38

Mott/Band Insulator Interfaces 2DEGs with extreme electron densities Designing a two-dimensional electron gas with onsite Coulomb repulsion Mott physics)?!" &$ ' -. &$ ' )* Ti 3+ O 4-2 Gd 3+ O 2- -1 +1!" &$ ' -. &$ ' )* Ti 3+ O 2 4- -1 &/01 0# *23 )*!" #$%&$ ' Gd 3+ O 2- Ti 4+/3+ O 4-2 Sr 2+ O 2- +1 3!10 14 cm -2 +, $ ' )*!" #$ ' +, $ ' )* 2 SrO layers Quantum well Ti 4+ O 2 4- &/01 0# *23 )*!" #$%&$ ' Sr 2+ O 2- Ti 4+ O 4-2 -. &$ ' )*!" &$ ' -. &$ ' )*!" &$ ' Very large 3D carrier densities in a SrTiO3 quantum well 2 SrO quantum well: only 1 electron/three Ti layers On-site Coulomb repulsion electron correlations)? 39

Electron Correlation Effects in High-Density 2DEGs! T ) =! 0 + AT 2 3 SrO!" &$ ' -. &$ ' )*!" &$ ' -. &$ ' )* &/01 0# *23 )*!" #$%&$ ' N. Hussey, J. Phys. Soc. Jpn. 74, 1107 2005). P. Moetakef, et al., Phys. Rev. B 86, 201102R) 2012) 3 SrO 0.8 nm &/01 0# *23 )* +, $ ' )*!" #$ ' +, $ ' )*!" #$ ' +, $ ' )*!" #$%&$ ' -. &$ ' )*!" &$ ' -. &$ ' )*!" &$ ' Quantum wells with thickness greater than 2 SrO layers are metallic Quadratic temperature dependence over a wide temperature range: Fermi liquid electron-electron scattering) A coefficient should decrease with carrier density 40

Electron Correlation Effects in High-Density 2DEGs! T ) =! 0 + AT 2 P. Moetakef, et al., Phys. Rev. B 86, 201102R) 2012) 3 SrO Okuda, et al., Phys. Rev. B 63, 113104 2001). Tokura, et al., Phys. Rev. Lett. 70, 2126 1993). 41 Above a critical carrier density of ~ 7 10 21 cm -3, A coefficient increases with carrier density For all titanates, including the thin SrTiO3 quantum wells Mass-enhancement in proximity to a Mott transition A coefficient should diverge at the transition* Short-range, on-site Coulomb interactions Mott-Hubbard physics) in a two-dimensional band insulator Carriers introduced by electrostatic doping *H. Maebashi, et al., J. Phys. Soc. Jpn. 67, 242 1998).

Electron Correlation Effects in High-Density 2DEGs Moetakef, et al., Phys. Rev. B 86, 201102R) 2012) 2 SrO!"&$' -.&$')*!"&$' -.&$')* &/010#*23)*!"#$%&$' +,$')* insulator!"#$' 2 SrO +,$')* &/010#*23)*!"#$%&$' -.&$')*!"&$' -.&$')* metal 3 SrO Quantum wells thinner than 2 u.c. are insulating Disorder/interface roughness scattering Anderson) or Mott transition? Anderson: variable range hopping VRH) At T > 200 K: thermally activated transport Small activation energy typical for small polarons* *H. D. Zhou and J. B. Goodenough, J. Phys. Condens. Matter 17, 7395 2005). 42!"&$' Variable range hopping! T ) ~ exp T0 T ) y y = 1/2 for strong electron interaction and Coulomb gap Efros-Shklovskii law) Arrhenius! T ) ~ exp!e kt )!

Electron Correlation Effects in High-Density 2DEGs t ~ 0.68eV t ~ 0.32eV Dimer Mott state R. Chen, S.B. Lee, and L. Balents, Phys. Rev. B 87, 161119R) 2013) Theory predicts a Dimer Mott Insulator state for 1 SrO layer Different orientation than experiments Structural distortions on the SrO layers are key 43

Electron Correlation Effects in High-Density 2DEGs Role of the Lattice? Nearly all properties of Mott insulators are coupled with structural distortions oxygen octahedra tilts) In RTiO3, large tilt angles favor ferromagnetism What are is the structure of extreme electron density SrTiO3 quantum wells? GdTiO3 SrTiO3 M. Mochizuki et al., J. Phys. Soc. Jpn. 73, 1833-1850 2004). H. D. Zhou and J. B. Goodenough, J. Phys. Condens. Matter 17, 7395 2005). 44

10 nm SrTiO3 Correlation with Structure? 10 nm SrTiO3 GdTiO3 8 SrO GdTiO3 4 SrO GdTiO3 Gd shifts suppressed at SrTiO3 interface 2 SrO GdTiO3 1 SrO GdTiO3 LSAT Gd positions form zigzag pattern in bulk Gd displacements are correlated with oxygen octahedral tilts 45

10 nm SrTiO3 Correlation with Structure? J. Y. Zhang, et al. Phys. Rev. Lett. 110, 256401 2013). Shown are the A-site displacements deviation from 180 angle in cubic SrTiO3) Sr atoms show displacements in the 2 SrO-thick, insulating quantum wells, consistent with octahedral tilts Sr atoms are not displaced in the metallic quantum wells The Gd displacements are reduced near the interface Structural changes coincide with the transition to insulating phase Similar to bulk RTiO3 46

Electron Correlation Effects in High-Density 2DEGs Oxide interfaces allow for narrow quantum wells bound by highdensity, two-dimensional electron liquids Extremely large carrier densities without chemical doping Access fundamental Mott physics Evidence for onset of short range Coulomb interactions in a band insulator Mass enhancement in metallic quantum wells A correlated insulator emerges at the highest densities thinnest quantum wells) Insulating state is correlated with structural distortions octahedral tilts), similar to bulk Mott insulators Pathway towards the Artificial Mott Insulator 47

Proximity Effects at Ferrimagnetic Insulator/2DEG Interfaces 30.8 SrO &/01 0# *23 )* &/01 0# *23 )*!" &$ ' -. &$ ' )*!" &$ ' -. &$ ' )*!" #$%&$ ' +, $ ' )*!" #$ ' +, $ ' )*!" #$ ' +, $ ' )*!" #$%&$ ' -. &$ ' )*!" &$ ' -. &$ ' )*!" &$ ' Very strong ferromagnetic hysteresis, provided that quantum wells are thinner than about 4 SrO layers Angle-dependent behavior consistent with anisotropic magnetoresistance AMR) Spin-polarized, high-density 2DEG at an epitaxial oxide interface Negative AMR ΔρA = ρ ρ < 0) Similar to III-V 2DEGs under compressive strain Indicative of spin-orbit coupling in the 2DEG! xx =!! + "! A m x 2! xy =!! A m x m y m x = cos! cos" m y = sin! cos" P. Moetakef, et al., Phys. Rev. X 2, 021014 2012). C. A. Jackson and S. Stemmer, accepted, PRB Rapid. arxiv:1311.0337

Proximity Effects at Ferrimagnetic Insulator/2DEG Interfaces 30.8 SrO &/01 0# *23 )* &/01 0# *23 )*!" &$ ' -. &$ ' )*!" &$ ' -. &$ ' )*!" #$%&$ ' +, $ ' )*!" #$ ' +, $ ' )*!" #$ ' +, $ ' )*!" #$%&$ ' -. &$ ' )*!" &$ ' -. &$ ' )*!" &$ ' Ferromagnetism in SrTiO3 quantum well is distinct from that of GdTiO3 Metallic conducting is GdTiO3 not magnetic Onset of hysteresis in quantum well at about 5 K, vs. Tc = 20 K in GdTiO3 Coercive fields are different 4 nm GdTiO3 magnetism Tc ~ 20 K P. Moetakef, et al., Phys. Rev. X 2, 021014 2012). C. A. Jackson and S. Stemmer, accepted, PRB Rapid. arxiv:1311.0337

Proximity Effects at Ferrimagnetic Insulator/2DEG Interfaces 30.8 SrO &./0 /# *1- )* &./0 /# *1- )*!" &$ ' +- &$ ' )*!" &$ ' +- &$ ' )*!" #$%&$ ' +, $ ' )*!" #$ ' +, $ ' )*!" #$ ' +, $ ' )*!" #$%&$ ' +- &$ ' )*!" &$ ' +- &$ ' )*!" &$ ' Replace GdTiO3 with SmTiO3 No hysteresis Ferromagnetism in SrTiO3 quantum well is a proximity effect SmTiO3 2DEG SrTiO3 2DEG SmTiO3 LSAT P. Moetakef, et al., Phys. Rev. X 2, 021014 2012). C. A. Jackson and S. Stemmer, accepted, PRB Rapid. arxiv:1311.0337

Summary: Proximity Effects in High-Density 2DEGs Proximity effects in correlated, high density 2DEGs at epitaxial interfaces Spin-polarized, high-density 2DEG Conditions favoring unusual states of matter are present in these quantum wells Noncentrosymmetry Strong electron correlations Proximate magnetism Spin-orbit coupling Can test more complex spin states and fluctuations, and other proximity effects, such as superconductivity 53

Thank you 54