Behnia, Kamran. (2014). Critical doping and superconductivity domes in doped strontium titanate. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/163092

Behnia, Kamran

University of Minnesota Digital Conservancy

Critical doping and superconductivity domes in doped strontium titanate  Kamran Behnia  LPEM-ESPCI Paris  Benoit Fauqué CNRS researcher Zengwei Zhu Now in Los Alamos Aurélie Callaudin PhD Xiao Lin Postdoc Group members German Bridoux Now in Bueons Aires Adrien Gourgout Now in Grenoble Lisa Buchauer Diploma Former members •First oxide superconductor  •First multi-band superconductor  •First semiconducting superconductor  •First superconducting dome Superconducting domes Basov & Chubukov 2011 Heavy fermions Cuprates  Pnictides Organic salts SnO  Doping can be tuned in commercially availabe crystals  3.8 1015 cm-3 3.8 1020 cm-3 Spinelli et al.PRB (2010) Reduced Nb-doped Resistive transitions  The superconducting dome Schooley et al.  1964 Tc = 86 mK@ n= 5.5 1017 The superconducting dome This work Schooley et al.  1964 K Ueno et. al., Nature Nanotechnology 6, 408 2011  “Semiconducting” superconductors STO is the most dilute superconductor system STO PbTe:Tl CuxBi2Se3 Si:B C:B SiC:B YBCO xc 10-5 3 10-3 9 10-2 ~ 10-2  ~10-2 ~ 10-2 5 10-2 Critical doping to induce superconductivity in doped insulators X. Blase et al., Nature Materials 8, 375-382 (2009) Is the normal state:  •An impurity-band metal?   •Or a metal with  sharp Fermi surface?  Fermi surface truncated by Landau tubes Quantum oscillations! Shoenberg 1984 Electrons share the same Fermi-Dirac distribution! Nernst effect • A thermal gradient, electrons produces an electric field.  • The Nernst effect refer to the transverse component of this field.  JQ TxEyEBTESxxTESNxyxy ][ TBExzyhot cold Sensitivity of the Nernst effect as a probe of Landau spectrum  Emergence of Nernst oscillations with underdoping Lin et al., PRX 2013 Emergence of Nernst oscillations with underdoping Lin et al., PRX 2013 Emergence of Nernst oscillations with underdoping Lin et al., PRX 2013 Emergence of Nernst oscillations with underdoping Lin et al., PRX 2013 Emergence of Nernst oscillations with underdoping Lin et al., PRX 2013 Emergence of Nernst oscillations with underdoping Lin et al., PRX 2013 A single frequency at the lowest concentration Lin et al., PRX 2013 A single frequency at the lowest concentration Lin et al., PRX 2013 Frequency (=18.2 T) FS Cross section FS volume Effective mass (m*=1.8me) (n=4.4 1017 cm-3) 1/eRH =5.5 1017 cm-3 KmkE FF 13*222FkA AeF2eVF=1.1meV S/T =(2/3)(kB/e) 1/TF TF= 12.9 k Lin et al., PRX 2013 Two ways to estimate the Fermi energy TF= 13 k Quantum oscillations Low-temperature Seebeck coefficient TF (13 K)  <<  QD  (400 K)  A serious challenge for phonon-mediated superconductivity! @n= 5.5 1017 cm-3 The standard BCS scenario needs TF >> QD!  In all  conventional (and most unconventional) superconductors,  this inequality holds!  But the opposite is true in STO (as in most heavy-fermion superconductors)! BCS Superconductivity K kF q~ QD / vs The attractive interaction is confined to a thin layer of electrons near the Fermi energy! ħkF1 ħkF2 ħ(kF1-q) ħ(kF2 +q) ħq If not, Cooper pairs would not be stable! Which low-energy boson is the glue? •Plasmons?  (cf. Takada)      •A phonon Soft mode ?  (cf. Appel)    •Ferroelectric quantum criticality? (cf . Lonzarich)  attractive repulsive Theoretical band structure in SrTiO3  by virtual crystal approximation  •Threefold degeneracy of a band centered at Γ-point is lifted. •The three bands are to be succesively filled. Xc1=6.8 1017 cm-3 Xc2=4.4 1019 cm-3 van der Marel, van Mechelen & Mazin, (2011) Bands and domes! One- band two- band three- band Large Tc/TF  regime The first critical doping Emergence of a new frequency ! Lin et al.  PRL  in press  (2014) Origin of split peaks The three faces of the Fermi surface in a multi-domain sample. Anisotropy of Femi surface ~ 1.3 S. J. Allen et al.  PRB (2013)   Old and new phase diagrammes Lin et al.  PRL  in press (2014) Caviglia et al.,  Nature (2008) Evolution of cyclotron mass with doping The effective mass in the lower band suddenly rises above nc2! The number of carriers in each band!  ARPES data Non-parabolic dispersion of the lower band van der Marel, van Mechelen & Mazin, (2011) Experiment Ab initio Theory m* (me) 1.8 0.7-0.9 nc1 (1017cm-3) 12 6.8  (meV) 2.2 5 Where does the mass enhancement come from? Band hierarchy crucially depends on the sign of the crystal field parameter Matheiss PRB 1972 Without spin-orbit With spin-orbit Tetragonal distortion Matheiss’ crystal field  parameters would make the middle band non-parabolic!  Summary • When one oxygen  out of 105  is missing in SrTiO3, it  superconducts and has a sharp Fermi surface.   • The smallest Fermi surface to suffer a superconducting instability emerges in the context of an extremely  long Bohr radius.  • Mechanism of superconductivity and symmetry of  the order parameter remain open issues. Superconductivity is strong coupling at small wave-vector and small energy.  What is a metal? “Everyone knows what a metal is and can describe many of its characteristics.   It is safe to say, however, that few people would define a metal as a ‘solid with a Fermi surface’.  This may nevertheless be the most meaningful definition of a metal and provides a precise explanation of the main physical properties ” A. R. Mackintosh  Scientific American 1963 Consequences of high mobility   •Quantum oscillations visible at accesible magnetic fields •Localisation is avoided at low concentration Two-band superconductivity seen by tunneling! Theory and experiment Theoretical references: 1. van der Marel, van Mechelen & Mazin,  PRB (2011) 2. Janotti, Steiauf & Van de Walle, PRB (2011) 3. Shirai & Yamanaka, JAP (2013) Experiment Ab initio Theory References m* (me) 1.8 0.7-0.9 1, 2, 3 nc1 (1017cm-3) 12 6.8 1  (meV) 2.2 5 1  nc1 m* Where does the mass enhancement come from? The Sr1-xLaxTiO3 system Okuda et al., 2001 Metal close to the band insulator Hayes et al., 1999 Robust AF close to the Mott insulator The Sr1-xLaxTiO3 system The Fermi surface grows and then suddenly vanishes! 

Critical doping and superconductivity domes in doped strontium titanate

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Critical doping and superconductivity domes in doped strontium titanate

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