Superconductivity in Ba1-XKXBiO3(BKBO) I’m Shouta Maki. I am a member of Kitaoka Lab. Today I talk about SC in BaKBiO3 called BKBO. Kitaoka Lab. M1 Maki Shouta H. Matsuura and K. Miyake, J. Phys. Soc. Jpn. 81 (2012) 113705 C. Varma PRL (1988) Physica B 296 (2001) 112}119 W.E. Pickett JETP LETTERS VOLUME 70, NUMBER 5 K. N. Mikhalev, S. V. Verkhovski et.al K.Kumagai.et,al Physica C 274 (l 997) 209-220 B. A. Baumert et.al. Barium Potassium Bismuth Oxide: A Review

Introduction Discussion Contents My work Summary -Ba1-XKXBiO3(BKBO)&BaBiO3(BBO) -Valence Skipper(VS) -VS relate to Superconductivity(SC) My work Summary This contents of my presentation are shown here. In Introduction, I talk about the history and properties of oxide SC. In discussion, First I talk about BKBO and BBO structure and K doping effect on BKBO. Second what is VS? and relationship of VS and SC. Next my work and summary. 1 contents

Introduction spin Spin + orbital phonon Spin/valence 1 1975 Tcmax~12K BaPbXBi1-XO3 1988 TCmax~30K Spin + orbital Ba1-XKXBiO3 First, I introduce the history of searching high-Tc SC. In 1975, BaPbBiO3 was discovered. The Tc was 12K and this was the first SC in oxides. After that, the related oxide BaKBiO3 was discovered in 1988. The Tc was about 30K which was twice higher than BPBO. At that time, people believe that these SC can be explained within the BCS thory. But, now, we know that there are many SC mechanisms. For example, the SC of cuprate must be explained by spin mechanism, that of heavy electron system is by spin or valence, iron based system is by spin and orbital and so on. So we try to reconsider the mechanism of BKBO again. 1988年には銅酸化物と同じペロブスカイト構造を取る酸化物のBa1-xKxBiO3[9]が30 Kで超伝導を示す物質として発見されました。現在でも銅酸化物を除 いた酸化物超伝導体の中では、最高のTcを持っています。この物質では、電荷密度波(CDW = Charge Density Wave)が超伝導と密接に関連してるのではないかといわれています。 phonon Spin/valence 1 Introduction

Phase diagram in Ba1-XKXBiO3(BKBO) K concentration X TC~30K at X=0.37 On set Off set No magnetic phase Low carrier=5×1021/cm3 Next. In this slide, I talk about the properties of BKBO. The BKBO has the perovskite structure like this. Please look at right figure. When K concentration is smaller than 30%, the BKBO is not SC. However when K concentration is over 37%, the BKBO become SC suddenly. The BKBO doesn’t have magnetic phase and has high Tc irrespective of low carrier density. Today the Tc is the highest in oxide without cuprate. So this BKBO SC mechanism attracts much attention again, recently Highest TC in oxide (without cuprate) 2 introduction-BKBO

Previous study of BKBO system Please look at the figure. The Tc was plotted as a function of 6s electron of Bi or Pb. The number of 6s electron is changed by replacing the Ba with K. And the relationship of the number of 6s electron and Tc among the related oxides is summarized in this figure. This means that Tc becomes high when number of 6s electron approaches one Bi(Pb) 6s electrons 3 introduction-BKBO

Parent material BaBiO3(BBO) Band calculation H. Matsuura and K. Miyake, J. Phys. Soc. Jpn. 81 (2012) 113705 Ba Bi4+ 2+ 2- Tilting and Breathing Insulator Band gap 2eV Ionic radii (Å) Ba2+ 　1.61 Bi3+ 　1.03 Bi4+(6s)1 Bi5+ 　0.76 metallic (6s)2 charge density wave(CDW) state If this Perovskite structure is Cubic , the behavior is metallic when we calculate the band gap. R q (6s)0 Bi3+ Bi5+ -2e 1 discussion-BKBO 0e

Crystal structure and distortion I2/m Ibmm Pm3m lattice systems  Space group Lattice image  rhombohedral  monoclinic orthorhombic  cubic R3 T(K) solubility limit I2/m Ibmm Pm3m Ba1-XKXBiO3(BKBO) SC 2 discussion-BKBO B. A. Baumert et.al. Barium Potassium Bismuth Oxide: A Review

K doping effect in Ba1-XKXBiO3(BKBO) R3 I2/m Ibmm Pm3m K dope ↓ Hole dope Ionic radii (Å) K+ 　1.64 Ba2+ 　1.61 T(K) solubility limit Commensurate CDW 　→　Incommensurate CDW Tcmax~30K on set off set Temperature↑ and K concentration↑ X~0.37 suppression of structural distortion K concentration X 3 discussion-BKBO

Properties of Ba1-XKXBiO3(BKBO) I2/m Ibmm Pm3m solubility limit T(K) SC × 0.1 0.37 0.5 Insulator Semiconductor Metallic Monoclinic Orthorhombic Cubic Tilting & breathing No? Distortion Structure Band gap 4 discussion-BKBO

Superconductivity gap in BKBO ＋ 2Δ/kTC =3.5±0.5 Full gap Week-coupling SC 5 discussion-BKBO

× BCS superconductivity? TC∝ ∝(1/M)α high TC Physica B 296 (2001) 112}119 W.E. Pickett α TC∝ ∝(1/M)α M:isotope mass BCS × Low carrier=5×1021/cm3 high TC Electron-phonon interaction constant λ=0.2 We can not explain the high TC in this material with BCS The valence skip is important in the study of "Charge Kondo effect" as well as valence - fluctuation induced SC New theory Valence Skipper relate to SC mechanism? 6 discussion-BKBO

What is Valence Skipper? Missing valence state (ns)1 For example Bi3+ Bi5+ [Xe](4f)14(5d)10(6s)2(6p)0 [Xe](4f)14(5d)10(6s)0(6p)0 Bi4+ [Xe](4f)14(5d)10(6s)1(6p)0 induce negative U 6s0 6s1 6s2 for example, Tl and In form compounds with the valence states +1 and +3, Bi and Sb form with +3 and +5 states, and Pb and Sn with +2 and +4 valence state. H. Matsuura and K. Miyake, J. Phys. Soc. Jpn. 81 (2012) 113705 condition 7 discussion-VS

Theory of SC by VS CDW SC t≪Δ eliminate the flexibility of oxygen x C. Varma PRL(1988) U:intra-atomic repulsion parameter(Bi-Bi) t:hopping(Bi-O) V:intra-atomic repulsion parameter(Bi-O) Δ:level CDW SC x t≪Δ eliminate the flexibility of oxygen attraction-repulsion AF SC x ccccccccc Bi3+ Bi5+ 9 discussion-BKBO

? 39K-NMR in Ba1-XKXBiO3(BKBO) × R3 Ibmm Pm3m half-height 3kHz. I2/m Ibmm Pm3m solubility limit half-height 3kHz. 39K NMR X=0.5 X=0.4 Spectrum dose not change by T and K concentration X=0.3 Here T1e-1 is the contribution due to the interaction of nuclear spins with the conduction electrons ~Korringa contribution! and T1Q-1 is the contribution due to the interaction of the quadrupole moment of potassium with the electric field gradient ~EFG!, modulated by motion in the lattice. The smallness of this value and the fact that the relaxation rates for all experimental samples at T520 K are essentially the same, suggests that the Korringa contribution is the same for all the samples investigated, and it can be subtracted from the experimental data. × K’s s electron Conduction band ? 9 discussion-BKBO JETP LETTERS VOLUME 70, NUMBER 5 K. N. Mikhalev, S. V. Verkhovski et.al

39K-NMR in Ba1-XKXBiO3(BKBO) JETP LETTERS VOLUME 70, NUMBER 5 K. N. Mikhalev, S. V. Verkhovski et.al T1-1(s-1) T(K) X=0.5 X=0.4 X=0.3 T1Q-1(s-1) 1000/T(1/K) X=0.5 X=0.4 X=0.3 x small → peak large T1-1(s-1) T(K) Normal metallic K.Kumagai.et,al Physica C 274 (l 997) 209-220 BaPbXBi1-XO3 137Ba/135Ba-NMR T1Q-1 (137eQ/135eQ)=2.4 Valence fluctuation large T1e-1 (137γ/135γ)=1.2 eQ : Quadrupole moment γ : gyromagnetic ratio 10 discussion-BKBO (137T1-1/135T1-1)=2.1 at T＞80K

Evidence of valence fluctuation R3 I2/m Ibmm Pm3m T1Q-1(s-1) 1000/T(1/K) X=0.5 X=0.4 X=0.3 T(K) solubility limit Valence fluctuation is largest nearly Tcmax on set off set CDW X~0.37 11 discussion-BKBO K concentration X

Evidence of valence fluctuation T1Q-1(s-1) 1000/T(1/K) X=0.5 X=0.4 X=0.3 X~0.37 K concentration X CDW Likely behavior Heavy electron system Cuprate 12 discussion-BKBO

Bi(Pb) 6s electrons relate to TC? on set off set 6s0.4 6s1 K concentration X There is a tendency for TC to become high, so that 6s electron is close to 1. Bi(Pb) 6s electrons TCmax~50K is limit ? 13 discussion-BKBO H. Matsuura and K. Miyake, J. Phys. Soc. Jpn. 81 (2012) 113705

My work Pb1-xTlxTe Low carrier ~ 1018~19/cm3 VS 1 TC~0.3K at X=0.3% 6s X(at.%) TC~0.3K at X=0.3% Pb1-xTlxTe 0.646nm image NaCl structure (space group Fm3m) VS 6s Tl+ ・・・ Tl3+ Tl+ Tl3+ 0e -2e 1 My work

Summary Ba1-XKXBiO3(BKBO) reaches highest TC at X=0.37 irrespective of low carrier density. Some results are consistent with BCS theory. In Tcmax, valence fluctuation becomes maximum. Valence Skipper Bi3+ Bi5+ Tl1+ Tl3+ ⇔ Finally, let me summarize my talk. BKBO has high TC irrespective of low carrier density. Some results are consistent with BCS theory however any results are not. In sample with highest Tc, valence fluctuation becomes maximum. So SC may be explained by VS mechanism which cause the high Tc SC. Thus VS is so interesting in researching high Tc SC. High TCSC ? 1 Summary

Thank you for your listening END

appendix

Theory of SC by VS CDW SC ~ 1 – t4/z2|U|2V2 C. Varma PRL(1988) U:intra-atomic repulsion parameter(Bi-Bi) t:hopping(Bi-O) V:intra-atomic repulsion parameter(Bi-O) Δ:level attraction-repulsion CDW SC ~ 1 – t4/z2|U|2V2 x t≪Δ eliminate the flexibility of oxygen 9 discussion-BKBO x

Phase diagram in Ba1-XKXBiO3(BKBO) K concentration X TC~30K at X=0.37 On set Off set No magnetic phase Low carrier Bi(Pb) 6s electrons Highest TC in oxide (without cuprate) 2 intriduction-BKBO

? × × BCS superconductivity? TC∝ ∝(1/M)α 6 Physica B 296 (2001) 112}119 W.E. Pickett α TC∝ ∝(1/M)α M:isotope mass × BCS theory Low-carrier high TC ? We can not explain the high TC in this material with BCS The valence skip is important in the study of "Charge Kondo effect" as well as valence - fluctuation induced SC × Electron-phonon interaction constant λ=0.2 K concentration X 6 discussion-BKBO New theory Valence Skipper relate to SC mechanism?

CDW SC Properties of Ba1-XKXBiO3(BKBO) U,V ⇒ larger ~ 1 – t4/z2|U|2V2 I2/m Ibmm Pm3m CDW SC U,V ⇒ larger T(K) High TC??? ~ 1 – t4/z2|U|2V2 x × 0.1 0.37 0.5 Insulator Semiconductor Metallic Monoclinic Orthorhombic Cubic Tilting & breathing No? Distortion Structure Band gap 13 discussion-BKBO

Theory of SC by VS CDW SC t≪Δ eliminate the flexibility of oxygen x C. Varma PRL(1988) U:intra-atomic repulsion parameter(Bi-Bi) t:hopping(Bi-O) V:intra-atomic repulsion parameter(Bi-O) Δ:level CDW SC x Bi3+ Bi5+ t≪Δ eliminate the flexibility of oxygen attraction-repulsion AF SC x Heavy electron system ccccccccc 9 discussion-BKBO

charge density wave(CDW) state Bi+3 Bi+5 charge density wave(CDW) state R q Bi3+ Bi5+

CDW SC ~ 1 – t4/z2|U|2V2 AF SC AF SC x Heavy electron system x AF + SC (K) Hole or electron dope (high TC SC) Pressure (heavy electron system) CDW SC ~ 1 – t4/z2|U|2V2 x AF + SC AF SC x Heavy electron system

Phase Diagram of HF system TK ∝ W exp(-1/J cf D(εF)) TRKKY ∝ D(εF) Jcf2 AFM : antiferromagnetism HF　 : heavy fermion state QCP : quantum critical point < ( ) γ＝ρ(f)J 30

SC ,which has VS in the origin ,appearing condition Summary 1.BKBO SC ,which has VS in the origin ,appearing condition 1.nearing CDW (due to VS) 2.condition which chemical potential is pinned when VS is doped How to rise the TC 1.control CDW (structure) 2.negative U become large 1 Summary 2.PbTlTe

同位体効果 TC∝(1/M)αj

Properties of Ba1-XKXBiO3(BKBO) K dope ↓ Hall dope Ionic radii (Å) K+ 　1.64 Ba2+ 　1.61 Incommensurate CDW Tcmax=30K Temperature and K substitution on set off set Tc≒30K　and　has metallic behavior　at X≧0.37 suppression of structural distortion X~0.37 K concentration X 2 discussion-BKBO

まとめ ・バレンススキッピング起源の超伝導 が出てきそうな所 １．バレンススキッパー起源のCDW付近 ２．バレンススキッパーをドープしていき、 　　化学ポテンシャルがピン止めされるところ ３．Ag酸化物の可能性 ・転移温度を上げる方法 1. 価数を制御する（→結晶構造の制御） 2. 波動関数の広がりが大きいと ネガティブ-Uが大きくなる。 周期表で下の元素を使う。

What is charge density wave(CDW)? Ionic radii (Å) K+ 　1.64 Ba2+ 　1.61 Bi3+ 　1.03 Bi5+ 　0.76 5 Introduction-VS

すこし理論の話 C. Varma PRL(1988) 引力-斥力変換の対応 酸素の自由度の消去 引力-斥力変換 二次摂動

"Tilting" and "Breathing" distortion Breathing refers to distotion due to the BiO6 octahedra expanding and shrinking alternatly in the perovskite structure. tilting of BiO6 octahedra brings about the lowering of the symmetry of the structure from cubic to monoclinic or rhombohedral 5 Introduction-VS

同位体効果

No-tilt sample (thin film)

5 × 0.1 0.37 0.5 Insulator Semiconductor Metallic Monoclinic 0.37 0.5 Insulator Semiconductor Metallic Monoclinic Orthorhombic Cubic Tilting & breathing No? Distortion Structure Band gap 5 Summary

X Charge density

R q Bi3+ Bi5+ ρ(μΩ) TC~11K BaPb0.8Bi0.2O3

BaBiO3(BBO)&Ba1-XKXBiO3(BKBO) These material has Perovskite structure with “tilting” and “breathing”. In addition to band structure calcuration , BBO is metallic.However BBO is insulater　with band gap 2eV . 5 Introduction-BKBO