Post on 28-Jul-2020
Polymorphism in Ca(BHx)2: towards superconductivity
in ternary hydrides!Simone Di Cataldo, Graz University of Technology,!Sapienza, Università di Roma!L. Boeri, La Sapienza, Università di Roma!W. Von der Linden, Graz University of Technology!
!
!
Superconductivity in hydrides!Hydrogen-rich materials: rising star for high-Tc superconductivity (SH3, LaH10, YH6)!Challenges still open:!1. Pressures needed above 1 Mbar!2. All binary compounds (AxHy) computationally explored!3. Ternary compounds (AxByHz): challenging phase space!! Look at compounds known from experiment!! CaxByHz molecular crystals, known but unexplored!! Studied for hydrogen storage, rich in H!!
(PRB, 82, 174107 (2010))!
2!
𝑇↓𝑐 = ⟨𝜔↓𝐷 ⟩/1.20 exp(− 1.04(1+𝜆)/𝜆− 𝜇↑∗ −0.62𝜆𝜇↑∗ )!
McMillan, Phys. Rev. 167, (1968) !
𝜆 = 𝑁(𝜀↓𝐹 ) 𝐼↑2 /𝑀⟨𝜔↑2 ⟩ !Hopfield, Phys. Rev. 186, (1969) !
H is the lightest element (large ⟨𝜔↓𝐷 ⟩)!Large 𝜆 if !
! 𝐼↑2 is large: strong bonds!
! 𝑁( 𝜀↓𝐹 ) is large: good metal!
!Problem: strong bond (usually) found for insulators!Solutions:!1. Band overlap (high pressure)!2. Doping!
Outline!Our work!Structural search of ternary calcium boron hydrides (CaxByHz) at room and higher pressure using DFT and genetic algorithms (USPEX). !! Which are the stable stoichiometries under pressure?!! Is there a structural pattern?!! Are there candidates for low pressure superconductivity?!
3!
Convex hull:!0 GPa!
! Sampling of ~4000 structures (USPEX)!
! Four pressures: !0, 50, 100, 300 GPa!
! Phase diagram until 300 GPa!
4!
Stable!Metastable!
ΔH
(meV/atom
)!330!
0.0!
Convex hull:!0 GPa!
! Sampling of ~4000 structures!
! Inclusion of experimentally known structures!
! Keep metastable!
! Further relaxation: !forces down to <1 meV/atom!
5!
Stable!Metastable!
Convex hull:!0 GPa!
! Sampling of ~4000 structures!
! Inclusion of all known
structures !
! Keep metastable!
! Further relaxation:!forces down to <1 meV/atom!
! Ca(BHn)2, n=0,1,2,3,4!
! Stable above 50 GPa!
! Focus on 0 – 50 Range!
! Focus on Ca(BHx)2 line!6!
Stable!Metastable!
“Carbonized” boron!
" Molecular crystals!
" Hydrocarbon-like!
" B-H and B-B, softened covalent bonds!
" Interstitial calcium!
7!Ca(BH3)2 - ethane! Ca(BH4)2 - methane!
Ca(BH) - polyacetylene! Ca(BH2)2 - polyethylene!
“Carbonized” boron!
" Molecular crystals!
" Hydrocarbon-like!
" B-H and B-B, softened covalent bonds!
" Interstitial calcium!
" Insulating!!
8!Ca(BH3)2 - ethane! Ca(BH4)2 - methane!
Ca(BH) - polyacetylene! Ca(BH2)2 - polyethylene!
(poor) metal! GAP: 2.65 eV!
GAP: 4.59 eV! GAP: 5.68 eV!
Ca(BH2)2!
“Carbonized” Ca(BH2)2 !
" Decreased band width!
" Decreased band gap!
" Doping easier than in polyethylene!
" Doped polyethylene: 35 K!
9!
CH2!
“Superconductivity in doped polyethylene at high pressure”!J. Flores-Livas et al, Eur. Phys. J. B., 91: 126 (2018)!
“Carbonized” Ca(BH2)2 !
10!
" Rigid band calculations: estimated doping, rough estimate of Tc!
" Doping: holes or electrons, Tc ( 𝜇↑∗ =0.1) ~15 to 50 K (±0.5 e/fu)!
Effect of doping and H content !
! Holes more effective than electrons!
! Tc grows at higher H content!
! Sizable Tc at reasonable doping!
11!
Summary!
! Which are the stable stoichiometries under pressure?!
" Found stable stoichiometries along the Ca(BHx)2 line!
! Is there a structural pattern?!" Various polymorphic carbon-like structures!" Covalent B-H and B-B bonds!
! Are there candidates for low pressure superconductivity?!
" Doping easier than hydrocarbons!" Tc as high as 50 -100 K at room pressure!
" In progress!! Suitable dopant (Na or Y)!! Calculation for doped structure!! High pressure phases!
12!
Polymorphism in Ca(BHx)2: towards superconductivity
in ternary hydrides!
Simone Di Cataldo!Graz University of Technology!
La Sapienza, Università di Roma!
!L. Boeri, La Sapienza, Università di Roma!W. Von der Linden, Graz University of Technology!
Thanks for your attention!!
“Carbonized” Ca(BHx)2 (0 GPa)!
" B-H and B-B, softened covalent bonds!
" Boron covalent bonds ~13% longer!
14!
Element (room press.)
B – B distance (Å)
C – C distance (Å)
B – H distance (Å)
C – H distance (Å)
Polyacetylene! 1.67! 1.45! 1.26! 1.09!
Polyethylene! 1.81! 1.53! 1.26! 1.10!
Ethane! 1.74! 1.52! 1.24! 1.10!
Methane! NA! NA! 1.24! 1.10!
“Carbonized” boron!
" Molecular crystals!
" Hydrocarbon-like!
" B-H and B-B, softened covalent bonds!
!
15!
“Superconductivity in doped polyethylene at high pressure”!J. Flores-Livas et al, Eur. Phys. J. B., 91: 126 (2018)!
“Carbonized” Ca(BH2)2 !
" Molecular crystals!
" Hydrocarbon-like!
" B-H and B-B, softened covalent bonds!
" Decreased band width!
" Decreased band gap!
16!
Ca(BH2)2!CH2!
Polyacetylene!
" Molecular crystal!
" Hydrocarbon-like!
" Conductive polymer!
" B-H and B-B, softened
covalent bonds!
17!Ca(BH)2 polyacetylene-like!
100 GPa!
18!
! New metastable phase appears!
Stable!Metastable!
300 GPa!
19!
! Off-stoichiometric, metallic phases!
Stable!Metastable!
Calculation parameters (phase diagram)!
20!
PAW pseudopotential (semi-core)!PBE functional!PW expansion up to 600 eV!!Forces:!up to 1 meV/Å!Distance in k-space 0.20 (2 π/a )!Smearing 0.08 eV!!Total energy:!Distance in k-space 0.20 (2 π/a )!Tetrahedron method with Blöchl corrections!
Calculation parameters (electron phonon)!
21!
PAW pseudopotential (semi-core)!PBE functional!PW expansion up to 80 Ry (1088 Ry)!!Charge density:!up to 1 meV/Å!K-grid 6x6x6 for 2 f.u., 4x4x4 for 4 f.u.!Smearing 0.06 Ry (0.8 eV)!!Electron phonon:!𝜆!K-grid: 16x16x16!Smearing: 0.010 Ry!Tc!𝜆/𝑁( 𝜀↓𝐹 )(1) × 𝑁( 𝜀↓𝐹 )(2) !
CaBH phase - 300 GPa!
22!
CaBH, polyacetylene-like!
Outline!
Hydrogen-rich materials: rising star for high-Tc superconductivity (SH3, LaH10, YH6)!Challenges still open:!
1) Pressures needed above 1 Mbar!2) All binary compounds (AxHy) computationally explored!3) Ternary compounds (AxByHz): challenging phase space!! Look at compounds known from experiment!! CaxByHz molecular crystals, known but unexplored!! Studied for hydrogen storage, rich in H!!
(PRB, 82, 174107 (2010))!!
Our work!Structural search of ternary calcium boron hydrides (CaxByHz) at room and higher pressure using DFT and genetic algorithms (USPEX). !! Which are the stable stoichiometries under pressure?!! Is there a structural pattern?!! Are there candidates for superconductivity?!
23!
Why is H good for superconductivity?!
!
" H is the lightest element (large ⟨𝜔↓𝐷 ⟩)!
" Large 𝜆 if !
! 𝐼↑2 is large: strong bonds!
! 𝑁( 𝜀↓𝐹 ) is large: good metal!
!Problem: strong bond (usually) found for insulators!Solutions:!1. Band overlap (high pressure)!2. Doping!
24!
𝑇↓𝑐 = ⟨𝜔↓𝐷 ⟩/1.20 exp(− 1.04(1+𝜆)/𝜆− 𝜇↑∗ −0.62𝜆𝜇↑∗ )!
McMillan, Phys. Rev. 167, (1968) !
𝜆 = 𝑁(𝜀↓𝐹 ) 𝐼↑2 /𝑀⟨𝜔↑2 ⟩ !
Hopfield, Phys. Rev. 186, (1969) !