Development of density functional theory for plasmon assisted superconductors. Ryotaro Arita Univ. Tokyo/PRESTO
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1 Development of density functional theory for plasmon assisted superconductors Ryotaro Arita Univ. Tokyo/PRESTO
2 In collaboration with Ryosuke Akashi (Univ. Tokyo) Poster 28 (arxiv: , ) Poster 29 (arxiv: ) SCDFT study on Alkali-doped fullerides Yusuke Nomura (Univ. Tokyo) Poster 26 (arxiv: ) Ab initio downfolding method for electron-phonon coupled systems & Application to iron-based superconductors
3 Outline Lecture by Prof. Profeta! DFT for superconductors (SCDFT) Gross et al., 1988, 2001, 2005! Formalism free from empirical parameters (such as µ* in the Migdal-Eliashberg theory)! T c reproduced successfully for conventional superconductors (such as simple metals, MgB 2, CaC 6 )! Development of SCDFT for unconventional SC! Plasmon mechanism! Application to Li under high pressure (T c >10K)
4 DFT for normal state v ρ (Nuclei are treated by the Born-Oppenheimer approx.)
5 DFT for superconductors [v,δ] [ρ,χ]
6
7 F xc T c without adjustable parameters
8 Migdal-Eliashberg Theory Σ
9 ω! i = "Z i! i " 1 tanh[ K ph ee (! / 2)!!( 2 ij + K ij ) j ]!! j j j ~ ω D µ ξ φ i [ev]
10 ! i = "Z i! i " 1 2! j K ph ee ( ij + K ij ) tanh[ (! / 2)! j ]! j! j
11
12 to MgB 2 Δ [ mev] T [ K]
13 to unconventional SC MNX M=Zr, Hf X= Cl, Br, I
14 It is an interesting challenge to formulate DFT for unconventional SC spin-fluctuation mediated SC orbital-fluctuation mediated SC exciton mechanism plasmon mechanism
15 Proposed by Y. Takada JPSJ (1978) Superconducting ground state for large r s
16 SrTiO 3 Y. Takada JPSJ (1980) GIC Y. Takada JPSJ (1982), JPSJ (2009) Cooperation of phonon & plasmon enhances pairing instability
17 Field-induced SC has been observed in a variety of band insulators K. Ueno et al., Nature Nanotechnology (2011) J.T. Ye et al., Science (2012) Tc has a dope-like shape Peak in low density region
18 Kohn-Sham perturbation theory (F, D, V c are obtained from first-principles calc.) F (anomalous Green fn.) F (anomalous Green fn.) D(ω) F xc e-ph = F xc e-e = V c
19 Kohn-Sham perturbation theory (F, D, V c are obtained from first-principles calc.) F (anomalous Green fn.) F (anomalous Green fn.) D(ω) F xc e-ph = F xc e-e = V c (ω) with plasmon-pole approximation
20 Kohn-Sham perturbation theory (F, D, V c are obtained from first-principles calc.) F (anomalous Green fn.) F (anomalous Green fn.) D(ω) F xc e-ph = F xc e-e = V c (ω) with plasmon-pole approximation
21 Band structure ~ Nearly Free Electron (NFE) model
22 Struzhkin et al., Science 298, 1213 (2002) Shimizu et al., Nature 419, 597 (2002) T c ~20K at 48GPa Deemyad and Schilling, PRL 91, (2003)
23 Pressure [GPa] Ele-ph coupling (λ) Consistent with T. Bazirov et al., PRB 82, (2010)
24 Δ
25 Struzhkin et al., Science 298, 1213 (2002) Shimizu et al., Nature 419, 597 (2002) T c ~20K at 48GPa (highest T c of any elements) Deemyad and Schilling, PRL 91, (2003)
26 V c (ω) F xc e-e = K ij Hxc =! 2 (E H + F xc )!" i*!" j
27 V c (ω) F xc e-e = K ij Hxc =! 2 (E H + F xc )!" i*!" j
28 V c (ω) F xc e-e = K ij Hxc =! 2 (E H + F xc )!" i*!" j
29
30
31
32
33 Summary & Outlook! Development of SCDFT for unconventional SC! Plasmon assisted SC! Application to Li under high pressure! Application to other systems such as MoS 2, HfNCl,! Development of SCDFT for other mechanisms! Spin fluctuation mediated SC!
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