Abstract
While 203 K high temperature superconductivity in H3S has been interpreted by BCS theory in the dirty limit here we focus on the effects of hydrogen zero-point-motion and the multiband electronic structure relevant for multigap superconductivity near Lifshitz transitions. We describe how the topology of the Fermi surfaces evolves with pressure giving different Lifshitz-transitions. A neck-disrupting Lifshitz-transition (type 2) occurs where the van Hove singularity, vHs, crosses the chemical potential at 210 GPa and new small 2D Fermi surface portions appear with slow Fermi velocity where the Migdal-approximation becomes questionable. We show that the neglected hydrogen zero-point motion ZPM, plays a key role at Lifshitz transitions. It induces an energy shift of about 600 meV of the vHs. The other Lifshitz-transition (of type 1) for the appearing of a new Fermi surface occurs at 130 GPa where new Fermi surfaces appear at the Γ point of the Brillouin zone here the Migdal-approximation breaks down and the zero-point-motion induces large fluctuations. The maximum Tc = 203 K occurs at 160 GPa where EF/ω0 = 1 in the small Fermi surface pocket at Γ. A Feshbach-like resonance between a possible BEC-BCS condensate at Γ and the BCS condensate in different k-space spots is proposed.
Highlights
Since H3S is a multiband metal and Lifshitz transitions could occur by increasing pressure[3,4] it has been proposed that it is a multigap superconductior near Lifshitz transitions[27,28,29], where multi scale phase separation[32] at a the Lifshitz transition could appear, similar to what has been observed in the cuprates[34,35,36,37]
We study the effect of the zero point motion on the van Hove singularity and we find a very large energy shift of the order of 600 meV of the vHs due to ZPM
The calculated band structure for an ordered H3S lattice as a function of pressure clearly shows multiple Lifshitz transitions for appearing of new Fermi surface spots in the pressure range showing high Tc superconductivity, which together with quantum hydrogen zero point motion puts the system beyond the Migdal approximation
Summary
The high pressure phase of metallic H3S has the cubic Space Group: 229 with Im3m lattice symmetry. In order to investigate the pressure effects on the electronic structure we show in Fig. 3 the different total DOS for different lattice constant a of the perovskite structure changing from 6.2 to 5.6 a.u. The total DOS at EF per S-atom is about 3.5 (Ry)−1 and 1 (Ry)−1 per H-site, compared to the order 20 per V in V3Si or in elementary V and Nb. The total DOS at EF per S-atom is about 3.5 (Ry)−1 and 1 (Ry)−1 per H-site, compared to the order 20 per V in V3Si or in elementary V and Nb This is not surprising because of the large width of the wide band in H3S having its bottom at 2 Ry below the chemical potential, see Fig. 3, while for increasing number of (d-) electrons in transition metal A15 compounds the total band width is more like 2/3 of a Ry47. The charge within the H WS-sphere increases from 1.3 to 1.4 el./H when the lattice constant decreases from 6.2 to 5.6 a.u., and the H-s charge goes from 0.95 to 1.0 This fact justifies somewhat the use of LSDA for H even though atomic H with exactly 1 electron is best described by the Hartree potential only. The shift is small in the figure because of the large energy scale
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