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Breakdown of the Migdal approximation at Lifshitz transitions with giant zero-point motion in the H3S superconductor.

Jarlborg T, Bianconi A - Sci Rep (2016)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: DPMC, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland.

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.

No MeSH data available.


Related in: MedlinePlus

The upper panel (a) shows the S-H bond length in the pressure range between 120 and 180 GPa where without the hydrogen ZPM, the R3m structure was expected to be stable with the S-H bond splitting into a long (blue squares) and short (violet squares) sulfur-hydrogen bond. The amplitude of the calculated ZPM of the S-H bond is indicated by the red error bars34. The S-H amplitude of the zero point motion, ZPM, is larger than the S-H splitting in the range 130–180 GPa therefore in this pressure range the ZPM stabilizes the  structure4 in agreement with experiments2. The panel (b) shows the Fermi energy EF4 in the small hole Fermi pocket at Γ as a function pressure. The top of this band crosses the chemical potential at 130 GPa giving the Lifshitz transition of type 1 for the appearing of a new Fermi surface. The position of the vHs E2 remains below the chemical potential but it remains in the energy range of pairing interaction. Panel (c) shows the variation of the experimental isotope coefficient calculated from data in ref. 2 which shows a divergence from 0.3 at 180 GPa to 1.5 at 135 GPa, which is not predicted by the BCS theory. The critical temperature decreases toward zero with a decrease of about 60 K in a range of 30 GPa, beteen 160 GPa and 130 GPa which is not predicted by the BCS theory. Both phenomena are predicted by the general theory of multigap superconductivity near a Lifshitz transition34.
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f11: The upper panel (a) shows the S-H bond length in the pressure range between 120 and 180 GPa where without the hydrogen ZPM, the R3m structure was expected to be stable with the S-H bond splitting into a long (blue squares) and short (violet squares) sulfur-hydrogen bond. The amplitude of the calculated ZPM of the S-H bond is indicated by the red error bars34. The S-H amplitude of the zero point motion, ZPM, is larger than the S-H splitting in the range 130–180 GPa therefore in this pressure range the ZPM stabilizes the structure4 in agreement with experiments2. The panel (b) shows the Fermi energy EF4 in the small hole Fermi pocket at Γ as a function pressure. The top of this band crosses the chemical potential at 130 GPa giving the Lifshitz transition of type 1 for the appearing of a new Fermi surface. The position of the vHs E2 remains below the chemical potential but it remains in the energy range of pairing interaction. Panel (c) shows the variation of the experimental isotope coefficient calculated from data in ref. 2 which shows a divergence from 0.3 at 180 GPa to 1.5 at 135 GPa, which is not predicted by the BCS theory. The critical temperature decreases toward zero with a decrease of about 60 K in a range of 30 GPa, beteen 160 GPa and 130 GPa which is not predicted by the BCS theory. Both phenomena are predicted by the general theory of multigap superconductivity near a Lifshitz transition34.

Mentions: In Fig. 11 we have plotted in panel a the S-H bond length as a function of pressure and the amplitude of the calculated spread of this bond length due to the hydrogen zero point motion indicated by the red error bars. The USPEX theory1213 predicts the second order phase transition from to R3m structure at 180 GPa where the sulfur atoms remain in the same sites of the bcc unit cell while hydrogen ions are frozen in one of the two minima of their double well potential due to the hydrogen bond like in ice structural transitions. On the contrary this transition is forbidden in the pressure range 120–180 GPa since the quantum zero point motion amplitude which is larger than the difference between the short and long hydrogen bonds expected in the R3m structure, Therefore the ZPM stabilizes the structure in the pressure range 130–180 GPa3 in agreement with recent experiments2.


Breakdown of the Migdal approximation at Lifshitz transitions with giant zero-point motion in the H3S superconductor.

Jarlborg T, Bianconi A - Sci Rep (2016)

The upper panel (a) shows the S-H bond length in the pressure range between 120 and 180 GPa where without the hydrogen ZPM, the R3m structure was expected to be stable with the S-H bond splitting into a long (blue squares) and short (violet squares) sulfur-hydrogen bond. The amplitude of the calculated ZPM of the S-H bond is indicated by the red error bars34. The S-H amplitude of the zero point motion, ZPM, is larger than the S-H splitting in the range 130–180 GPa therefore in this pressure range the ZPM stabilizes the  structure4 in agreement with experiments2. The panel (b) shows the Fermi energy EF4 in the small hole Fermi pocket at Γ as a function pressure. The top of this band crosses the chemical potential at 130 GPa giving the Lifshitz transition of type 1 for the appearing of a new Fermi surface. The position of the vHs E2 remains below the chemical potential but it remains in the energy range of pairing interaction. Panel (c) shows the variation of the experimental isotope coefficient calculated from data in ref. 2 which shows a divergence from 0.3 at 180 GPa to 1.5 at 135 GPa, which is not predicted by the BCS theory. The critical temperature decreases toward zero with a decrease of about 60 K in a range of 30 GPa, beteen 160 GPa and 130 GPa which is not predicted by the BCS theory. Both phenomena are predicted by the general theory of multigap superconductivity near a Lifshitz transition34.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4837402&req=5

f11: The upper panel (a) shows the S-H bond length in the pressure range between 120 and 180 GPa where without the hydrogen ZPM, the R3m structure was expected to be stable with the S-H bond splitting into a long (blue squares) and short (violet squares) sulfur-hydrogen bond. The amplitude of the calculated ZPM of the S-H bond is indicated by the red error bars34. The S-H amplitude of the zero point motion, ZPM, is larger than the S-H splitting in the range 130–180 GPa therefore in this pressure range the ZPM stabilizes the structure4 in agreement with experiments2. The panel (b) shows the Fermi energy EF4 in the small hole Fermi pocket at Γ as a function pressure. The top of this band crosses the chemical potential at 130 GPa giving the Lifshitz transition of type 1 for the appearing of a new Fermi surface. The position of the vHs E2 remains below the chemical potential but it remains in the energy range of pairing interaction. Panel (c) shows the variation of the experimental isotope coefficient calculated from data in ref. 2 which shows a divergence from 0.3 at 180 GPa to 1.5 at 135 GPa, which is not predicted by the BCS theory. The critical temperature decreases toward zero with a decrease of about 60 K in a range of 30 GPa, beteen 160 GPa and 130 GPa which is not predicted by the BCS theory. Both phenomena are predicted by the general theory of multigap superconductivity near a Lifshitz transition34.
Mentions: In Fig. 11 we have plotted in panel a the S-H bond length as a function of pressure and the amplitude of the calculated spread of this bond length due to the hydrogen zero point motion indicated by the red error bars. The USPEX theory1213 predicts the second order phase transition from to R3m structure at 180 GPa where the sulfur atoms remain in the same sites of the bcc unit cell while hydrogen ions are frozen in one of the two minima of their double well potential due to the hydrogen bond like in ice structural transitions. On the contrary this transition is forbidden in the pressure range 120–180 GPa since the quantum zero point motion amplitude which is larger than the difference between the short and long hydrogen bonds expected in the R3m structure, Therefore the ZPM stabilizes the structure in the pressure range 130–180 GPa3 in agreement with recent experiments2.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: DPMC, University of Geneva, 24 Quai Ernest-Ansermet, CH-1211 Geneva 4, Switzerland.

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.

No MeSH data available.


Related in: MedlinePlus