1. Soft phonon mode and superconducting properties of 2H-NbS2
Maxime Leroux
P. Rodière, K. Hasselbach, T. Klein, C. Marcenat (a), L. Cario (b), P. Diener (c), M-A. Measson (d), M. Le Tacon (e)
Institut Néel CNRS/UJF – Grenoble, FRANCE
(a) CEA-INAC-SPSMS Grenoble, FRANCE
(b) IMN Nantes, FRANCE
(c) SRON, Utrecht, NETHERLANDS
(d) LMPQ, CNRS/Univ Paris Diderot-Paris 7, FRANCE
(e) Max Planck Institut Stuttgart, GERMANY
I am a second year PhD student at Néel Institute in Grenoble, in the former CRTBT. My superviser are Pierre Rodière and Klaus Hasselbach. I will present our/my work on the superconducting properties and the phonons of 2H-NbS2. 1

2. Framework: Superconductivity and electronic orderings
Temperature
previously
2H-NbSe2
our work
2H-NbS2
High Tc: Pnictides (SDW), cuprates (AF, YBaCuO)
Heavy fermions: CeIn3 (AF), CeRh/CoIn5 (AF), UGe2 (F)
Organic: AF,SDW,CDW
more or less strange Fermi liquid
electronic ordering: AF, SDW, CDW...
accroche
The framework of our studies is the existence of superconductivity close to another electronic ordering. By « close », I mean close in a phase diagram Temperature as a function of Pressure or doping typically. Since this type of phase diagram is very widespread among superconducting compounds, the questions are: are these orderings related ? Are they competing or collaborating ? And does the mechanism of superconductivity come from the ordered phase ? In our case we are particularly interested in the ordering known as Charge Density Wave. For example it is long known that 2H-NbSe2 has a CDW and unconventionnal superconducting properties, whereas the parent compound 2H-NbS2 is the only superconducting 2H-dichalcogenide which does not develop a charge density wave (CDW). SC
External parameter: pressure, doping concentration...
Collaboration or competition ? 2

3. isoelectronic compounds
2H-NbS2 and 2H-NbSe2
hexagonal lattice
isoelectronic compounds Nb
mass decreases
lower orbitals P S Cl As Se Br
S or Se
2H-NbSe2 :
Tc = 7 K
Unconventional superconductivity
TCDW = 33 K
2H-NbS2 :
Tc = 6 K
No CDW
présenter les composés
More precisely the main differences between 2H-NbSe2 and 2H-NbS2 is the lower atomic mass of sulphur and the lower orbitals involved. But they have the same cristallographic structure, they are isolectronic and they have very similar temperature of superconducting transition. 3

4. STM: local electronic density of states
2H-NbSe2
2H-NbS2
T=100 mK
E=EF - 4 meV
superperiodicity = CDW
atomic lattice
No CDW
Intro partie 2 lien avec CDW
So NbSe2 and NbS2 have similar unconventional distribution of superconducting gap. But NbSe2 is the only one to show a modulation of the spatial distribution of charges, a so called CDW, as confirmed by STM. Here you can see an homogeneous distribution of charges corresponding to the atomic lattice, whereas on NbSe2 you can see an additionnal periodic modulation. It is also confirmed by X-ray measurements. So the CDW may have nothing to do with the unconventional superconducting properties. But for going further I need to make a brief recall about CDW.
Coll. Madrid : I. Guillamon & al, PRL 2008 4

5. Unconventional superconducting properties ?
2H-NbS2
Unconventional superconducting properties ?
Any traces of a CDW ?
objectifs de l’étude
So the questions we want to address are : Does NbS2 show unconventionnal superconducting properties ? And are there some traces of the CDW order in the parent compound ? 5

6. Small superconducting gap in 2H-NbS2 and 2H-NbSe2
λ : Magnetic penetration depth
previously
2H-NbSe2
2H-NbS2
2H-NbS2
2H-NbSe2 Δ0
1.2(1) kBTc
1.1(1) kBTc
BCS model
same fast increase
Δ 0 =1.2(1) 𝑘 𝐵 𝑇 𝑐
small gap
For BCS isotropic gap
Same small energy scale compared to BCS theory
𝛿𝜆(𝑇)∝ 𝜋 Δ 0 2 𝑘 𝐵 𝑇 𝑒 − Δ 0 𝑘 𝐵 𝑇
Regarding the superconducting properties, we performed magnetic penetration depth measurement with an extremely precise RF oscillator technique, giving angstrom resolution. The temperature dependence of the magnetic penetration depth is closely related to the nature of the gap. A few years ago we observed, in 2H-NbSe2, the clear signature of a superconducting gap smaller than the 1,76kTc from the BCS theory, cf Fletcher et al. Now, in 2H-NbS2 we also clearly observed an exponential temperature dependence of lambda ab(T) at low temperature, signing the presence of a fully open superconducting gap. This compound is the only superconducting 2H-dichalcogenide which does not develop a charge density wave (CDW). However as previously observed in 2H-NbSe2, this gap (1.1kTc) is significantly smaller than the standard BCS weak coupling value. At higher temperature, a larger gap (1.8kTc) has to be introduced to describe the data which are compatible with a two gap model. The superconducting gaps are hence very similar in NbS2 and NbSe2.
To make a more quantitative comparison, we plotted the normalized superfluid density as a function of T/Tc. It seems clear that the Cooper pairs are broken faster than expected when the temperature increases. It looked like there was the same unconventionnal superconducting properties in both NbS2 and NbSe2 even if there is no CDW in NbS2. However there is a free parameter in this figure since the absolute value of lambda at zero temperature was unknown in NbS2 ! So it needed to be determined by way of another experiment.
Fletcher, Carrington, Diener, Rodière et al. PRL 98, (057003) 2007
Diener, Leroux, Cario, Klein, and Rodiere PRB, 84 (054531) 2011 6

7. Independent measurements
Scanning Tunneling spectroscopy
Coll. Madrid I. Guillamon, H.Suderow et al, PRL 2008
T=100 mK
1st critical field measurement
First our collaborators from madrid did scanning tunneling spectroscopy in the superconducting state, showing that electronic excitations clearly present two energy scales. The magnitude of the small one being coherent with the one we determined earlier!
Secondly as a further confirmation we measured the first critical field, this is the field at which it’s thermodynamically favorable to let enter a quantum of magnetic flux inside the superconductor. The interesting point is that Hc1 is related to the absolute value of the magnetic penetration depth, so that we can confirm its temperature dependance. 7

8. Magnetic field measurement with « micro »-Hall probes
network of 10 probes, sensitivity : 700 Ω/T = 70 mΩ/G
20 µm
Probes: Martin Konczykowski and Vincent Mosser
sample stuck with grease
(1 G=10-4 T)
Présentation manip
For this we uses recent « micro »-Hall probes, that can measure the magnetic field locally, on a a tenth of microns scale, with a great sensitivity.
We stick the sample with grease on a network of probes, and we are then able to determine the field at which the first vortices enter in the sample with a few Gauss/1e-4T resolution.
2e-15 Weber/(20e-6 m)^2=5 µT soit 3,5 mOhm (1e-4Ohm/700 =1e-7 =1,4 mG)
Magnetic field B : profile
outside
sample
Probe number 8

9. Temperature dependence of Hc1 in NbS2 by micro-Hall probe
Same deviation from BCS
small energy scale confirmed by Hc1
Confirmation par Hc1+?incohérence car incompatible BCS?
So we measured Hc1 down to 1.2 K. Now from Hc1 extrapolated at T=0K we can compute the absolute value of the penetration depth. This lead to a penetration depth of 60 nm in the ab plane. Far from the 240 nm expected. However, the temperature dependence of Hc1 is in accordance with a penetration depth of 240 nm and not 60 nm! At least we can say that the usual « one isotropic BCS gap » model fails in this system, which is another hint that something is unusual. Anyway, Hc1 decreases faster than BCS, so it confirms the presence of a small energy scale.
Hc1(T) for H // c
Diener, Leroux, Cario, Klein, and Rodiere PRB, 84 (054531) 2011 9

10. 2H-NbS2 Unconventional superconducting properties ?
Any traces of a CDW in 2H-NbS2 ?
2H-NbSe2 : CDW preceded by a soft phonon mode
Inelastic X-ray Scattering
objectifs de l’étude
So the questions we want to address are : Does NbS2 show unconventionnal superconducting properties ? And are there some traces of the CDW order in the parent compound ? 10

11. Ab initio phonon calculation versus experiment
calculation : T= 0 K
Matteo Calandra
IXS
phonon
𝑄 = 𝑘 𝑖 − 𝑘 𝑓
E=ℏ 𝜔 𝑖 −ℏ 𝜔 𝑓
sample
𝑘 𝑖 ,ℏ 𝜔 𝑖
Incident beam
𝑘 𝑓 , ℏ 𝜔 𝑓
2H-NbS2
Scattered beam
with
e--phonon coupling
center of Brillouin zone
edge of Brillouin zone 𝑄 11

12. Ab initio phonon calculation versus experiment
computation : T= 0 K
experiment
In the case of 2H-NbS2 ab initio phonons calculations predicted that it should present a soft phonon mode, which should even lead a CDW, that was never observed though. So we measured the longitudinal phonons spectrum at low energy in 2H-NbS2, using the IXS ID28 beamline at the ESRF. And we actually found that 2H-NbS2 do present a phonon mode whose energy strongly decreases with temperature, exactly like in NbSe2! 12

13. Soft phonon mode of 2H-NbSe2 and 2H-NbS2
NbS2 : IXS
NbSe2 : Inelastic X-ray Scattering , Weber, …, Reznik 2011
NbSe2 : Inelastic Neutron Scattering, Ayache 1992
mode mou ne tombe pas à zéro donc pas de CDW, et compatible avec un exposant champ moyen de ½
However this soft phonon mode never reaches zero. Contrary to 2H-NbSe2 where the soft mode tends to zero at the temperature of the CDW transition, as measured by INS or IXS. This may explain why there is no CDW in 2H-NbS2, but at least the interesting point is that we are very close to a CDW. So we propose that the electron phonon coupling is strong but not strong enough to trigger the CDW. anisotropie du couplage e-phonon.
However since phonon energy dispersion curves along the other crystallographic direction doesn’t show any softening, it suggest that NbS2 has the same strongly anisotropic electron-phonon coupling, which may be sufficient to explain the distribution of superconducting gaps in both 2H-NbSe2 and NbS2 !
The soft mode does not become static in NbS2
C. Ayache and R. Currat and P. Molinié, Physica B, 180 & 181 ( ), 1992
F. Weber , …, and Reznik., arXiv: , 2011 (accepted for PRL) 13

14. Conclusion consequences on superconductivity ?
Correlation :
2H-NbSe2 soft phonon mode
0 meV
CDW
2H-NbS2 soft phonon mode
0 meV
No CDW
consequences on superconductivity ?
anisotropic electron-phonon coupling
Beneficial or detrimental ?
Van Hove singularity ?
Thanks for your attention! 14