# Critical field of 2H-NbSe_{2} down to 50mK

- Adel Nader
^{1}Email author and - Pierre Monceau
^{2}

**3**:16

https://doi.org/10.1186/2193-1801-3-16

© Nader and Monceau; licensee Springer. 2014

**Received: **14 June 2013

**Accepted: **26 December 2013

**Published: **9 January 2014

## Abstract

Critical field of 2*H*-NbSe_{2} is determined for the field perpendicular to the conducting planes down to 50 mK, by magnetoresistance measurements. It is the first time that such a measurement is extended below 1 K. Variations are almost linear down to 1 K, with a little upward curvature, and the slope of *H*_{c 2⊥} (*T*) decreases below 1 K. The reduced critical field extrapolates to 0.9 when the temperature approaches zero, higher than the WHH upper limit of 0.69 conformably with the extension of this model for anisotropic superconductors.

Angular dependence of the critical field is also determined at 5.5 K. Variations are the same as expected for a 3D-anisotrpic superconductor and the anisotropy value confirms previous results.

### Keywords

*C*ritical fields 2H-NbSe

_{2}

*L*ayered superconductor

## Introduction

The structure of 2*H*-NbSe_{2} consists of three-layer packets, inside which the layers are ordered in the Se-Nb-Se sequence with covalent binding between them, whereas the packets are bound by van der Waals coupling. Due to this weak coupling in the dichacogenides family, adjacent packets may be oriented in different ways relative one to another and as a consequence the possibility of polytypism. The most widely encountered poly-type for NbSe_{2} is the 2*H*, where 2 is the number of packets in the unit cell and *H* stands for hexagonal. The structure of 2*H*-NbSe_{2} was reviewed by Meerschaut and Deudon (2001).

This compound has been extensively studied for its superconductivity and the formation of a CDW state. It shows a superconducting transition at 7.2 K (Toyota et al. 1976 Sanchez et al. 1995 Soto et al. 2007) with an upper critical magnetic field anisotropy, induced by the layered structure, of about 3.

The CDW state appears in 2*H*-NbSe_{2} below *T*_{CDW} ~ 33 K (Moncton et al. 1977 Higemoto et al. 2003). It can be seen as an anomaly in the resistivity curve that the amplitude is tightly proportional with the sample purity (Iwaya et al. 2003)

An interesting aspect in the superconducting state of this compound which still attracts lots of attention is the peak effect (Banerjee et al. 1998). This effect appears as a maximum in the critical current curve in function of temperature.

Another interesting aspect in this compound is the two gaps structure (Huang et al. 2007 Rodrigo and Vieira 2004) which was evidenced, mainly, by specific heat measurement under magnetic field.

Though, it has been believed for a long time that 2H-NbSe_{2} has just an anisotropic superconducting gap and some experimental results were explained into this framework (Toyota et al. 1976)

The behavior of the critical magnetic field has been subject to discussion since the seventies since its behavior depends tightly on the Fermi Surface geometry. As a result many theoretical calculations (Werthamer et al. 1966 Arai and Kita 2004) concluded that the critical field perpendicular to the layers vary linearly near T_{c} and its slope decreases at lower temperatures. Though an upward curvature is expected for the critical field in the parallel direction (Arai and Kita 2004).

The perpendicular critical field saturation at very low temperatures has never been investigagted experimentally.

In this work critical magnetic field of this compound is determined by mean of magneto-resistance measurement down to 50mK for the first time. It shows a behavior as expected by theoretical models mentioned above with almost a linear variations near T_{c} and a slope decreas at very low temperature. Angular dependence of the critical field is also determined at 5.5 K, it confirms previous results.

## Experimental details

The NbSe_{2} powder is prepared starting from constituting elements at stoechiometric ratio, and then the crystals are grown by thermal gradient using the iodine as a transport agent. Single crystals of these compounds are in platelet form with a diameter in the range of 2 mm and a thickness of 50 μm.

Measurements down to 50 mK are done using a top loading dilution refrigerator and a 8 Tesla superconducting magnet. The anisotropy is measured at 5.5 K using a rotating system with an accuracy of 0.1°.

## Results and discussion

*H*

_{c 2⊥}(

*T*). It shows a little upward curvature near Tc. Though, by experience, upward curvature near T

_{c}may be induced by a rather wide resistive transition, a better discussion of such an aspect would then need a better quality sample, with a sharpest transition. Nevertheless, such an upward curvature was expected by by Arai and Kita (2004) for the parallel critical field or for layer compounds of higher anisotropies (Woollam et al. 1974).

Below 1 K the slope of *H*_{
c
}_{2⊥} (*T*) decreases as expected by Werthamer et al. (1966) for a dirty superconductor and by Arai and Kita (2004)).

Our results are similar to that found in (Toyota et al. 1976) where the measurements were done only down to 1.3 K. Though, no upward curvature near T_{c} was mentioned in (Toyota et al. 1976), probably because samples were of a much better quality; their RRR ratio was always higher than 30, although, for our sample it is less than 10.

*h*(

*t*), which is the upper critical field normalized as in (Werthamer et al. 1966) i.e.

*t*=

*T*/

*T*

_{ c }and

*h*=

*H*

_{c 2}/(-

*dH*

_{c 2}/

*dt*).

*h*(

*t*) extrapolates to 0.9 when

*t*→ 0.

Werthamer et al. (1966) extended the calculation of the upper critical field for a bulk superconductor by taking in account Pauli spin paramagnetism and spin-orbit impurity scattering. According to this model this value should not be greater than 0.69. Though, in (Hohenberg and Werthamer 1967) it was shown that this is possible for anisotropic superconductors when Fermi surface is no more spherical.

Also, the sketch of *h (t)* seems to be in good agreement with the reduced critical field curve calculated using the Fermi surface obtained by local density approximation (LDA) by Arai and Kita (2004) (see Figure 1 in this reference). According to this calculation *h* (0)extrapolates to about 0.95.

*H*

_{c 2}(

*θ*) at 5.5 K, where

*θ*is the angle between the conducting planes and the magnetic field. The following formula was given by Lawrence and Doniach (1971):

*ϵ*is the ratio of the parallel critical field to the perpendicular one at

*T*.

The fit with this formula gives an anisotropy of 3.2. This value approaches those found in (Toyota et al. 1976 Sanchez et al. 1995).

Though, Lawrence and Doniach simple model based on the effective mass anisotropy was proven not to be sufficient to describe the critical field anisotropy in layered superconductors as shown by Toyota et al. (1976) and that other assumptions should be made such as the gap anisotropy, but it could be used as a first approximation to extract anisotropy from the *H*_{c 2} (*θ*, *T*) curve.

Let us note also that the critical field anisotropy is temperature dependent, and the parallel critical field shows an upward curvature in (Toyota et al. 1976 Muto et al. 1973).

In plane and out-of-plane coherence lengths are then *ξ*_{||} (0) =74 Å and *ξ*_{⊥} (0) = 23 Å respectively. *ξ*_{⊥} (0) is much greater than the distance separating the centers of two successive conducting planes, which confirms that 2*H*-NbSe_{2} is a 3D-anisotropic superconductor.

Coherence lengths as well as the critical field anisotropy are of the same range as found in (Sanchez et al. 1995) by specific heat measurements.

## Conclusion

Critical magnetic field measurement of 2*H*-NbSe_{2} is extended down to 50 mK. The slope of *H*_{
c
}_{2⊥} (*T*) decreases below 1 K and varies almost linearly near T_{c} with a little upward curvature, probably induced by a rather large superconducting transition.

Also, the anisotropy is the same as obtained in previous works.

## Declarations

### Acknowledgement

I wish to thank Prof. I. Othmann Director General of Atomic Energy Commission of Syria for his support.

## Authors’ Affiliations

## References

- Arai M, Kita T: Ab initio calculations of Hc2 for Nb, NbSe2, and MgB2.
*J Phys Soc Jpn*2004, 73: 2924-2927. 10.1143/JPSJ.73.2924View ArticleGoogle Scholar - Banerjee SS,
*et al*.: Generic phase diagram for vortex matter via a study of peak effect phenomenon in crystals of 2H-NbSe2.*Physica C*1998, 308: 25-32. 10.1016/S0921-4534(98)00500-0View ArticleGoogle Scholar - Higemoto W, Nagamine K, Kuroda S, Takita K: Charge density wave in 2H-NbSe2 probed by muons.
*Physica B*2003, 326: 540-544. 10.1016/S0921-4526(02)01685-XView ArticleGoogle Scholar - Hohenberg PC, Werthamer NR: Anisotropy and temperature dependence of the upper critical field of type-II superconductors.
*Phys Rev*1967, 153: 493-497. 10.1103/PhysRev.153.493View ArticleGoogle Scholar - Huang CL,
*et al*.: Experimental evidence for a two gap structure of superconducting NbSe2: a specific-heat study in external magnetic fields.*Phys Rev B*2007, 76: 21250.Google Scholar - Iwaya K,
*et al*.: Electronic state of NbSe2 investigated by STM/STS.*Physica B*2003, 329-333: 1598-1599.View ArticleGoogle Scholar - Lawrence WE, Doniach S Proc. 12
^{th}int. Conf. on Low Temp. Phys., ed. E. Kanada (academic 1971).*Theory of layer structure superconductors*1971, 361-362.Google Scholar - Meerschaut A, Deudon C: Crystal structure studies of the 3R-Nb1.09S2 and the 2H-NbSe2 compounds: correlation between nonstoichiometry and stacking type (= polytypism).
*Mater Res Bull*2001, 36: 1721-1727. 10.1016/S0025-5408(01)00646-8View ArticleGoogle Scholar - Moncton DE, Axe JD, Di Salvo FJ: Neutron scattering study of the charge-density wave transitions in 2H-TaSe
_{2}and 2H-NbSe_{2}.*Phys Rev B*1977, 16: 801-819. 10.1103/PhysRevB.16.801View ArticleGoogle Scholar - Muto Y,
*et al*.: Temperature dependence of ratio,*H*_{c 2}/*H*_{c 21⊥}, for NbSe2.*Phys Lett*1973, 45: 99-100.View ArticleGoogle Scholar - Rodrigo JG, Vieira S: STM study of multiband superconductivity in NbSe2 using a superconducting tip.
*Physica C*2004, 404: 306-310. 10.1016/j.physc.2003.10.030View ArticleGoogle Scholar - Sanchez D, Junod A, Muller J, Berger H, Levy F: Specific heat of 2H-NbSe2 in high magnetic fields.
*Phys B*1995, 204: 167-175. 10.1016/0921-4526(94)00259-XView ArticleGoogle Scholar - Soto F,
*et al*.: Electric and magnetic characterization of NbSe2 single crystals: Anisotropic superconducting fluctuations above T.*Physica C*2007, 460-462: 789-790.View ArticleGoogle Scholar - Toyota N,
*et al*.: Temeprature and angular dependences of upper critical fields for the layer structure supercionductor 2H-NbSe_{2}.*J Low Temp Phys*1976, 25: 485-498. 10.1007/BF00655842View ArticleGoogle Scholar - Werthamer NR, Helfand E, Hohenburg PC: Temperature and purity dependence of the superconducting critical field, H
_{c2}. III. electron spin and spin-orbit effects.*Phys Rev*1966, 147: 295-302. 10.1103/PhysRev.147.295View ArticleGoogle Scholar - Woollam JA, Somoano RB, O'Connor P: Positive Curvature of
*H*_{ c2 }-versus-*T*_{ c }bounbaries in layered superconductors.*Phys Rev Lett*1974, 32: 712-714. 10.1103/PhysRevLett.32.712View ArticleGoogle Scholar

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