Superconductivity and Charge Density Wave in ZrTe3-xSex.

Charge density wave (CDW), the periodic modulation of the electronic charge density, will open a gap on the Fermi surface that commonly leads to decreased or vanishing conductivity. On the other hand superconductivity, a commonly believed competing order, features a Fermi surface gap that results in infinite conductivity. Here we report that superconductivity emerges upon Se doping in CDW conductor ZrTe3 when the long range CDW order is gradually suppressed. Superconducting critical temperature Tc(x) in ZrTe3-xSex (0 ≤ x ≤ 0.1) increases up to 4 K plateau for 0.04 ≤ x ≤ 0.07. Further increase in Se content results in diminishing Tc and filametary superconductivity. The CDW modes from Raman spectra are observed in x = 0.04 and 0.1 crystals, where signature of ZrTe3 CDW order in resistivity vanishes. The electronic-scattering for high Tc crystals is dominated by local CDW fluctuations at high temperatures, the resistivity is linear up to highest measured T = 300 K and contributes to substantial in-plane anisotropy.

Charge density wave (CDW) and superconductivity (SC), both Fermi surface instabilities and low-temperature collective orders in solids, are commonly believed to compete with each other12. Recently, dynamic CDW fluctuations have also been discussed in copper oxide superconductors3 in connection with quantum critical transition between CDW and superconductivity. CDW favors low dimensional systems, especially transition metal (M) MX2 and MX3 chalcogenides (X represents S, Se and Te)14. Among them, ZrTe3 is of interest since its crystal structure (Fig. 1a) is quasi-two dimensional (2D), yet it contains two quasi-one dimensional (1D) trigonal prismatic ZrTe6 chains with inversion symmetry along the b-axis5. From the view along c-axis (Fig. 1b), the top Te2/Te3 atoms form a rectangular network with the distances of 0.279/0.310 nm along the a axis and 0.393 nm along the b-axis. The first principle calculation gives evidence that the electron-type band (Te2/Te3 5p in origin) provides the major contribution, whereas the contribution of the partially filled hole-type band that originates in Te1 5p and orbitals is minor at the Fermi surface5. Angular resolved photoemission (ARPES) demonstrates that CDW originates from the Te2/Te3 5p band6.

Figure 1

(a) Crystal structure of ZrTe3. (b) Top Te2/Te3 rectangular network layer viewed from c-axis. The quasi 1D ZrTe6 chains run along the b-axis, with the shortest Zr-Zr distance and Te1-Te1 distance of 0.393 nm. Solid line denotes the alternately spaced Te2/Te3 chain. (c) Temperature dependence of normalized ρ(ρ/ρ(300 K)) for ZrTe3−Se. The inset shows a typical photograph of cleaved ZrTe3−Se crystal. Some fibers along b-axis can be observed. (d) The T is determined from the dips in the differential curves of ρ/ρ(300 K) − T (shown in the inset). Solid rectangular, circle and triangle represent x = 0, 1% and 2%, respectively. The arrows mark the T. (e) Low temperature ρ/ρ(300 K) − T. Superconducting T is determined as the midpoint of the superconducting transition. (f) The temperature dependence of magnetic susceptibility (χ) measured for ZrTe2.96Se0.04, ZrTe2.93Se0.07, and ZrTe2.9Se0.1. The applied magnetic field(H) is 2 Oe and parallel to the b axis of crystal.

ZrTe3 features not only a CDW transition temperature (T) ~63 K with a CDW vector but also a nearly isotropic in-plane and quasi-two-dimensional (2D) electronic transport578. There is a filamentary SC in a stoichiometric single crystal with higher onset of T for a-axis from resistivity measurement than for b-axis59. Heat capacity data suggest that SC transitions in ZrTe3 are successive from filamentary-to-bulk with local pair fluctuations above T; SC phase first condenses into filaments along a-axis, becoming phase coherent below 2 K9. Pressure(P), intercalation, and disorder can tune ZrTe3 into bulk SC with suppression of CDW order101112.

Here we provide evidence for the pronounced upper critical field H(T) anisotropy and emerging 1D electronic transport along the ZrTe6 chain-direction b axis in ZrTe3−Se (0 ≤ x ≤ 0.1). The H(T) anisotropy and new Raman modes suggest coexistence of local CDW modes and enhanced superconducting T(x) in ZrTe3−Se.

Results

Normalized ρ [ρ/ρ(300 K)] [Fig. 1(c)] shows that the CDW anomaly is suppressed with increasing Se content. The T [Fig. 1(d)] decreases whereas the bulk superconductivity sets in [Fig. 1(e,f)]. For x ≤ 0.04, as shown in Fig. 1(e), the superconducting transition temperature (T) determined from the ρ(T) curves tends to increase, and transition width decreases. With increasing Se content x ≥ 0.04, [Fig. 1(f)], somewhat lower T = 4 K is observed for x = 0.07, and the superconducting transition becomes wide and filamentary for x = 0.1 with T ~ 3.1 K. ZrTe2.96Se0.04 shows typical behaviour of a type-II superconductor, whose field cooling (FC) χ is smaller than in zero field cooling process (ZFC) [Fig. 1(f)].

The ρ and ρ are almost identical to each other in ZrTe3 (x = 0), however with increasing Se content x, room temperature ρ tends to increase, while ρ tends to decrease [Fig. 2(a)]. This indicates that ZrTe3−Se becomes highly conducting along b-axis in the normal state. If ZrTe3−Se is an anisotropic superconductor with dominant quasi-1D (super)conductivity along the b-axis, upper critical field along b axis () should be larger than , according to the single band anisotropic Ginzburg-Landau theory since

Figure 2

(a) The log-plots of ρ(solid square) and ρ(solid circle) versus Se doping content. (b) The temperature dependence of the upper critical field (H) (determined as the midpoint of the superconducting transition; the error bars are the difference from the 10% and 90% resistivity drop) of ZrTe2.96Se0.04 for H ∥ a, H ∥ b and H ∥ c. The solid lines represents the fitts of the two band model (see text). Inset shows the magnetic hysteresis (M − H) loop for ZrTe2.96Se0.04 measured at 2 K.

To confirm this, we choose the ZrTe2.96Se0.04 crystal where the ratio of ρ(T)/ρ(T) is about 10 at 300 K [Fig. 2(a)]. The magnetic hysteresis (M − H) loop for ZrTe2.96Se0.04 [Fig. 2(b) inset] confirms that it is a typical type-II superconductor with some electromagnetic granularity. In ZrTe2.96Se0.04, relation can be observed [Fig. 2(b)]. This is in contrast to the b-axis quasi-1D conductivity in the normal state suggesting multiband effects and/or additional factors that can contribute to mass tensor anisotropy. The upward curvature of H-T curves implies that the multiband effects should be considered.

The H(T) for the two-band BCS model with orbital pair breaking is13:

where t = T/T, ψ(x) is the digamma function, η = D2/D1, D1 and D2 are band 1 and band 2 diffusivities, h = HD1/(2ϕ0T), and ϕ0 = 2.07 × 10−15 Wb is the magnetic flux quantum. , a1 = 1 + λ−/λ0, and a2 = 1 − λ−/λ0, where , , and λ− = λ11 − λ22. Interband coupling in two bands is given by λ12 and λ21 whereas λ11 and λ22 are intraband coupling constants in band 1 and 2, when D1 = D2, this simplifies to the one-band model orbital pair breaking in the dirty limit14. Dominant intraband (interband) coupling is obtained for . The fits to the multiband model using λ i, j = 1, 2 in Table 1 are excellent [solid lines in Fig. 2(b)]. Overall, the fitting results indicate dominant intraband coupling1516. Interestingly, the η ≈ 0.10(4) suggest different D1 and D2, i.e. approximately an order of magnitude different carrier mobilities in the two bands. This difference in the intraband diffusivities could be due to differences in scattering or effective masses1315.

Table 1

Citting parameters of H for Cu0.05ZrTe3.

Hc2∥	η	λ11	λ12	λ21	λ22
a	0.098	0.60	0.25	0.25	0.80
b	0.124	0.60	0.50	0.50	0.60
c	0.145	0.60	0.25	0.25	0.80

Figure 3(a) depicts the T(x) phase diagram of T and T versus Se content x for ZrTe3−Se. With increasing Se content x, the CDW order detected by a-axis resistivity anomaly is suppressed, vanishing around x = 0.03. SC T gradually increases up to the maximum T = 4.4 K around x = 0.04. With further increase in Se the superconducting T appears to have onset near 4 K, becoming much broader and with smaller shielding factor suggesting percolative nature of SC. Even though the sample with higher Se content cannot be grown at present, it is clear that the SC should decrease to T = 0 since ZrSe3 is a band insulator with a band gap of 1 eV17. In contrast, Hf substitution on Zr site in Zr1−HfTe3 does not suppress the CDW order, and no SC is observed. This is different from IrTe2, in which only 5d Ir site substitution can suppress the charge/orbital order and induce SC18. The Hf doping does not alter the Te2/Te3 bands, which explains why Hf doping cannot suppress the CDW order and induce SC.

Figure 3

(a) The phase diagram of T and T versus Se doping content; insets show electronic specific heat and the Kadowaki - Woods ratio for ZrTe2.96Se0.04 (refs 26,27). The a = 0.4 μΩcm mol2 K2 J−2 and a = 10 μΩcm mol2 K2 J−2 are values seen in the transition metals and heavy fermions, respectively. Even though values of electron-electron scattering rate A and mass renormalization γ are smaller than in strongly correlated materials, it appears that the scaling A/γ2 in ZrTe3 is similar to NaCoO2 and Sr2RuO4. (b) The normalized Raman scatering spetra for ZrTe3, ZrTe2.96Se0.04, and ZrTe2.9Se0.1 measured at 5 K and 300 K with Z(XX)Z polarization. The two CDW modes at 115 cm−1 and 152 cm−1 are marked by arrows.

In what follows we compare the Raman signal of superconducting crystals to Raman signal of pure ZrTe3 with long range CDW order. Figure 3(b) depicts the Raman spectra normalized to 86 cm−1 mode of ZrTe3−Se measured at 5 K and 300 K with Z(XX)Z polarization for different Se content. Small Se doping should not change the phonon spectrum at the room temperature and indeed, the 300 K spectra nearly overlap with each other. As expected, the Raman spectrum of ZrTe3 measured at 5 K is different from the one measured at 300 K. Two new modes appear around 115 cm−1 and 152 cm−1, which we assign to CDW (CDW mode)1920. Periodic lattice distortions in the CDW state will result in the new phonon modes below T and some (CDW modes) can be observed in the Raman spectra, for example in 1T-TiSe221 and 2H-NbSe222. The 108 cm−1, 140 cm−1 and 145 cm−1 modes are suppressed to low intensity with small temperature dependent shift at low temperature. The intensity of the two CDW modes 115 at cm−1 and 152 cm−1 becomes weaker for x = 0.04 and 0.1. It should be noted that CDW modes are detected outside the phase boundary of CDW order. The normalized amplitudes of the two CDW modes exist for x = 0.04 and 0.1, in crystals with no CDW signature in resistivity. This suggests a coexistence of superconductivity and CDW-related lattice distortions.

Discussion

Fermi surface of ZrTe3 contains multiple bands with both flat and dispersive portions as well as substantial hybridization of high mobility chalcogen-derived bands with low mobility metal-derived bands5. We note that in ZrTe3 CDW fluctuations affect the angular resolved photoemission spectral function A(k, ω) at temperatures above 200 K23. Scattering in such multiband CDW electronic system in the presence of local CDW fluctuations is dominated by scattering off collective CDW excitations below T [ρ(T) ~ AT2; where A is a constant parameter] and the electron-phonon and impurity-like scattering off local CDW fluctuations above the T [ρ(T) ~ aT + b]24. Both ρ and ρ are perfecly linear from about 60 K up to highest measured temperature of 300 K, whereas a ~ T2 resistivity is observed from superconducting T up to about 80 K [Fig. 4(a,b)]. With suppression of the CDW order by pressure or doping, CDW mode should vanish25, and indeed the absence of characteristic CDW-related hump is observed in resistivity. However as evident in Fig. 4(c), the signature of CDW mode in ZrTe3−Se appears below about 100 K suggesting that the crystallographic vibration of the unit cell still senses CDW presence, but we speculate with no phase coherence.

Figure 4

(a,b) The a- and b-axis resistivity fits of ZrTe2.96Se0.04. Below 63 K ρ(T) ~ AT2 and above that temperature ρ(T) ~ aT + b up to highest measured 300 K. The fitting parameters are A = 0.0107(1), A = 0.0019(1); a = 0.250(1), a = 1.66(1) and b = −9.0(2) and b = −68(1). (c) Raman scattering in ZrTe2.96Se0.04 where CDW mode can be traced below about 100 K.

The resistivity shows that electron-electron scattering due to CDW fluctuations dominates over the electron-phonon scattering and provides ρ ~ AT2 temperature dependence with relatively high values of coefficient A. As a result, Kadowaki-Woods scaling A/γ2 is comparable to Tl2Ba2CuO6, Sr2RuO4 or Na0.7CoO2 [Fig. 3(a) insets]262728. In ZrTe3, with increasing P, CDW order is first enhanced and reaches maximum T around 2 GPa10, then decreases, vanishing around 5 Gpa, whereas superconducting T increases monotonically up to highest pressures. The phase diagram in Fig. 4b is different from this but Se could act as a chemical pressure due to its smaller size. Therefore slight increase in band filling of the quasi-1D Fermi surface sheet seen in pure ZrTe3 under pressure could be the mechanism for the in-plane anisotropy and promotion of SC29. However, due to very small Se content (up to about 3 atomic %) and no appreciable change in the unit cell parameters, this would imply strong sensitivity of CDW to substitutions on Te site and possibly to disorder.

As doping increases beyond x = 0.04 the superconducing T forms a weak dome or plateau-like temperature dependence similar to PrFeAsO1−F30. Charge-mediated attraction is involved in both CDW and SC. For well nested Fermi surface long range CDW is stable and superconductivity is only filamentary along a axis arising in the Te2/Te3 5p band59. With Se doping the CDW is no longer detected in scattering but dominant intraband interaction could ensure that patches of CDW still survive, as seen by Raman. The small Se substitution is unlikely to remove the nesting condition but may perturbe the long range phase coherence of CDW and consequently resistivity hump. Broad superconducting transition, small reduction of SC transition temperature and significant decrease in the superconducting volume fraction suggest that the percolative SC is independent of Se content once the CDW-related resistivity anomaly is absent.

The above discussion suggests a possibility for a CDW-fluctuation induced heavy-fermion-like mass enhancement contribution to mass tensor anisotropy31. Moreover, superconductivity on the verge of the breakdown of the long-range CDW order is reminiscent to magnetic fluctuation mediated superconductivity in copper oxide and heavy fermion materials where the magnetic order is tuned by doping or pressure to T → 0 at the Quantum Critical Point32333435.

Conclusion

In summary, we show that superconductivity in ZrTe3−Se single crystals arises in the background of CDW fluctuations that contribute to significant anisotropy of the both normal state resistivity and the upper critical field in the superconducting state. The CDW fluctuations exist outside of the phase boundary of CDW order.

Methods

Single crystals of ZrTe3−Se were grown via iodine vapor transport method11. The as grown single crystals can be easily cleaved along b-axis and c-axis, which usually produces needle- or tape- like crystals along b-axis in the ab plane (shown in inset of Fig. 1c). Elemental analysis was performed by energy-dispersive X-ray spectroscopy (EDS) on an FEI Helios Nanolab 600i to determine the Se content. The Se content in as grown crystal is found to be less than the content in the starting material; measured EDS values are presented in figures. Powder X ray diffraction confirms phase purity however there were no appreciable changes of the lattice parameters (below 0.002 Å for a, b and below 0.005 Å for c lattice parameter), as expected for atomic substitution of up to about 3%. The crystal size becomes smaller when the Se content x increases, reducing from about 3 × 5 mm2 for x = (0–0.04) down to 1.5 × 1.5 mm2 in ab-plane for x = 0.1. Magnetization was measured in Quantum Design MPMS-XL-5. Resistance and magneto-resistance were measured by four probe method on Quantum Design PPMS-9 and PPMS-16. Raman spectra were measured on Horiba T64000, with excitation wavelength 647.4 nm and the power density was kept below 20 mW cm−2 in order to minimize the heating effects.

Additional Information

How to cite this article: Zhu, X. et al. Superconductivity and Charge Density Wave in ZrTe3−Se. Sci. Rep. 6, 26974; doi: 10.1038/srep26974 (2016).