We report scanning tunneling spectroscopy imaging of the vortex lattice in single crystalline MgB2. By tunneling parallel to the c axis, a single superconducting gap (Delta=2.2 meV) associated with the pi band is observed. The vortices in the pi band have a large core size compared to estimates based on H(c2) and show an absence of localized states in the core. Furthermore, superconductivity between the vortices is rapidly suppressed by an applied field. These results suggest that superconductivity in the pi band is, at least partially, induced by the intrinsically superconducting sigma band.
The anisotropy gamma of the superconducting state of high quality single crystals of MgB2 was determined, using torque magnetometry with two different methods. The anisotropy of the upper critical field was found to be temperature dependent, decreasing from gamma approximately 6 at 15 K to 2.8 at 35 K. Reversible torque data near T(c) reveal a field dependent anisotropy, increasing nearly linearly from gamma approximately equal to 2 in zero field to 3.7 in 10 kOe. The unusual temperature dependence is a true bulk property and can be explained by nonlocal effects of anisotropic pairing and/or the k--> dependence of the effective mass tensor.
The ab-plane thermal conductivity κ of single-crystalline hexagonal MgB2 has been measured as a function of magnetic field H with orientations both parallel and perpendicular to the c-axis and at temperatures between 0.5 and 300 K. In the mixed state, κ(H) measured at constant temperatures reveals features that are not typical for common type-II superconductors. The observed behavior may be associated with the field-induced reduction of two superconducting energy gaps, significantly different in magnitude. A nonlinear temperature dependence of the electronic thermal conductivity is observed in the field-induced normal state at low temperatures. This behavior is at variance with the law of Wiedemann and Franz, and suggests an unexpected instability of the electronic subsystem in the normal state at T ≈ 1 K.
The growth of carbon-substituted magnesium diboride Mg͑B 1−x C x ͒ 2 single crystals with 0 ഛ x ഛ 0.15 is reported, and the structural, transport, and magnetization data are presented. The superconducting transition temperature decreases monotonically with increasing carbon content in the full investigated range of substitution. By adjusting the nominal composition, T c of substituted crystals can be tuned in a wide temperature range between 10 and 39 K. Simultaneous introduction of disorder by carbon substitution and significant increase of the upper critical field H c2 is observed. Comparing with the nonsubstituted compound, H c2 at 15 K for x = 0.05 is enhanced by more than a factor of 2 for H oriented both perpendicular and parallel to the ab plane. This enhancement is accompanied by a reduction of the H c2 -anisotropy coefficient ␥ from 4.5 ͑for the nonsubstituted compound͒ to 3.4 and 2.8 for the crystals with x = 0.05 and 0.095, respectively. At temperatures below 10 K, the single crystal with larger carbon content shows H c2 ͑defined at zero resistance͒ higher than 7 and 24 T for H oriented perpendicular and parallel to the ab plane, respectively. Observed increase of H c2 cannot be explained by the change in the coherence length due to the disorder-induced decrease of the mean free path only.
We present the results of the first directional point-contact spectroscopy experiments in highquality MgB2 single crystals. Due to the directionality of the current injection into the samples, the application of a magnetic field allowed us to separate the contributions of the σ and π bands to the total conductance of our point contacts. By using this technique, we were able to obtain the temperature dependency of each gap independent of the other. The consequent, strong reduction of the error on the value of the gap amplitude as function of temperature allows a stricter test of the predictions of the two-band model for MgB2.PACS numbers: 74.50.+r, 74.80.Fp, 74.70.Ad During the last year, the consensus has been growing within the scientific community on the fact that most of the features of MgB 2 discovered so far can be properly explained by admitting that two band systems are present in this new superconductor: quasi-2D σ bands arising from hybrid sp 2 orbitals in the boron planes, and 3D π bands that stem from the out-of-plane p z orbitals [1,2]. The unusual consequence of this band structure is that two different energy gaps can be observed in clean limit [2,3,4]: ∆ σ (the larger) and ∆ π (the smaller). Both gaps are expected to close at the same temperature T c because of an inter-band pair-scattering mechanism [5] but, while ∆ σ (T ) should approximately follow a BCSlike curve, a marked reduction of ∆ π (T ) with respect to a BCS-like behavior is expected at T > ∼ 20 K [3,4]. So far, one of the most convincing experimental supports of this model has been the observation of two gaps by tunneling [6] and point-contact spectroscopy [7] in polycrystal samples and films. However, a direct and accurate test of the predictions of the two-band model has been so far impossible due to the lack of high-quality single crystals large enough to be used for directioncontrolled point-contact and tunnel spectroscopy.In this Letter, we present the results of the first directional point-contact measurements in large single crystals of MgB 2 . We injected current along the ab plane or along the c axis, and applied a magnetic field either parallel or perpendicular to the ab planes. This allowed us to separate the partial contributions of the σ and π bands to the total conductance, and to fit them obtaining the temperature dependency of each gap with great accuracy. We will show that all the results of this technique confirm very well the predictions of the two-band model.The high-quality MgB 2 single crystals used for our point-contact experiments were produced at ETH (Zürich) by starting from a mixture of Mg and B. This mixture was put into a BN container and the crystals were grown at a pressure of 30-35 kbar in a cubic anvil device. The thermal process includes a one-hour heating up to 1700-1800 • C, a plateau of 1-3 hours, and a final cooling lasting 1-2 hours. MgB 2 plate-like crystals up to 200 µg in weight and 1.5 × 0.9 × 0.2 mm 3 in size can be obtained by using this technique, even though the crystals used in our me...
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