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We report a significant enhancement of the upper critical field H c2 of different MgB 2 samples alloyed with nonmagnetic impurities. By studying films and bulk polycrystals with different resistivities ρ, we show a clear trend of H c2 increase as ρ increases. One particular high resistivity film had zero-temperature H c2 (0) well above the H c2 values of competing non-cuprate superconductors such as Nb 3 Sn and Nb-Ti. Our high-field transport measurements give record values H c2 ⊥ (0) ≈ 34T and H c2 || (0) ≈ 49 T for high resistivity films and H c2 (0) ≈ 29 T for untextured bulk polycrystals. The highest H c2 film also exhibits a significant upward curvature of H c2 (T), and temperature dependence of the anisotropy parameter γ(T) = H c2 || / H c2⊥ opposite to that of single crystals: γ(T) decreases as the temperature decreases, from γ(T c ) ≈ 2 to γ(0) ≈ 1.5. This remarkable H c2 enhancement and its anomalous temperature dependence are a consequence of the two-gap superconductivity in MgB 2 , which offers special opportunities for further H c2 increase by tuning of the impurity scattering by selective alloying on Mg and B sites. Our experimental results can be explained by a theory of two-gap superconductivity in the dirty limit. The very high values of H c2 (T) observed suggest that MgB 2 can be made into a versatile, competitive high-field superconductor.

We report quantum oscillations in underdoped YBa2Cu3O6.56 over a significantly large range in magnetic field extending from ≈ 24 to 101 T, enabling three well-spaced low frequencies at ≈ 440 T, 532 T, and 620 T to be clearly resolved. We show that a small nodal bilayer coupling that splits a nodal pocket into bonding and antibonding orbits yields a sequence of frequencies, F0 − ∆F , F0 and F0 + ∆F and accompanying beat pattern similar to that observed experimentally, on invoking magnetic breakdown tunneling at the nodes. The relative amplitudes of the multiple frequencies observed experimentally in quantum oscillation measurements are shown to be reproduced using a value of nodal bilayer gap quantitatively consistent with that measured in photoemission experiments in the underdoped regime. PACS numbers: 71.45.Lr, 71.20.Ps, 71.18.+y Discerning the electronic structure of underdoped YBa 2 Cu 3 O 6+x in the normal state is a crucial step to understanding the origin of unconventional superconductivity in these materials [1]. While quantum oscillation measurements in underdoped YBa 2 Cu 3 O 6+x have revealed multiple frequency components [2][3][4], it has been challenging to distinguish an electronic structure from the numerous possibilities that can uniquely explain the observed frequencies. Recent measurements of the chemical potential oscillations [5] in underdoped YBa 2 Cu 3 O 6+x in strong magnetic fields have helped narrow down these possibilities by determining the multiple frequencies to arise from a single carrier pocket − likely located at the nodal region of the Brillouin zone [6] and supported by other experiments sensitive to the density-of-states at the Fermi energy [7][8][9]. An intriguing question therefore arises as to how such a single pocket can give rise to the multiple observed frequencies.In this paper, we show measurements of quantum oscillations in YBa 2 Cu 3 O 6+x made using a contactless resistivity technique over an unprecedented range in magnetic field extending from ≈ 24 T to 101 T (see Fig. 1) [10]. The large window in inverse magnetic field (∆( 1 B ) ≈ 0.032 T −1 ) affords clear resolution of three well-separated low frequencies, namely ≈ 440 ± 10 T, 532 ± 2 T and 620 ± 10 T − the experimental limit for distinguishing closely-spaced frequencies being 1/∆( 1 B ) ≈ 32 T. We use the unique form of the multiple frequency quantum oscillation spectrum, in which the central frequency at 532 T is equidistantly flanked by two frequencies 532 − 90 T and 532 + 90 T, as a clue to infer a possible electronic structure that describes the system. We show that an electronic structure comprising a single bilayer-split nodal pocket combined with magnetic breakdown tunnelling would give rise to such a frequency spectrum, and potentially provide an explanation for the angular dependence of the observed frequencies [4,11,12]. Similar instances of multiple frequencies arising from magnetic breakdown, are for instance found in heavy fermion and ferromagnetic families of materials [13,14]. A prerequisite for...

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