arXiv subjects

H. -S. Lee

Publications and source records attributed to H. -S. Lee.

6 recordsLinked to original sources

arXiv2023

Global gradient estimates for the mixed local and nonlocal problems with measurable nonlinearities

A non-homogeneous mixed local and nonlocal problem in divergence form is investigated for the validity of the global Calderón-Zygmund estimate for the weak solution to the Dirichlet problem of a nonlinear elliptic equation. We establish an optimal Calderón-Zygmund theory by finding not only a minimal regularity requirement on the mixed local and nonlocal operators but also a lower level of geometric assumption on the boundary of the domain for the global gradient estimate. More precisely, assuming that the nonlinearity of the local operator, whose prototype is the classical $(-Δ_p)^1$-Laplace operator with $1<p<\infty$, is measurable in one variable and has a small BMO assumption for the other variables, while the singular kernel associated with the nonlocal $(-Δ_q)^s$-Laplace operator with $0<s<1<q<\infty$ is merely measurable, and that the boundary of the domain is sufficiently flat in Reifenberg sense, we prove that the gradient of the solution is as integrable as that of the associated non-homogeneous term in the divergence form.

math.AP↗

arXiv2019

Strain-Driven Disproportionation at a Correlated Oxide Metal-Insulator Transition

Metal-to-insulator phase transitions in complex oxide thin films are exciting phenomena which may be useful for device applications, but in many cases the physical mechanism responsible for the transition is not fully understood. Here we demonstrate that epitaxial strain generates local disproportionation of the NiO6 octahedra, driven through changes in the oxygen stoichiometry, and that this directly modifies the metal-to-insulator phase transition in epitaxial (001) NdNiO3 thin films. Theoretically, we predict that the Ni-O-Ni bond angle decreases, while octahedral tilt and local disproportionation of the NiO6 octahedra increases resulting in a small band gap in otherwise metallic system. This is driven by an increase in oxygen vacancy concentration in the rare-earth nickelates with increasing in-plane biaxial tensile strain. Experimentally, we find an increase in pseudocubic unit-cell volume and resistivity with increasing biaxial tensile strain, corroborating our theoretical predictions. With electron energy loss spectroscopy and x-ray absorption, we find a reduction of the Ni valence with increasing tensile strain. These results indicate that epitaxial strain modifies the oxygen stoichiometry of rare-earth perovskite thin films and through this mechanism affect the metal-to-insulator phase transition in these compounds.

cond-mat.mtrl-sci↗

arXiv2003

Two-band Effects in the Angular Dependence of Hc2 of MgB2 Single Crystals

The angular dependence of the upper critical field Hc2 of MgB2 single crystals is studied at various temperatures by means of specific heat and transport measurements in magnetic fields up to 17 T. Clear deviations from Ginzburg-Landau behavior are observed at all temperatures and are explained by two-band effects. The angular- and temperature dependence of the deviations are in qualitative agreement with theoretical predictions based on band-structure calculations. Quantitative agreement is obtained with an interband coupling slightly stronger than the calculated, enabling band-structure anisotropies and interband coupling strength to be experimentally estimated. This provides a new pathway to the study of disorder and doping effects in MgB2.

cond-mat.supr-con↗

arXiv2003

Surface Contribution to the Superconducting Properties of MgB2 Single Crystals

We demonstrate direct evidence of possible surface superconductivity on small, well-shaped MgB2 single crystals. Transport measurements in the range H < 1.6 Hc2^c, where Hc2^c is the bulk upper critical field for the c axis, show non-Ohmic and strongly angular dependent resistivity. Studies of the alignment of H with selected crystal surfaces, transport and specific heat measurements on the same crystal, and a physical sculpturing of the crystal surfaces using a focused ion beam all support the conclusion. Similar, albeit less pronounced results are obtained for fields in the basal plane.

cond-mat.supr-con↗

arXiv2002

Anisotropy of the Upper Critical Field and Critical Current in Single Crystal MgB$_2$

We report on specific heat, high magnetic field transport and $ac-$susceptibility measurements on magnesium diboride single crystals. The upper critical field $H_{c2}$ for magnetic fields perpendicular and parallel to the Mg and B planes is presented for the first time in the entire temperature range. A very different temperature dependence has been observed in the two directions which yields to a temperature dependent anisotropy with $Γ\sim$ 5 at low temperatures and about 2 near $T_c$. A peak effect is observed in susceptibility measurements for $H \sim $2 T parallel to the $c-$axis and the critical current density presnts a sharp maximum for $H$ parallel to the ab-plane.

cond-mat.supr-con↗

arXiv2002

Superconducting Transition and Phase Diagram of Single Crystal MgB2

The superconducting phase diagram of MgB2 was determined from magnetization, magneto-transport and the first single-crystal specific heat measurements. A zero-temperature in-plane coherence length of 8 nm is determined. The superconducting anisotropy increases from a value around 2 near Tc to above 4.5 at 22 K. For H||c a pronounced peak effect in the critical current occurs at the upper critical field. Evidence for a surface superconducting state is presented for H||c which might account for the wide spread in reported values of the anisotropy.

cond-mat.supr-con↗