arXiv subjects

Daniel Campbell

Publications and source records attributed to Daniel Campbell.

22 records · Page 2Linked to original sources

arXiv2020

Comparison between the non-crossing and the non-crossing on lines properties

In the recent paper [2], it was proved that the closure of the planar diffeomorphisms in the Sobolev norm consists of the functions which are non-crossing (NC), i.e., the functions which can be uniformly approximated by continuous one-to-one functions on the grids. A deep simplification of this property is to consider curves instead of grids, so considering functions which are non-crossing on lines (NCL). Since the NCL property is way easier to check, it would be extremely positive if they actually coincide, while it is only obvious that NC implies NCL. We show that in general NCL does not imply NC, but the implication becomes true with the additional assumption that $\det(Du)>0$ a.e., which is a very common assumption in nonlinear elasticity.

math.FA↗

arXiv2020

A sense preserving Sobolev homeomorphism with negative Jacobian almost everywhere

For every $1\leq p<\frac{3}{2}$ we construct a Sobolev homeomorphism $f\in W^{1,p}([-1,1]^4,[-1,1]^4)$ such that $f(x)=x$ for every $x\in \partial[-1,1]^4$ but $J_f<0$ a.e.

math.AP↗

arXiv2019

Unconventional Charge Density Wave Order in the Pnictide Superconductor Ba(Ni$_{1-x}$Co$_x$)$_2$As$_2$

Ba(Ni$_{1-x}$Co$_x$)$_2$As$_2$ is a structural homologue of the pnictide high temperature superconductor, Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$, in which the Fe atoms are replaced by Ni. Superconductivity is highly suppressed in this system, reaching a maximum $T_c$ = 2.3 K, compared to 24 K in its iron-based cousin, and the origin of this $T_c$ suppression is not known. Using x-ray scattering, we show that Ba(Ni$_{1-x}$Co$_x$)$_2$As$_2$ exhibits a unidirectional charge density wave (CDW) at its triclinic phase transition. The CDW is incommensurate, exhibits a sizable lattice distortion, and is accompanied by the appearance of $α$ Fermi surface pockets in photoemission [B. Zhou et al., Phys. Rev. B 83, 035110 (2011)], suggesting it forms by an unconventional mechanism. Co doping suppresses the CDW, paralleling the behavior of antiferromagnetism in iron-based superconductors. Our study demonstrates that pnictide superconductors can exhibit competing CDW order, which may be the origin of $T_c$ suppression in this system.

cond-mat.str-el↗

arXiv2018

Evolution of Structure and Superconductivity in Ba(Ni$_{1-x}$Co$_x$)$_2$As$_2$

The effects of Co-substitution on Ba(Ni$_{1-x}$Co$_x$)$_2$As$_2$ ($0\leq x\leq 0.251$) single crystals grown out of Pb flux are investigated via transport, magnetic, and thermodynamic measurements. BaNi$_2$As$_2$ exhibits a first order tetragonal to triclinic structural phase transition at $T_s=137 K$ upon cooling, and enters a superconducting phase below $T_c=0.7 K$. The structural phase transition is sensitive to cobalt content and is suppressed completely by $x\geq0.133$. The superconducting critical temperature, $T_c$, increases continuously with $x$, reaching a maximum of $T_c=2.3 K$ at the structural critical point $x=0.083$ and then decreases monotonically until superconductivity is no longer observable well into the tetragonal phase. In contrast to similar BaNi$_2$As$_2$ substitutional studies, which show an abrupt change in $T_c$ at the triclinic-tetragonal boundary that extends far into the tetragonal phase, Ba(Ni$_{1-x}$Co$_x$)$_2$As$_2$ exhibits a dome-like phase diagram centered around the first-order critical point. Together with an anomalously large heat capacity jump $ΔC_e/γT\sim 2.2$ at optimal doping, the smooth evolution of $T_c$ in the Ba(Ni$_{1-x}$Co$_x$)$_2$As$_2$ system suggests a mechanism for pairing enhancement other than phonon softening.

cond-mat.supr-con↗