Effects of self field and low magnetic fields on the normal-superconducting phase transition

Researchers have studied the normal-superconducting phase transition in the high-$T_c$ cuprates in a magnetic field (the vortex-glass or Bose-glass transition) and in zero field. Often, transport measurements in “zero field” are taken in the Earth’s ambient field or in the remnant field of a magnet. We show that fields as small as the Earth’s field will alter the shape of the current vs voltage curves and will result in inaccurate values for the critical temperature $T_c$ and the critical exponents $\nu$ and $z$, and can even destroy the phase transition. This indicates that without proper screening of the magnetic field it is impossible to determine the true zero-field critical parameters, making correct scaling and other data analysis impossible. We also show, theoretically and experimentally, that the self field generated by the current flowing in the sample has no effect on the current vs voltage isotherms.

Figure 1

(Color online) $I\text{−}V$ curves for a $2200\mathrm{\AA }$ thick film with bridge dimensions $8\mu \mathrm{m}\times 40\mu \mathrm{m}$. We can see that even a field as small as the Earth’s magnetic field $\left(50\mu \mathrm{T}\right)$ is enough to alter the shape of the $I\text{−}V$ curves, and twice the Earth’s field $\left(100\mu \mathrm{T}\right)$ can significantly change the shape of the isotherms. A field of $1\mathrm{mT}$ can create ohmic tails in isotherms which are nonlinear in zero field. The $I\text{−}V$ curves are independent of the direction of the magnetic field. The isotherms are separated by $0.2\mathrm{K}$.

Figure 2

Approximation of the $I\text{−}V$ bridge as a collection of $N=w∕d$ wires of radius $r=d∕2$. The strongest fields occur at the edges of the wires, denoted by $B$ in the figure.

Figure 3

(Color online) The self field generated at the edges of an $I\text{−}V$ bridge for three values of $N=w∕d$. We see that for $J\approx {10}^8\mathrm{A}∕{\mathrm{m}}^2$, $B\approx 10\mu \mathrm{T}$, which may be large enough to affect the sample. Our bridges have $N=40$.

Figure 4

(Color online) $I\text{−}V$ curves for a $2050\mathrm{\AA }$ thick YBCO film with bridge dimensions $8\mu \mathrm{m}\times 40\mu \mathrm{m}$. A bridge of gold of thickness $2000\mathrm{\AA }$ was patterned directly on top of the YBCO film. The gold and YBCO bridges were separated by a layer of photoresist $1.1\mu \mathrm{m}$ thick. The solid lines are isotherms with no current flowing in the gold bridge. The $I\text{−}V$ points measured with different currents in the gold bridge are represented as triangles: ▿ if the current in the gold bridge flows in the same direction as the current in the YBCO bridge, ▵ if it flows against the current in the YBCO bridge. The colors represent the amount of current in the gold bridge: black, ${10}^{-7}\mathrm{A}$; red, ${10}^{-6}\mathrm{A}$; green, ${10}^{-4}\mathrm{A}$; blue, ${10}^{-2}\mathrm{A}$. These colors make little difference, as the current in the gold bridge has no effect on the $I\text{−}V$ curves until we flow $10\mathrm{mA}$ of current in the gold bridge, which heats the YBCO bridge underneath. The isotherms are separated by $0.1\mathrm{K}$. The error in the points is the size of the points.