Final Draft Lab 3 (LL and NZ) Determination of Carrier Density through Hall Measurements and Determination of Transition Temperature (\(Tc\)) in a High-Tc Superconductor


Editor’s note: I have added clarifying wording /corrected confusing wording as shown below in bold

An electromagnet was used to provide a magnetic field to 3 different conducting samples: n type Geranium (n-Ge), p type Geranium (p-Ge), and silver (Ag). A calibrated Hall probe was used to obtain the current (\(\vec{I}_{mag}\)) to magnetic field (\(\vec{B}\)) calibration of the iron-core electromagnet. The Hall voltages (\(V_H\)) produced by each of the three samples were plotted against \(B\), and a linear line was produced, as expected. The slope (\(\frac{\Delta V_H}{\Delta B}\)) of each of the graphs were used to calculate the Hall coefficient for each sample, which we found to be \(-4.99\cdot 10^{-3}\pm -0.0998 \cdot 10^{-3} (\textrm{Vm}/ \textrm{AT})\), \((5.64 \pm 0.11) \cdot 10^{-3} (\textrm{Vm}/ \textrm{AT})\), \((-2.24 \pm -0.04) \cdot 10^{-10} (\textrm{Vm}/ \textrm{AT})\) respectively. These values have the same signs and similar orders of magnitude as the nominal values of \(-5.6\cdot 10^{-3}\frac{\textrm{Vm}}{\textrm{AT}}\) for n-Ge, \(6.6\cdot 10^{-3}\frac{\textrm{Vm}}{\textrm{AT}}\) for p-Ge, and \(-8.9\cdot 10^{-11}\frac{\textrm{Vm}}{\textrm{AT}}\) for silver given by the manufacturer, but do not agree within our measured uncertainty. The uncertainty in the manufacturer’s values is unknown. Using the Hall coefficients, we found of \((-1.25\pm 0.025) \cdot 10^{21} \textrm{m}^{-3}\) for n-Ge, \((1.11\pm 0.02) \cdot 10^{21} \textrm{m}^{-3}\) for p-Ge, \((-2.79 \pm 0.06)\cdot 10^{28} \textrm{m}^{-3}\) for silver, which are all in the same order of magnitude as the given absolute values of \(1.2 \cdot 10^{21} \textrm{m}^{-3}\), \(1.1 \cdot 10^{21} \textrm{m}^{-3}\), \(6.6 \cdot 10^{28} \textrm{m}^{-3}\), and confirm that the primary charge carriers are negatively-charged electrons for n-Ge and Ag but are positively charged ‘holes’ for p-Ge, as expected.

In a separate experiment, a current was applied to the superconductor Bi\(_2\)Sr\(_2\)Ca\(_2\)Cu\(_3\)O\(_{10}\) which was cooled in liquid nitrogen until it became superconducting, and was allowed to warm slowly. Its voltage and temperature were monitored in the warming process which we used to produce a graph of voltage against temperature. The graph showed a transition temperature of about \(118\textrm{K}\pm 2\textrm{K}\), similar to the nominal critical temperature of \(108\textrm{K}\).

Editor’s Note: later in your paper, you argue that your measured zero resistance critical temperature is actually \(108\textrm{K}\pm 2\textrm{K}\). If so, shouldn’t you quote a measured value of \(108\textrm{K}\pm 2\textrm{K}\) instead of a value of \(118\textrm{K}\pm 2\textrm{K}\) ?