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

Abstract

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\