Pronounced effects of additional resistance in Andreev reflection spectroscopy

We present a systematic investigation of the additional resistance $({R}_{E})$, which is an unavoidable consequence of pseudo-four-probe electrical measurements, on the point-contact Andreev reflection (PCAR) spectrum by both modeling and experiments. Instead of considering the total resistance between the two voltage leads across a point contact as a sum of a contact resistance $({R}_{C})$ and a fixed sample resistance $({R}_{S})$, it is essential to treat the total resistance as a sum of the Andreev resistance ${R}_{\text{AR}}$ and the additional resistance ${R}_{E}$, which are, respectively, the resistances affected and unaffected by the Andreev reflection process. We show a detailed formalism of taking ${R}_{E}$ into account in modeling and demonstrate that the PCAR spectrum can be drastically affected by the presence of ${R}_{E}$. Experimentally, we have found that not only ${R}_{E}$ cannot be readily measured or even estimated, it is in fact different for each contact, depending on the contact resistance and whether the contact is near the purely ballistic regime or the purely diffusive regime. A self-consistent process is necessary to analyze the entire PCAR spectrum, properly normalize the conductance, determine ${R}_{E}$, and other parameters including the spin polarization and the superconducting gap for each contact. We determine ${R}_{E}$ for various contacts on specimens with different resistivity and resolve the causes of ${R}_{E}$. For contacts close to the diffusive regime, there are two sources of ${R}_{E}$: a dominant contribution which is linearly proportional to the total resistance and a constant value from the sample resistance. We also address the effects of additional resistance when PCAR is administered in the ballistic limit and in the diffusive limit. With the proper treatment of the additional resistance, we demonstrate that PCAR can quantitatively extract essential information of spin polarization and superconducting gap.