Investigation of Size-Dependent Electrical Transport in Single Nanowire La$_{1-x}$A$_{x}$MnO$_{3}$ ($x$ = 0.3 & 0.5 for A = Ca and $x$ = 0.5 for A = Sr) Using Nanolithography-Based Device Fabrication

This work investigates the integration of single nanowire La <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{1-x}$</tex-math></inline-formula> A<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{x}$</tex-math></inline-formula>MnO <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> = 0.3 & 0.5 for A = Ca; <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> = 0.5 for A = Sr) nano-devices via advanced nanolithography techniques for transport measurements. The comparative study of resistivity in bulk and nanowire forms highlights a significant size-dependent enhancement in transport behavior. Notably, the resistivity data for La<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{1-x}$</tex-math></inline-formula> A<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{x}$</tex-math></inline-formula>MnO<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> = 0.3 & 0.5 for A = Ca; <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> = 0.5 for A = Sr) nanowires could not be fully explained by conventional models like Mott Variable Range Hopping (VRH) model, Efros-Shklovskii (ES) localization model, adiabatic small polaron hopping (ASPH) model etc. A hybrid model incorporating fluctuation-induced tunneling and disorder-induced localization more accurately captures the resistivity variation across temperature ranges. This refined approach successfully models transport behavior, particularly in the insulating regime, validating its applicability over previous models. The study establishes a robust methodology combining precise lithographic fabrication and improved theoretical modeling, paving the way for accurate transport characterization in complex oxide nanowires.