This book presents a comprehensive study of zero-dimensional (0D) quantum systems — including Quantum Dots (QDs), magneto-quantum MOSFETs, quantum well field-effect transistors (QWFETs), magneto size-quantized systems, magneto quantum well superlattices (SLs), magneto negative-ion potential islands (NIPIs), and quantum dot superlattices (QDSLs) — which are central to low-dimensional electronics, nanotechnology, and quantum device engineering. It investigates key properties such as Magneto Thermoelectric Power (MTP) in nanoscale thermoelectric conversion, Einstein's Photoemission (EP) in semiconductor nanostructures, Activity Coefficients (AC) in confined carrier systems, and carrier contributions to elastic constants (CEC) in advanced quantum materials.The text covers a wide range of semiconductors and nanostructured compounds, including CdGeAs2, Cd3As2, III-V, II-VI materials, GaP, Ge, Te, PtSb2, HgTe, Pb(1-x)GexTe, GaSb, stressed n-InSb, Bi, IV-VI and II-V systems, Bi2Te3, Sb, Zn3P2, three-dimensional quantized NIPIs, strained superlattices with graded interfaces, and effective-mass engineered HgTe/CdTe SLs. We have investigated the quantum signatures for the said systems with respect to Quantum Capacitance, ID-VD equation, the relaxation time and the Raghi-Leduc coefficient respectively. We have derived the complex distribution function for HD materials which generate three new concepts We have also suggested experimental methods for the determination of Einstein's relation, the Elastic constants, and the Debye screening length together with the fact that the book covers 24 different applications in the field of quantized materials.This book contains circa 250 multi-dimensional open research problems which form the integral part of the text and are useful for both PhD aspirants and researchers. It is written for post graduate students of various departments of different academic organizations, engineers and professionals in the fields of solid state electronics, materials science, solid state sciences, nano-science, nanotechnology and nano materials in general. This book will be invaluable to all those researching in academic and industrial laboratories in the said cases worldwide.