The f-electrons of Ce- and Yb-based compounds hybridize with conduction electrons, resulting in many interesting electronic properties such as heavy fermions, topological Kondo insulators, and superconductivity in the strongly correlated systems. This dissertation covers the discovery of new compounds in two families of compounds, R3T4Ge13 (3-4-13) and RT3M7 (1-3-7), which were poorly explored until recently. The objective of the work is to (i) synthesize high quality single crystals with the interest of understanding diverse electronic properties such as superconductivity, magnetism, low-carrier density in Kondo systems, and heavy fermions and (ii) characterize and explore quantum phenomena of these compounds using magnetization, specific heat, electrical resistivity, Hall effect, neutron, and optical measurements.

These 3-4-13 germanides compounds show very diverse electronic properties such as superconductivity, magnetism, intermediate valence, and Kondo behavior. All seven Lu3T4Ge13-x (T = Co, Rh, Ir, Os) and Y3T4Ge13-x (T = Ir, Rh, Os) compounds are bulk superconductors with semimetallic normal state Other non-superconducting compounds change their electronic properties upon chemical substitution in the magnetic or transition metal site. Intermediate valence behavior upon Co doping into the Rh site in Yb3(Rh1-xCox)4Ge13 is persistent, while Ir doping into the Rh site in Yb3(Rh1-xIrx)4Ge13 drives the system into a heavy fermion state. Magnetic order T*mag = 0.9 K is observed for Yb3Ir4Ge13 and the quantum critical point is tuned around xc = 0.5 in Yb3(Rh1-xIrx)4Ge13. Furthermore, the low-carrier density nature is revealed in both magnetic Yb3Ir4Ge13 and non-magnetic reference Lu3Ir4Ge13 from electrical transport and optical measurements.

In the 1-3-7 class of compounds, we discovered the first time YbRh3Si7, YbIr3Ge7, and CeIr3Ge7 compounds, including the first two Yb heavy fermion compounds in the series. YbRh3Si7 is the first Kondo system in this ScRh3Si7 structure type, which shows antiferromagnetic ordering below TN = 7.5 K with spins in the ab plane, and the metamagnetic phase transitions along the hard c axis. YbIr3Ge7 shows ferromagnetic ordering along the crystal electric field (CEF) hard direction with TC = 2.4 K. By contrast, CeIr3Ge7 does not show Kondo behavior, but it has strong CEF anisotropy with a surprisingly low TN = 0.63 K.