We report here on the successful growth by molecular beam epitaxy of high crystalline quality ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}:\mathrm{Bi}/{\mathrm{Pb}}_{1-y}{\mathrm{Eu}}_y\mathrm{Se}$ quantum wells (QWs) with $x=0.25$ and $y=0.1$, and on their magnetotransport characterization as a function of the QW thickness between 10 and 50 nm, temperatures down to 300 mK, perpendicular and tilted magnetic fields up to 36 T. The character of weak antilocalization magnetoresistance and universal conductance fluctuations points to a notably long phase-coherence length. It is argued that a relatively large magnitude of the dielectric constant of IV-VI compounds suppresses the decoherence by electron-electron scattering. The observation of Shubnikov–de Haas oscillations and the quantum Hall effect, together with multiband $k·p$ modeling, have enabled us to assess valley degeneracies, the magnitude of strain, subbands effective masses, and the topological phase diagram as a function of the QW thickness. Our results demonstrate that further progress in controlling Sn content, carrier densities, and magnetism in ${\mathrm{Pb}}_{1-x}{\mathrm{Sn}}_x\mathrm{Se}/{\mathrm{Pb}}_{1-y}{\mathrm{Eu}}_y\mathrm{Se}$ QWs will allow for the exploration of the topologically protected quantized edge transport even in the absence of an external magnetic field.

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• Integer quantum Hall effect
• Quantum transport
• Weak antilocalization
• Narrow band gap systems
• Quantum wells
• Topological insulators
• k dot p method