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In multivalley systems, the valley pseudospin offers rich physics going from encoding of information by its polarization (valleytronics), to exploring novel phases of matter when its degeneracy is changed. Here, by strain engineering, we reveal fully valley-polarized quantum Hall (QH) phases in the Pb1-xSnxSe Dirac system. Remarkably, when the valley energy splitting exceeds the fundamental band gap, we observe a bipolar QH phase, heralded by the coexistence of hole and electron chiral edge states at distinct valleys in the same quantum well. This suggests that spatially overlaid counter-propagating chiral edge states emerging at different valleys do not interfere with each other.

Weyl and Dirac relativistic fermions are ubiquitous in topological matter. Their relativistic character enables high energy physics phenomena like the chiral anomaly to occur in solid state, which allows to experimentally probe and explore fundamental relativistic theories. Here we show that on smooth interfaces between a trivial and a topological material, massless Weyl and massive Dirac fermions intrinsically coexist. The emergence of the latter, known as Volkov-Pankratov states, is directly revealed by magneto-optical spectroscopy, evidencing that their energy spectrum is perfectly controlled by the smoothness of topological interface. Simultaneously, we reveal the optical absorption of the zero-energy chiral Weyl state, whose wavefunction is drastically transformed when the topological interface is smooth. Artificial engineering of the topology profile thus provides a novel textbook system to explore the rich relativistic energy spectra in condensed matter heterostructures., Comment: 21 pages 10 figures