  The quantum Hall effect (QHE) is traditionally considered a purely
two-dimensional (2D) phenomenon. Recently, a three-dimensional (3D) version of
the QHE has been reported in the Dirac semimetal ZrTe5. It was proposed to
arise from a magnetic-field-driven Fermi surface instability, transforming the
original 3D electron system into a stack of 2D sheets. Here, we report
thermodynamic, thermoelectric and charge transport measurements on ZrTe5 in the
quantum Hall regime. The measured thermodynamic properties: magnetization and
ultrasound propagation, show no signatures of a Fermi surface instability,
consistent with in-field single crystal X-ray diffraction. Instead, a direct
comparison of the experimental data with linear response calculations based on
an effective 3D Dirac Hamiltonian suggests that the quasi-quantization of the
observed Hall response is an intrinsic property of the 3D electronic structure.
Our findings render the Hall effect in ZrTe5 a truly 3D counterpart of the QHE
in 2D systems.
