We report on observation of an unconventional structure of the quantum Hall effect (QHE) in a p-type HgTe/CdxHg1−xTe double quantum well (DQW) consisting of two HgTe layers of critical width. The observed QHE is a reentrant function of magnetic field between two i = 2 states (plateaus at ρxy = h/ie 2) separated by an intermediate i = 1 state, which looks like some anomalous peak on the extra-long i = 2 plateau when weakly expressed. The anomalous peak apparently separates two different regimes: a traditional QHE at relatively weak fields for a small density of mobile holes ps and a high-field QH structure with a 2 − 1 plateau-plateau transition corresponding to much larger ps. We show that only a part of holes, residing in an additional light hole subband in the DQW, participate in QHE at weak fields while the rest of holes is excluded into the reservoir formed in the lateral maximum of the valence subband. All the holes come into play at high fields due to a peculiar behavior of the zero-mode levels.

We investigated quantum Hall states in an inverted HgTe quantum well (QW) close to the critical thickness using transconductance fluctuation (TF) measurements. In the conduction band, several integer quantum Hall states were observed, corresponding to filling factors ν=1,2,3,4. For magnetic fields above 2 T, quantum Hall states ν=0 were observed in the normal gap. These observations agreed well with the previous studies of quantum Hall states on GaAs QWs and graphene. Interestingly, TFs corresponding to anomalous positive filling factor ν were clearly observed in the valence band. We attribute the emergence of those TFs to the localization and charging of the heavy holes located in the side maxima of the valence band.

We report on the far-infrared magnetospectroscopy of HgTe quantum wells with inverted band ordering at different electron concentrations. We particularly focus on optical transitions from zero-mode Landau levels, which split from the edges of electron-like and hole-like bands. We observe a pronounced dependence of the transition energies on the electron concentration varied by persistent photoconductivity effect. This is striking evidence that in addition to the already well-documented crystalline and interface asymmetries, electron-electron interactions also have a significant impact on the usual behavior of the optical transitions from zero mode Landau levels.

By using the self-consistent Born approximation, we investigate disorder effect induced by the short-range impurities on the band gap in two-dimensional Dirac systems with the higher order terms in momentum. Starting from the Bernevig-Hughes-Zhang (BHZ) model, we calculate the density of states as a function of the disorder strength. We show that due to quadratic corrections to the Dirac Hamiltonian, the band gap is always affected by the disorder even if the system is gapless in the clean limit. Finally, we explore the disorder effects by using an advanced effective Hamiltonian describing the side maxima of the valence subband in HgTe quantum wells. We show that the band gap and disorder-induced topological phase transition in the real structures may differ significantly from those predicted within the BHZ model.

We address the problem of hybridization between topological surface states and a non-topological flat bulk band. Our model, being a mixture of three-dimensional Bernevig–Hughes–Zhang and two-dimensional pseudospin-1 Hamiltonian, allows explicit treatment of the topological surface state evolution by continuously changing the hybridization between the inverted bands and an additional ‘parasitic’ flat band in the bulk. We show that the hybridization with a flat band lying below the edge of the conduction band converts the initial Dirac-like surface states into a branch below and one above the flat band. Our results univocally demonstrate that the upper branch of the topological surface states is formed by Dyakonov–Khaetskii surface states, known for HgTe since the 1980s. Additionally we explore an evolution of the surface states and the arising of Fermi arcs in Dirac semimetals when the flat band crosses the conduction band.

HgTe quantum wells (QWs) are two-dimensional semiconductor systems that change their properties at the critical thickness dc, corresponding to the band inversion and topological phase transition. The motivation of this work was to study magnetotransport properties of HgTe QWs with thickness approaching dc, and examine them as potential candidates for quantum Hall effect (QHE) resistance standards. We show that in the case of d > dc (inverted QWs), the quantization is influenced by coexistence of topological helical edge states and QHE chiral states. However, at d ≈ dc, where QW states exhibit a graphene-like band structure, an accurate Hall resistance quantization in low magnetic fields (B ≤ 1.4 T) and at relatively high temperatures (T ≥ 1.3 K) may be achieved. We observe wider and more robust quantized QHE plateaus for holes, which suggests—in accordance with the “charge reservoir” model—a pinning of the Fermi level in the valence band region. Our analysis exhibits advantages and drawbacks of HgTe QWs for quantum metrology applications, as compared to graphene and GaAs counterparts.