We present theoretical investigations of pressure and temperature driven phase transitions in HgTe quantum wells grown on CdTe buffer. Using the 8-band k·p Hamiltonian we calculate evolution of energy band structure at different quantum well width with hydrostatic pressure up to 20 kBar and temperature ranging up 300 K. In particular, we show that in addition to temperature, tuning of hydrostatic pressure allows to drive transitions between semimetal, band insulator and topological insulator phases. Our realistic band structure calculations reveal that the band inversion under hydrostatic pressure and temperature may be accompanied by non-local overlapping between conduction and valence bands. The pressure and temperature phase diagrams are presented.

It has recently been shown that electronic states in bulk gapless HgCdTe offer another realization of pseudo-relativistic three-dimensional particles in condensed matter systems. These single valley relativistic states, massless Kane fermions, cannot be described by any other relativistic particles. Furthermore, the HgCdTe band structure can be continuously tailored by modifying cadmium content or temperature. At critical concentration or temperature, the bandgap collapses as the system undergoes a semimetal-to-semiconductor topological phase transition between the inverted and normal alignments. Here, using far-infrared magneto-spectroscopy we explore the continuous evolution of band structure of bulk HgCdTe as temperature is tuned across the topological phase transition. We demonstrate that the rest mass of Kane fermions changes sign at critical temperature, whereas their velocity remains constant. The velocity universal value of (1.07±0.05) × 106 m s−1 remains valid in a broad range of temperatures and Cd concentrations, indicating a striking universality of the pseudo-relativistic description of the Kane fermions in HgCdTe.

We report on the study of the exchange enhancement of the g-factor in the two-dimensional (2D) electron gas in n-type narrow-gap semiconductor heterostructures. Our approach is based on the eight-band k⋅p Hamiltonian and takes into account the band nonparabolicity, the lattice deformation, the spin-orbit coupling and the Landau level broadening in the δ-correlated random potential model. Using the 'screened' Hartree-Fock approximation we demonstrate that the exchange g-factor enhancement not only shows maxima at odd values of Landau level filling factors but, due to the conduction band nonparabolicity, persists at even filling factor values as well. The magnitude of the exchange enhancement, the amplitude and the shape of the g-factor oscillations are determined by both the screening of the electron-electron interaction and the Landau level width. The 'enhanced' g-factor values calculated for the 2D electron gas in InAs/AlSb quantum well heterostructures are compared with our earlier experimental data and with those obtained by Mendez et al (1993 Phys. Rev. B 47 13937) in magnetic fields up to 30 T.

HgTe quantum wells possess remarkable physical properties as for instance the quantum spin Hall state and the “single-valley” analog of graphene, depending on their layer thicknesses and barrier composition. However, double HgTe quantum wells yet contain more fascinating and still unrevealed features. Here we report on the study of the quantum phase transitions in tunnel-coupled HgTe layers separated by CdTe barrier. We demonstrate that this system has a 3/2 pseudo spin degree of freedom, which features a number of particular properties associated with the spin-dependent coupling between HgTe layers. We discover a specific metal phase arising in a wide range of HgTe and CdTe layer thicknesses, in which a gapless bulk and a pair of helical edge states coexist. This phase holds some properties of bilayer graphene such as an unconventional quantum Hall effect and an electrically-tunable band gap. In this “bilayer graphene” phase, electric field opens the band gap and drives the system into the quantum spin Hall state. Furthermore, we discover a new type of quantum phase transition arising from a mutual inversion between second electron- and hole-like subbands. This work paves the way towards novel materials based on multi-layered topological insulators.

We report a direct observation of temperature-induced topological phase transition between the trivial and topological insulator states in an HgTe quantum well. By using a gated Hall bar device, we measure and represent Landau levels in fan charts at different temperatures, and we follow the temperature evolution of a peculiar pair of "zero-mode" Landau levels, which split from the edge of electronlike and holelike subbands. Their crossing at a critical magnetic field B_{c} is a characteristic of inverted band structure in the quantum well. By measuring the temperature dependence of B_{c}, we directly extract the critical temperature T_{c} at which the bulk band gap vanishes and the topological phase transition occurs. Above this critical temperature, the opening of a trivial gap is clearly observed.

We propose a minimal effective two-dimensional Hamiltonian for HgTe/CdHgTe quantum wells (QWs) describing the side maxima of the first valence subband. By using the Hamiltonian, we explore the picture of helical edge states in tensile and compressively strained HgTe QWs. We show that both dispersion and probability density of the edge states can differ significantly from those predicted by the Bernevig-Hughes-Zhang (BHZ) model. Our results pave the way towards further theoretical investigations of HgTe-based quantum spin Hall insulators with direct and indirect band gaps beyond the BHZ model.The inverted HgTe/CdHgTe quantum well (QW) is the first two-dimensional (2D) system, in which a quantum spin Hall insulator (QSHI) state was theoretically predicted 1 and then experimentally observed 2-4 . The origin of the topologically nontrivial QSHI state is caused by inverted band structure of bulk HgTe, which leads to a peculiar confinement effect in HgTe/CdHgTe QWs. Specifically, in narrow QWs, the first electron-like subband E 1 lies above the first hole-like level H 1, and the system is characterized by normal band ordering with trivial insulator state. As the QW width d is varied (see Fig. 1a), the E 1 and H 1 subbands are crossed 5 , and the band structure mimics a linear dispersion of massless Dirac fermions 6 . When d exceeds the critical width d c , an inversion of the E 1 and H 1 levels drives the system in QSHI state with a pair of gapless helical edge states topologically protected due to time-reversal symmetry 1 .So far, theoretical description of the phase transition between trivial and QSHI states in HgTe QWs has been based on the Bernevig-Hughes-Zhang (BHZ) 2D model 1 . The latter is derived from the Kane Hamiltonian 7 , which includes Γ 6 , Γ 8 , Γ 7 bulk bands with the confinement effect. Within the representation defined by the basis states |E 1,+ , |H 1,+ , |E 1,-, |H 1,-, the effective 2D Hamiltonian has the form:

We propose a new III–V semiconductor system hosting a large-gap quantum spin Hall insulator and unconventional metal states.

Using the 'screened' Hartree-Fock approximation based on the eight-band k·p Hamiltonian, we have extended our previous work (Krishtopenko et al 2011 J. Phys.: Condens. Matter 23 385601) on exchange enhancement of the g-factor in narrow-gap quantum well heterostructures by calculating the exchange renormalization of quasiparticle energies, the density of states at the Fermi level and the quasiparticle g-factor for different Landau levels overlapping. We demonstrate that exchange interaction yields more pronounced Zeeman splitting of the density of states at the Fermi level and leads to the appearance of peak-shaped features in the dependence of the Landau level energies on the magnetic field at integer filling factors. We also find that the quasiparticle g-factor does not reach the maximum value at odd filling factors in the presence of large overlapping of spin-split Landau levels. We advance an argument that the behavior of the quasiparticle g-factor in weak magnetic fields is defined by a random potential of impurities in narrow-gap heterostructures.