Higher-order topological insulator in cubic semiconductor quantum wells.

The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order topological insulator state in quantum wells based on the most common semiconducting materials. By successively deriving the bulk and boundary Hamiltonians, we theoretically prove the existence of topological corner states due to cubic symmetry in quantum wells with double band inversion.

Hybridization of topological surface states with a flat band.

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.

Quantum spin Hall insulator with a large bandgap, Dirac fermions, and bilayer graphene analog.

The search for room temperature quantum spin Hall insulators (QSHIs) based on widely available materials and a controlled manufacturing process is one of the major challenges of today's topological physics. We propose a new class of semiconductor systems based on multilayer broken-gap quantum wells, in which the QSHI gap reaches 60 meV and remains insensitive to temperature. Depending on their layer thicknesses and geometry, these novel structures also host a graphene-like phase and a bilayer graphene analog.

Temperature-Induced Topological Phase Transition in HgTe Quantum Wells.

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.

Temperature-driven massless Kane fermions in HgCdTe crystals.

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.