We present a theory of the electron structure and the Zeeman effect for the helical edge states emerging in two-dimensional topological insulators based on HgTe/HgCdTe quantum wells with strong natural interface inversion asymmetry. The interface inversion asymmetry, reflecting the real atomistic structure of the quantum well, drastically modifies both bulk and edge states. For the inplane magnetic field, this asymmetry leads to a strong anisotropy of the edge-state effective g-factor which becomes dependent on the edge orientation. The interface inversion asymmetry also couples the counter propagating edge states in the out-of-plane magnetic field leading to the opening of the gap in the edge-state spectrum by arbitrary small fields.

We describe the fine structure of Dirac states in HgTe/CdHgTe quantum wells of critical and close-to-critical thickness and demonstrate the formation of an anticrossing gap between the tips of the Dirac cones driven by interface inversion asymmetry. By combining symmetry analysis, atomistic calculations, and k•p theory with interface terms, we obtain a quantitative description of the energy spectrum and extract the interface mixing coefficient. The zero-magnetic-field splitting of Dirac cones can be experimentally revealed in studying magnetotransport phenomena, cyclotron resonance, Raman scattering, or THz radiation absorption.

Atomically thin semiconductors provide an ideal testbed to investigate the physics of Coulomb-bound many-body states. We shed light on the intricate structure of such complexes by studying the magnetic-field-induced splitting of biexcitons in monolayer WS_{2} using polarization-resolved photoluminescence spectroscopy in out-of-plane magnetic fields up to 30 T. The observed g factor of the biexciton amounts to about -3.9, closely matching the g factor of the neutral exciton. The biexciton emission shows an inverted circular field-induced polarization upon linearly polarized excitation; i.e., it exhibits preferential emission from the high-energy peak in a magnetic field. This phenomenon is explained by taking into account the hybrid configuration of the biexciton constituents in momentum space and their respective energetic behavior in magnetic fields. Our findings reveal the critical role of dark excitons in the composition of this many-body state.

We report on the observation of a circular photogalvanic current excited by terahertz laser radiation in helical edge channels of two-dimensional (2D) HgTe topological insulators (TIs). The direction of the photocurrent reverses by switching the radiation polarization from a right-handed to a left-handed one and, for fixed photon helicity, is opposite for the opposite edges. The photocurrent is detected in a wide range of gate voltages. With decreasing the Fermi level below the conduction band bottom, the current emerges, reaches a maximum, decreases, changes its sign close to the charge neutrality point (CNP), and again rises. Conductance measured over a ≈3 μm distance at CNP approaches 2e 2 /h, the value characteristic for ballistic transport in 2D TIs. The data reveal that the photocurrent is caused by photoionization of helical edge electrons to the conduction band. We discuss the microscopic model of this phenomenon and compare calculations with experimental data. DOI: 10.1103/PhysRevB.95.201103 The quantum spin Hall (QSH) effect occurs in 2D TIs and rests on the existence of conducting helical edge states while the bulk is insulating [1][2][3][4]. In contrast to the quantum Hall effect, the formation of these edge states requires no magnetic field: they stem from the band inversion caused by strong spin-orbit interaction and are topologically protected by time reversal symmetry. Given that the spin-up and spin-down electrons propagate along an edge in opposite directions, i.e., the spin projection is locked to the k vector, the edge channels are helical in nature. The first experimental evidence for the QSH effect was obtained in HgTe quantum wells (QWs) [5] by observing a resistance plateau around h/2e 2 in the longitudinal resistance of a mesoscopic Hall bar. Here h is Planck's constant and e is the electron charge. This observation was further confirmed by nonlocal experiments in the ballistic [6] and diffusive [7] transport regime. Conducting edge channels were later probed by scanning SQUID microscopy [8], scanning gate microscopy [9], microwave impedance microscopy [10], and by analyzing supercurrents [11]. The spin polarization of the edge states was investigated so far by electrical means only: by detecting the spin to charge conversion in devices utilizing the inverse spin Hall effect [12] or with ferromagnetic contacts [13].Here we use circularly polarized terahertz radiation to excite selectively spin-up and spin-down electrons circling clockwise and counterclockwise around a sample. We show that the excitation causes an imbalance in the electron distribution between positive and negative wave vectors. This is probed as the associated photogalvanic [14,15] current, which reverses its direction upon switching the helicity.The experiments have been carried out on Hg 0.3 Cd 0.7 Te/HgTe/Hg 0.3 Cd 0.7 Te single QW structures with a well width of 8 nm having inverted band ordering. We used this width to maximize the energy gap to about 25 meV [4,5]. Structures were grown by molecular beam epitaxy o...

We present a microscopic theory of the magnetic field induced mixing of heavy-hole states ±3/2 in GaAs droplet dots grown on (111)A substrates. The proposed theoretical model takes into account the striking dot shape with trigonal symmetry revealed in atomic force microscopy. Our calculations of the hole states are carried out within the Luttinger Hamiltonian formalism, supplemented with allowance for the triangularity of the confining potential. They are in quantitative agreement with the experimentally observed polarization selection rules, emission line intensities and energy splittings in both longitudinal and transverse magnetic fields for neutral and charged excitons in all measured single dots.