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The critical filling factor v_c where Shubnikov-de Haas oscillations become spin split is investigated for a set of GaAs-GaAlAs heterojunctions. Finite temperature magnetoresistance measurements are used to extract the value of v_c at zero temperature. The critically point is where the disorder potential has the same magnitude as the exchange energy, leading to the empirical relationship v_c = g* n t h / 2 m_0. This is valid for all the samples studied, where the density n and single particle lifetime t both vary by more than an order of magnitude and g* the exchange enhanced g-factor has a weak dependence on density. For each sample the spin gap energy shows a linear increase with magnetic field. Experiments in tilted magnetic field show the spin gap is the sum of the bare Zeeman energy and an exchange term. This explains why measurements of the enhanced g-factor from activation energy studies in perpendicular field and the coincidence method in tilted fields have previously disagreed.
Electron exchange and correlations emerging from the coupling between ionic vibrations and electrons are addressed. Spin-dependent electron-phonon coupling originates from the spin-orbit interaction, and it is shown that such electron-phonon coupling
Disorder such as impurities and dislocations in Weyl semimetals (SMs) drives a quantum critical point (QCP) where the density of states at the Weyl point gains a non-zero value. Near the QCP, the asymptotic low energy singularities of physical quanti
Exploiting the valley degree of freedom to store and manipulate information provides a novel paradigm for future electronics. A monolayer transition metal dichalcogenide (TMDC) with broken inversion symmetry possesses two degenerate yet inequivalent
The electronic structure of the ferromagnetic semiconductor EuO is investigated by means of spin- and angle-resolved photoemission spectroscopy and density functional theory. Our spin-resolved data reveals that, while the macroscopic magnetization of
The ratio of the Zeeman splitting to the cyclotron energy ($M=Delta E_Z / hbar omega_c$), which characterizes the relative strength of the spin-orbit interaction in crystals, is examined for the narrow gap IV-VI semiconductors PbTe, SnTe, and their a