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Register a new userRobustness of equilibrium off-diagonal current fluctuation against localization of electron states in macroscopic two-dimensional systems
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We study the off-diagonal current fluctuation in a macroscopic quantum system measured in an ideal manner that is as close as possible to the classical ideal measurement. We show rigorously that not only extended but also localized states contribute to the off-diagonal current fluctuation. This result contrasts with the fact that only the extended states affect the off-diagonal (Hall) conductivity and apparently contradicts the naive expectation from the fluctuation-dissipation theorem that might directly connect these two quantities. More specifically, we study the off-diagonal current fluctuation in a disordered two-dimensional electron system in a strong magnetic field at low temperatures. The fluctuation is almost unchanged from that of the pure system reflecting the property mentioned above, being approximately proportional to the Landau level filling factor with high accuracy. Our finding paves the way to estimate the filling factor and the electron density from the off-diagonal current fluctuation observed in macroscopic systems.
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Precise nature of MBL transitions in both random and quasiperiodic (QP) systems remains elusive so far. In particular, whether MBL transitions in QP and random systems belong to the same universality class or two distinct ones has not been decisively resolved. Here we investigate MBL transitions in one-dimensional ($d!=!1$) QP systems as well as in random systems by state-of-the-art real-space renormalization group (RG) calculation. Our real-space RG shows that MBL transitions in 1D QP systems are characterized by the critical exponent $ u!approx!2.4$, which respects the Harris-Luck bound ($ u!>!1/d$) for QP systems. Note that $ u!approx! 2.4$ for QP systems also satisfies the Harris-CCFS bound ($ u!>!2/d$) for random systems, which implies that MBL transitions in 1D QP systems are stable against weak quenched disorder since randomness is Harris irrelevant at the transition. We shall briefly discuss experimental means to measure $ u$ of QP-induced MBL transitions.
Three-particle complexes consisting of two holes in the completely filled zero electron Landau level and an excited electron in the unoccupied first Landau level are investigated in a quantum Hall insulator. The distinctive features of these three-particle complexes are an electron-hole mass symmetry and the small energy gap of the quantum Hall insulator itself. Theoretical calculations of the trion energy spectrum in a quantizing magnetic field predict that, besides the ground state, trions feature a hierarchy of excited bound states. In agreement with the theoretical simulations, we observe new photoluminescence lines related to the excited trion states. A relatively small energy gap allows the binding of three-particle complexes with magnetoplasma oscillations and formation of plasmarons. The plasmaron properties are investigated experimentally.
We present a theory of the phonon-assisted nonlinear dc transport of 2D electrons in high Landau levels. The nonlinear dissipative resistivity displays quantum magneto-oscillations governed by two parameters which are proportional to the Hall drift velocity $v_H$ of electrons in electric field and the speed of sound $s$. In the subsonic regime, $v_H<s$, the theory quantitatively reproduces the oscillation pattern observed in recent experiments. We also find the $pi/2$ phase change of oscillations across the sound barrier $v_H=s$. In the supersonic regime, $v_H>s$, the amplitude of oscillations saturates with lowering temperature, while the subsonic region displays exponential suppression of the phonon-assisted oscillations with temperature.
A study of the conductance noise in a two-dimensional electron system (2DES) in Si at low temperatures (T) reveals the onset of large, non-Gaussian noise after cooling from an equilibrium state at a high T with a fixed carrier density n_s. This behavior, which signifies the falling out of equilibrium of the 2DES as T->0, is observed for n_s<n_g (n_g - glass transition density). A protocol where density is changed by a small value Delta n_s at low T produces the same results for the noise power spectra. However, a detailed analysis of the non-Gaussian probability density functions (PDFs) of the fluctuations reveals that Delta n_s has a qualitatively different and more dramatic effect than Delta T, suggesting that Delta n_s induces strong changes in the free energy landscape of the system as a result of Coulomb interactions. The results from a third, waiting-time (t_w) protocol, where n_s is changed temporarily during t_w by a large amount, demonstrate that non-Gaussian PDFs exhibit history dependence and an evolution towards a Gaussian distribution as the system ages and slowly approaches equilibrium. By calculating the power spectra and higher-order statistics for the noise measured over a wide range of the applied voltage bias, it is established that the non-Gaussian noise is observed in the regime of Ohmic or linear response, i.e. that it is not caused by the applied bias.
Time-periodic driving fields could endow a system with peculiar topological and transport features. In this work, we find dynamically controlled localization transitions and mobility edges in non-Hermitian quasicrystals via shaking the lattice periodically. The driving force dresses the hopping amplitudes between lattice sites, yielding alternate transitions between localized, mobility edge and extended non-Hermitian quasicrystalline phases. We apply our Floquet engineering approach to five representative models of non-Hermitian quasicrystals, obtain the conditions of photon-assisted localization transitions and mobility edges, and find the expressions of Lyapunov exponents for some models. We further introduce topological winding numbers of Floquet quasienergies to distinguish non-Hermitian quasicrystalline phases with different localization nature. Our discovery thus extend the study of quasicrystals to non-Hermitian Floquet systems, and provide an efficient way of modulating the topological and transport properties of these unique phases.
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