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Register a new userPlasmon dispersion in quasi-one and one-dimensional systems with non-magnetic impurities
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We calculate the plasmon dispersion in quasi-one-dimensional quantum wires, in the presence of non-magnetic impurities, taking into consideration the memory function formalism and the role of the forward scattering. The plasma frequency is reduced by the presence of impurities. We also calculate, analytically, the plasmon dispersion in the Born approximation, for the scattering of the electrons by the non-magnetic impurities. We compare our result with the numerical results of Sarma and Hwang.
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In the conventional theory of hopping transport the positions of localized electronic states are assumed to be fixed, and thermal fluctuations of atoms enter the theory only through the notion of phonons. On the other hand, in 1D and 2D lattices, where fluctuations prevent formation of long-range order, the motion of atoms has the character of the large scale diffusion. In this case the picture of static localized sites may be inadequate. We argue that for a certain range of parameters, hopping of charge carriers among localization sites in a network of 1D chains is a much slower process than diffusion of the sites themselves. Then the carriers move through the network transported along the chains by mobile localization sites jumping occasionally between the chains. This mechanism may result in temperature independent mobility and frequency dependence similar to that for conventional hopping.
As a potential window on transitions out of the ergodic, many-body-delocalized phase, we study the dephasing of weakly disordered, quasi-one-dimensional fermion systems due to a diffusive, non-Markovian noise bath. Such a bath is self-generated by the fermions, via inelastic scattering mediated by short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling. However, the expansion breaks down at long times, and is not stabilized by including a mean-field decay rate, signaling a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interactions perturbatively and the Coulomb interaction exactly. The latter provides a physical infrared regularization that stabilizes perturbation theory at long times, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. At first order in the diffusive bath coupling, we find an enhancement of the dephasing rate, but at second order we find a rephasing contribution. Our results differ qualitatively from those obtained via self-consistent calculations and are relevant in two different contexts. First, in the search for precursors to many-body localization in the ergodic phase. Second, our results provide a mechanism for the enhancement of dephasing at low temperatures in spin SU(2)-symmetric quantum wires, beyond the Altshuler-Aronov-Khmelnitsky result. The enhancement is possible due to the amplification of the triplet-channel interaction strength, and provides an additional mechanism that could contribute to the experimentally observed low-temperature saturation of the dephasing time.
A microwave setup for mode-resolved transport measurement in quasi-one-dimensional (quasi-1D) structures is presented. We will demonstrate a technique for direct measurement of the Greens function of the system. With its help we will investigate quasi-1D structures with various types of disorder. We will focus on stratified structures, i.e., structures that are homogeneous perpendicular to the direction of wave propagation. In this case the interaction between different channels is absent, so wave propagation occurs individually in each open channel. We will apply analytical results developed in the theory of one-dimensional (1D) disordered models in order to explain main features of the quasi-1D transport. The main focus will be selective transport due to long-range correlations in the disorder. In our setup, we can intentionally introduce correlations by changing the positions of periodically spaced brass bars of finite thickness. Because of the equivalence of the stationary Schrodinger equation and the Helmholtz equation, the result can be directly applied to selective electron transport in nanowires, nanostripes, and superlattices.
We investigate the spectral function of Bloch states in an one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel Polynomial Method, which has an $mathcal{O}(N)$ computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-perturbative spectral functions shaped as the probability distribution of the random on-site energies, even at low disorder strengths. In the case of disordered potentials with an algebraic power-spectrum, $proptoleft|kright|^{-alpha}$, we show that the spectral function is not self-averaging for $alphageq1$.
We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are $n$ barriers and wells with statistically independent intensities and with a spatial extension $l_c$ which may contain an arbitrary number $delta/2pi$ of wavelengths, where $delta = k l_c$. We analyze the average Landauer resistance and transmission coefficient of the chain as a function of $n$ and the phase parameter $delta$. For weak scatterers, we find: i) a regime, to be called I, associated with an exponential behavior of the resistance with $n$, ii) a regime, to be called II, for $delta$ in the vicinity of $pi$, where the system is almost transparent and less localized, and iii) right in the middle of regime II, for $delta$ very close to $pi$, the formation of a band gap, which becomes ever more conspicuous as $n$ increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with $n$ and $delta$. These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.
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