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Register a new userWannier-Stark ladder in the linear absorption of a random system with scale-free disorder
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We study numerically the linear optical response of a quasiparticle moving on a one-dimensional disordered lattice in the presence of a linear bias. The random site potential is assumed to be long-range-correlated with a power-law spectral density $S(k) sim 1/k^{alpha}$, $alpha > 0$. This type of correlations results in a phase of extended states at the band center, provided $alpha$ is larger than a critical value $alpha_c$ [F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett. textbf{81}, 3735 (1998)]. The width of the delocalized phase can be tested by applying an external electric field: Bloch-like oscillations of a quasiparticle wave packet are governed by the two mobility edges, playing now the role of band edges [F. Dom{i}nguez-Adame emph{et al.}, Phys. Rev. Lett. textbf{91}, 197402 (2003)]. We demonstrate that the frequency-domain counterpart of these oscillations, the so-called Wannier-Stark ladder, also arises in this system. When the phase of extended states emerges in the system, this ladder turns out to be a comb of doublets, for some range of disorder strength and bias. Linear optical absorption provides a tool to detect this level structure.
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Recently it was shown (I.A.Gruzberg, A. Klumper, W. Nuding and A. Sedrakyan, Phys.Rev.B 95, 125414 (2017)) that taking into account random positions of scattering nodes in the network model with $U(1)$ phase disorder yields a localization length exponent $2.37 pm 0.011$ for plateau transitions in the integer quantum Hall effect. This is in striking agreement with the experimental value of $2.38 pm 0.06$. Randomness of the network was modeled by replacing standard scattering nodes of a regular network by pure tunneling resp.reflection with probability $p$ where the particular value $p=1/3$ was chosen. Here we investigate the role played by the strength of the geometric disorder, i.e. the value of $p$. We consider random networks with arbitrary probability $0 <p<1/2$ for extreme cases and show the presence of a line of critical points with varying localization length indices having a minimum located at $p=1/3$.
We investigate site percolation in a hierarchical scale-free network known as the Dorogovtsev- Goltsev-Mendes network. We use the generating function method to show that the percolation threshold is 1, i.e., the system is not in the percolating phase when the occupation probability is less than 1. The present result is contrasted to bond percolation in the same network of which the percolation threshold is zero. We also show that the percolation threshold of intentional attacks is 1. Our results suggest that this hierarchical scale-free network is very fragile against both random failure and intentional attacks. Such a structural defect is common in many hierarchical network models.
Nonlinear photoionization of dielectrics and semiconductors is widely treated in the frames of the Keldysh theory whose validity is limited to small photon energies compared to the band gap and relatively low laser intensities. The time-dependent density functional theory (TDDFT) simulations, which are free of these limitations, enable to gain insight into non-equilibrium dynamics of the electronic structure. Here we apply the TDDFT to investigate photoionization of silicon crystal by ultrashort laser pulses in a wide range of laser wavelengths and intensities and compare the results with predictions of the Keldysh theory. Photoionization rates derived from the simulations considerably exceed the data obtained with the Keldysh theory within the validity range of the latter. Possible reasons of the discrepancy are discussed and we provide fundamental data on the photoionization rates beyond the limits of the Keldysh theory. By investigating the features of the Stark shift as a function of photon energy and laser field strength, a manifestation of the transient Wannier-Stark ladder states have been revealed which become blurred with increasing laser field strength. Finally, it is shown that the TDDFT simulations can potentially provide reliable data on the electron damping time that is of high importance for large-scale modeling.
We analyze the ground state localization properties of an array of identical interacting spinless fermionic chains with quasi-random disorder, using non-perturbative Renormalization Group methods. In the single or two chains case localization persists while for a larger number of chains a different qualitative behavior is generically expected, unless the many body interaction is vanishing. This is due to number theoretical properties of the frequency, similar to the ones assumed in KAM theory, and cancellations due to Pauli principle which in the single or two chains case imply that all the effective interactions are irrelevant; in contrast for a larger number of chains relevant effective interactions are present.
Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior in the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale $L^{ast} approx 32$ for the chosen parameters.
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