Impressive performance of hybrid perovskite solar cells reported in recent years still awaits a comprehensive understanding of its microscopic origins. In this work, the intrinsic Hall mobility and photocarrier recombination coefficient are directly measured in these materials in steady-state transport studies. The results show that electron-hole recombination and carrier trapping rates in hybrid perovskites are very low. The bimolecular recombination coefficient (10−11 to 10−10 cm3 s−1) is found to be on par with that in the best direct-band inorganic semiconductors, even though the intrinsic Hall mobility in hybrid perovskites is considerably lower (up to 60 cm2 V−1 s−1). Measured here, steady-state carrier lifetimes (of up to 3 ms) and diffusion lengths (as long as 650 μm) are significantly longer than those in high-purity crystalline inorganic semiconductors. We suggest that these experimental findings are consistent with the polaronic nature of charge carriers, resulting from an interaction of charges with methylammonium dipoles.
A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In certain sense, the RRG ensemble can be seen as infinitedimensional (d → ∞) cousin of Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from small (N Nc) to large (N Nc) system, where Nc is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wavefunction statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly non-trivial. Our results support an analytical prediction that states in the delocalized phase (and at N Nc) are ergodic in the sense that their inverse participation ratio scales as 1/N .Introduction. Anderson localization [1] is a fundamental quantum phenomenon that remains in the focus of current research. A disordered quantum system can be driven (e.g., by increasing disorder) through Anderson transition (AT) between delocalized and localized phase [2]. For some class of models (defined on the Bethe lattice, a tree with constant connectivity) the problem of the AT allows for an exact solution, making it possible to establish the transition point and the corresponding critical behavior [3][4][5][6][7][8]. Recently, the Anderson localization on tree-like graphs has attracted much attention in view of its connections with problems of many-body localization in quantum dots [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and in extended systems with localized single-particle states .
We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to L = 100 spins, i.e., much larger than L 20 that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent β which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent βΛ which characterizes the decay of a Schmidt gap in the entanglement spectrum, (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder Wc that separates the ergodic and many-body localized regimes, compared to the values of Wc in the literature. On the ergodic side of the transition, there is a broad interval of the strength of disorder with slow subdiffusive transport. In this regime, the exponents β and βΛ increase, with increasing L, for relatively small L but saturate for L 50, indicating that these slow power laws survive in the thermodynamic limit. From a technical perspective, we develop an adaptation of the "learning by confusion" machine learning approach that can determine Wc. arXiv:1807.05051v4 [cond-mat.dis-nn]
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