arXiv subjects

Fan Zheng

Publications and source records attributed to Fan Zheng.

33 records · Page 2Linked to original sources

arXiv2020

The lifespan of classical solutions for the inviscid Surface Quasi-geostrophic equation

We consider classical solutions of the inviscid Surface Quasi-geostrophic equation that are a small perturbation $ε$ from a radial stationary solution $θ=|x|$. We use a modified energy method to prove the existence time of classical solutions from $\frac{1}ε$ to a time scale of $\frac{1}{ε^4}$. Moreover, by perturbing in a suitable direction we construct global smooth solutions, via bifurcation, that rotate uniformly in time and space.

math.AP↗

arXiv2019

Long-term regularity of the periodic Euler--Poisson system for electrons in 2D

We study a basic plasma physics model--the one-fluid Euler--Poisson system on the square torus, in which a compressible electron fluid flows under its own electrostatic field. In this paper we prove long-term regularity of periodic solutions of this system in 2 spatial dimensions. Our main conclusion is that on a square torus of side length $R$, if the initial data is sufficiently close to a constant solution, then the solution is wellposed for a time at least $R/ε^2(\log R)^{O(1)}$, where $ε$ is the size of the initial data.

math.AP↗

arXiv2019

Borophosphene: a New Anisotropic Dirac Cone Monolayer with High Fermi Velocity and Unique Feature of Self-doping

Two-dimensional (2D) Dirac cone materials exhibit linear energy dispersion at the Fermi level, where the effective masses of carriers are very close to zero and the Fermi velocity is ultrahigh, only 2 ~ 3 orders of magnitude lower than the light velocity. Such the Dirac cone materials have great promise in high-performance electronic devices. Herein, we have employed the genetic algorithms methods combining with first-principles calculations to propose a new 2D anisotropic Dirac cone material, that is, orthorhombic boron phosphide (BP) monolayer named as borophosphene. Molecular dynamics simulation and phonon dispersion have been used to evaluate the dynamic and thermal stability of borophosphene. Because of the unique arrangements of B-B and P-P dimers, the mechanical and electronic properties are highly anisotropic. Of great interest is that the Dirac cone of the borophosphene is robust, independent of in-plane biaxial and uniaxial strains, and can also be observed in its one-dimensional (1D) zigzag nanoribbons and armchair nanotubes. The Fermi velocities are ~ 105 m/s, the same order of magnitude with that of graphene. By using a tight-binding model, the origin of the Dirac cone of borophosphene is analyzed. Moreover, a unique feature of self-doping can be induced by the in-plane biaxial and uniaxial strains of borophosphene and the Curvature effect of nanotubes, which is great beneficial to realizing high speed carriers (holes). Our results suggest that the borophosphene holds a great promise in high-performance electronic devices, which could promote the experimental and theoretical studies to further explore the potential applications of other 2D Dirac cone sheets.

cond-mat.mtrl-sci↗

arXiv2019

Observation of Rydberg exciton polaritons and their condensate in a perovskite cavity

The condensation of half-light half-matter exciton polaritons in semiconductor optical cavities is a striking example of macroscopic quantum coherence in a solid state platform. Quantum coherence is possible only when there are strong interactions between the exciton polaritons provided by their excitonic constituents. Rydberg excitons with high principle value exhibit strong dipole-dipole interactions in cold atoms. However, polaritons with the excitonic constituent that is an excited state, namely Rydberg exciton polaritons (REPs), have not yet been experimentally observed. Here, for the first time, we observe the formation of REPs in a single crystal CsPbBr3 perovskite cavity without any external fields. These polaritons exhibit strong nonlinear behavior that leads to a coherent polariton condensate with a prominent blue shift. Furthermore, the REPs in CsPbBr3 are highly anisotropic and have a large extinction ratio, arising from the perovskite's orthorhombic crystal structure. Our observation not only sheds light on the importance of many-body physics in coherent polariton systems involving higher-order excited states, but also paves the way for exploring these coherent interactions for solid state quantum optical information processing.

cond-mat.mtrl-sci↗

arXiv2017

Local polar fluctuations in lead halide perovskite crystals

Hybrid lead-halide perovskites have emerged as an excellent class of photovoltaic materials. Recent reports suggest that the organic molecular cation is responsible for local polar fluctuations that inhibit carrier recombination. We combine low frequency Raman scattering with first-principles molecular dynamics (MD) to study the fundamental nature of these local polar fluctuations. Our observations of a strong central peak in both hybrid (CH$_3$NH$_3$PbBr$_3$) and all-inorganic (CsPbBr$_3$) lead-halide perovskites show that anharmonic, local polar fluctuations are intrinsic to the general lead-halide perovskite structure, and not unique to the dipolar organic cation. MD simulations show that head-to-head Cs motion coupled to Br face expansion, on a few hundred femtosecond time scale, drives the local polar fluctuations in CsPbBr$_3$.

cond-mat.mtrl-sci↗

arXiv2016

Frequency-dependent dielectric function of semiconductors with application to physisorption

The dielectric function is one of the most important quantities that describes the electrical and optical properties of solids. Accurate modeling of the frequency-dependent dielectric function has great significance in the study of the long-range van der Waals (vdW) interaction for solids and adsorption. In this work, we calculate the frequency-dependent dielectric functions of semiconductors and insulators using the $GW$ method with and without exciton effects, as well as efficient semilocal density functional theory (DFT), and compare these calculations with a model frequency-dependent dielectric function. We find that for semiconductors with moderate band gaps, the model dielectric functions, $GW$ values, and DFT calculations all agree well with each other. However, for insulators with strong exciton effects, the model dielectric functions have a better agreement with accurate $GW$ values than the DFT calculations, particularly in high-frequency region. To understand this, we repeat the DFT calculations with scissors correction, by shifting DFT Kohn-Sham energy gap to match the experimental band gap. We find that scissors correction only moderately improves the DFT dielectric function in low-frequency region. Based on the dielectric functions calculated with different methods, we make a comparative study by applying these dielectric functions to calculate the vdW coefficients ($C_3$ and $C_5$) for adsorption of rare-gas atoms on a variety of surfaces. We find that the vdW coefficients obtained with the nearly-free electron gas-based model dielectric function agree quite well with those obtained from the $GW$ dielectric function, in particular for adsorption on semiconductors, leading to an overall error of less than 7% for $C_3$ and 5% for $C_5$. This demonstrates the reliability of the model dielectric function for the study of physisorption.

cond-mat.mtrl-sci↗

arXiv2015

Photoferroelectric and Photopiezoelectric Properties of Organometal Halide Perovskites

Piezoelectrics play a critical role in various applications. The permanent dipole associated with the molecular cations in organometal-halide perovskites (OMHPs) may lead to spontaneous polarization and thus piezoelectricity. Here, we explore the piezoelectric properties of OMHPs with density functional theory. We find that the piezoelectric coefficient depends sensitively on the molecular ordering, and that the experimentally observed light-enhanced piezoelectricity is due to to a non-polar to polar structural transition. By comparing OMHPs with different atomic substitutions in the $ABX_3$ architecture, we find that the displacement of the $B$-site cation contributes to nearly all the piezoelectric response, and that the competition between $A$-$X$ hydrogen bond and $B$-$X$ metal-halide bond in OMHPs controls the piezoelectric properties. These results highlight the potential of the OMHP architecture for designing new functional photoferroelectrics and photopiezoelectrics.

cond-mat.mtrl-sci↗

arXiv2015

Substantial optical dielectric enhancement by volume compression in LiAsSe$_2$

Based on first-principles calculations, we predict a substantial increase in the optical dielectric function of LiAsSe$_2$ under pressure. We find that the optical dielectric constant is enhanced threefold under volume compression. This enhancement is mainly due to the dimerization strength reduction of the one-dimensional (1D) As--Se chains in LiAsSe$_2$, which significantly alters the wavefunction phase mismatch between two neighboring chains and changes the transition intensity. By developing a tight-binding model of the interacting 1D chains, the essential features of the low-energy electronic structure of LiAsSe$_2$ are captured. Our findings are important for understanding the fundamental physics of LiAsSe$_2$ and provide a feasible way to enhance the material optical response that can be applied to light harvesting for energy applications.

cond-mat.mtrl-sci↗

arXiv2015

First-principles materials design of high-performing bulk photovoltaics with the LiNbO$_3$ structure

The bulk photovoltaic effect is a long-known but poorly understood phenomenon. Recently, however, the multiferroic bismuth ferrite has been observed to produce strong photovoltaic response to visible light, suggesting that the effect has been underexploited as well. Here we present three polar oxides in the LiNbO$_3$ structure that we predict to have band gaps in the 1-2 eV range and very high bulk photovoltaic response: PbNiO$_3$, Mg$_{1/2}$Zn$_{1/2}$PbO$_3$, and LiBiO$_3$. All three have band gaps determined by cations with $d^{10}s^0$ electronic configurations, leading to conduction bands composed of cation $s$-orbitals and O $p$-orbitals. This both dramatically lowers the band gap and increases the bulk photovoltaic response by as much as an order of magnitude over previous materials, demonstrating the potential for high-performing bulk photovoltaics.

cond-mat.mtrl-sci↗

arXiv2015

Rashba Spin-Orbit Coupling Enhanced Carrier Lifetime in Organometal Halide Perovskites

Organometal halide perovskites are promising solar-cell materials for next-generation photovoltaic applications. The long carrier lifetime and diffusion length of these materials make them very attractive for use in light absorbers and carrier transporters. While these aspects of organometal halide perovskites have attracted the most attention, the consequences of the Rashba effect, driven by strong spin-orbit coupling, on the photovoltaic properties of these materials are largely unexplored. In this work, taking the electronic structure of methylammonium lead iodide as an example, we propose an intrinsic mechanism for enhanced carrier lifetime in 3D Rashba materials. Based on first-principles calculations and a Rashba spin-orbit model, we demonstrate that the recombination rate is reduced due to the spin-forbidden transition. These results are important for understanding the fundamental physics of organometal halide perovskites and for optimizing and designing the materials with better performance. The proposed mechanism including spin degrees of freedom offers a new paradigm of using 3D Rashba materials for photovoltaic applications.

cond-mat.mtrl-sci↗

arXiv2015

Bulk photovoltaic effect enhancement via electrostatic control in layered ferroelectrics

The correlation between the shift current mechanism for the bulk photovoltaic effect (BPVE) and the structural and electronic properties of ferroelectric perovskite oxides is not well understood. Here, we study and engineer the shift current photovoltaic effect using a visible-light-absorbing ferroelectric Pb(Ni$_{x}$Ti$_{1-x}$)O$_{3-x}$ solid solution from first principles. We show that the covalent orbital character dicates the direction, magnitude, and onset energy of shift current in a predictable fashion. In particular, we find that the shift current response can be enhanced via electrostatic control in layered ferroelectrics, as bound charges face a stronger impetus to screen the electric field in a thicker material, delocalizing electron densities. This heterogeneous layered structure with alternative photocurrent generating and insulating layers is ideal for BPVE applications.

cond-mat.mtrl-sci↗

arXiv2014

First-Principles Calculation of the Bulk Photovoltaic Effect in the Polar Compounds LiAsS$_\text{2}$, LiAsSe$_\text{2}$, and NaAsSe$_\text{2}$

We calculate the shift current response, which has been identified as the dominant mechanism for the bulk photovoltaic effect, for the polar compounds LiAsS$_\text{2}$, LiAsSe$_\text{2}$, and NaAsSe$_\text{2}$. We find that the magnitudes of the photovoltaic responses in the visible range for these compounds exceed the maximum response obtained for BiFeO$_\text{3}$ by 10 - 20 times. We correlate the high shift current response with the existence of $p$ states at both the valence and conduction band edges, as well as the dispersion of these bands, while also showing that high polarization is not a requirement. With low experimental band gaps of less than 2 eV and high shift current response, these materials have potential for use as bulk photovoltaics.

cond-mat.mtrl-sci↗

arXiv2014

First-principles calculation of bulk photovoltaic effect in CH$_3$NH$_3$PbI$_3$ and CH$_3$NH$_3$PbI$_{3-x}$Cl$_{x}$

Hybrid halide perovskites exhibit nearly 20% power conversion efficiency, but the origin of their high efficiency is still unknown. Here, we compute the shift current, a dominant mechanism of bulk photovoltaic (PV) effect for ferroelectric photovoltaics, in CH$_3$NH$_3$PbI$_3$ and CH$_3$NH$_3$PbI$_{3-x}$Cl$_{x}$ from first principles. We find that these materials give approximately three times larger shift current PV response to near-IR and visible light than the prototypical ferroelectric photovoltaic BiFeO$_3$. The molecular orientations of CH$_3$NH$_3^{+}$ can strongly affect the corresponding PbI$_3$ inorganic frame so as to alter the magnitude of the shift current response. Specifically, configurations with dipole moments aligned in parallel distort the inorganic PbI$_3$ frame more significantly than configurations with near net zero dipole, yielding a larger shift current response. Furthermore, we explore the effect of Cl substitution on shift current, and find that Cl substitution at the equatorial site induces a larger response than does substitution at the apical site.

cond-mat.mtrl-sci↗

arXiv2013

Locating the first nodal set in higher dimensions

This paper estimates the location and the width of the nodal set of the first Neumann eigenfunctions on a smooth convex domain $Ω\subset \mathbb R^n$, whose length is normalized to be 1 and whose cross-section is contained in a ball of radius $ε$. In \cite{CJK2009}, an $O(ε)$ bound was obtained by constructing a coordinate system. In this paper, we present a simpler method that does not require such a coordinate system. Moreover, in the special case $n = 2$, we obtain an $O(ε^2)$ bound on the width of the nodal set, in analogy to the corresponding result in the Dirichlet case obtained in \cite{GJ1995}.

math.AP↗

arXiv2013

Gauss Sphere Problem with Polynomials

This paper provides an estimate of the sum of a homogeneous polynomial $P$ of degree $ν$ and mean zero over the lattice points inside a sphere of radius $R$. It is proved that $$ \sum_{\mathbf x \in \mathbb Z^3 \atop |\mathbf x| \le R} P(\mathbf x) = O_{ε,P}(R^{ν+ 83/64 + ε}) $$

math.NT↗