arXiv subjects

Zhiqing Han

Publications and source records attributed to Zhiqing Han.

5 recordsLinked to original sources

arXiv2021

Normalized ground states for Kirchhoff equations in ${\mathbb{R}}^{3}$ with a critical nonlinearity

This paper is concerned with the existence of ground states for a class of Kirchhoff type equation with combined power nonlinearities \begin{equation*} -\left(a+b\int_{\mathbb{R}^{3}}|\nabla u(x)|^{2}\right) Δu =λu+|u|^{p-2}u+u^{5}\quad \ \text{for some} \ λ\in\mathbb{R},\quad x\in\mathbb{R}^{3}, \end{equation*} with prescribed $L^{2}$-norm mass \begin{equation*} \int_{\mathbb{R}^{3}}u^{2}=c^{2} \end{equation*} in Sobolev critical case and proves that the equation has a couple of solutions $(u_{c},λ_{c})\in S(c)\times \mathbb{R}$ for any $c>0$, $a,b >0$ and $\frac{14}{3}\leq p< 6,$ where $S(c)=\{u\in H^{1}(\mathbb{R}^{3}):\int_{\mathbb{R}^{3}}u^{2}=c^{2}\}.$ \textbf{Keywords:} Kirchhoff type equation; Critical nonlinearity; Normalized ground states \noindent{AMS Subject Classification:\, 37L05; 35B40; 35B41.}

math.AP↗

arXiv2017

FeTe$_{1-x}$Se$_{x}$ monolayer films: towards the realization of high-temperature connate topological superconductivity

We performed angle-resolved photoemission spectroscopy studies on a series of FeTe$_{1-x}$Se$_{x}$ monolayer films grown on SrTiO$_{3}$. The superconductivity of the films is robust and rather insensitive to the variations of the band position and effective mass caused by the substitution of Se by Te. However, the band gap between the electron- and hole-like bands at the Brillouin zone center decreases towards band inversion and parity exchange, which drive the system to a nontrivial topological state predicted by theoretical calculations. Our results provide a clear experimental indication that the FeTe$_{1-x}$Se$_{x}$ monolayer materials are high-temperature connate topological superconductors in which band topology and superconductivity are integrated intrinsically.

cond-mat.supr-con↗

arXiv2016

Sudden gap-closure across the topological phase transition in Bi$_{2-x}$In$_{x}$Se$_{3}$

The phase transition from a topological insulator to a trivial band insulator is studied by angle-resoled photoemission spectroscopy on Bi$_{2-x}$In$_{x}$Se$_{3}$ single crystals. We first report the complete evolution of the bulk band structures throughout the transition. The robust surface state and the bulk gap size ($\sim$ 0.50 eV) show no significant change upon doping for $x$ = 0.05, 0.10 and 0.175. At $x$ $\geq$ 0.225, the surface state completely disappears and the bulk gap size increases, suggesting a sudden gap-closure and topological phase transition around $x \sim$ 0.175$-$0.225. We discuss the underlying mechanism of the phase transition, proposing that it is governed by the combined effect of spin-orbit coupling and interactions upon band hybridization. Our study provides a new venue to investigate the mechanism of the topological phase transition induced by non-magnetic impurities.

cond-mat.str-el↗

arXiv2016

Interplay between multiple charge-density waves and the relationship with superconductivity in Pd$_x$HoTe$_{3}$

HoTe$_{3}$, a member of the rare-earth tritelluride ($R$Te$_{3}$) family, and its Pd-intercalated compounds, Pd$_x$HoTe$_{3}$, where superconductivity (SC) sets in as the charge-density wave (CDW) transition is suppressed by the intercalation of a small amount of Pd, are investigated using angle-resolved photoemission spectroscopy (ARPES) and electrical resistivity. Two incommensurate CDWs with perpendicular nesting vectors are observed in HoTe$_{3}$ at low temperatures. With a slight Pd intercalation ($x$ = 0.01), the large CDW gap decreases and the small one increases. The momentum dependence of the gaps along the inner Fermi surface (FS) evolves from orthorhombicity to near tetragonality, manifesting the competition between two CDW orders. At $x$ = 0.02, both CDW gaps decreases with the emergence of SC. Further increasing the content of Pd for $x$ = 0.04 will completely suppress the CDW instabilities and give rise to the maximal SC order. The evolution of the electronic structures and electron-phonon couplings (EPCs) of the multiple CDWs upon Pd intercalation are carefully scrutinized. We discuss the interplay between multiple CDW orders, and the competition between CDW and SC in detail.

cond-mat.str-el↗

arXiv2014

Multiple solutions for a class of Kirchhoff equation with singular nonlinearity

In this article, we investigate the existence and multiplicity of solutions of Kirchhoff equation \begin{equation*} \left\{ \begin{aligned} -(1+b \int_{\mathbb{R}^3}|\nabla u|^2)Δu= k(x)\frac{|u|^2 u}{|x|} +λh(x)u,~~x\in\mathbb{R}^3\\ u(x)\rightarrow 0 ~~~~~~~~~~~~~~~~~~~~~~~as ~~~~|x|\rightarrow\infty \end{aligned} \right. \end{equation*} where the potential $k(x)$ allows sign changing. Making use of Nehari manifold method and Concentration-compactness principle, we obtain the existence and multiplicity of solutions for this equation.

math.AP↗