arXiv subjects

Lixuan Zheng

Publications and source records attributed to Lixuan Zheng.

8 recordsLinked to original sources

arXiv2023

Magnetic-field-induced electronic instability of Weyl-like fermions in compressed black phosphorus

Revealing the role of Coulomb interaction in topological semimetals with Dirac/Weyl-like band dispersion shapes a new frontier in condensed matter physics. Topological node-line semimetals (TNLSMs), anticipated as a fertile ground for exploring electronic correlation effects due to the anisotropy associated with their node-line structure, have recently attracted considerable attention. In this study, we report an experimental observation for correlation effects in TNLSMs realized by black phosphorus (BP) under hydrostatic pressure. By performing a combination of nuclear magnetic resonance measurements and band calculations on compressed BP, a magnetic-field-induced electronic instability of Weyl-like fermions is identified under an external magnetic field parallel to the so-called nodal ring in the reciprocal space. Anomalous spin fluctuations serving as the fingerprint of electronic instability are observed at low temperatures, and they are observed to maximize at approximately 1.0 GPa. This study presents compressed BP as a realistic material platform for exploring the rich physics in strongly coupled Weyl-like fermions.

cond-mat.str-el↗

arXiv2022

Emergent charge order and unconventional superconductivity in pressurized kagome superconductor CsV3Sb5

The discovery of multiple electronic orders in kagome superconductors AV3Sb5 (A = K, Rb, Cs) provides a promising platform for exploring unprecedented emergent physics. Under moderate pressure (< 2.2 GPa), the triple-Q charge density wave (CDW) order is monotonically suppressed by pressure, while the superconductivity displays a two-dome-like behavior, suggesting an unusual interplay between superconductivity and CDW order. Given that time-reversal symmetry breaking and electronic nematicity have been revealed inside the triple-Q CDW phase, understanding this CDW order and its interplay with superconductivity becomes one of the core questions in AV3Sb5. Here, we report the evolution of CDW and superconductivity with pressure in CsV3Sb5 by 51V nuclear magnetic resonance measurements. An emergent CDW phase, ascribed to a possible stripe-like CDW order with a unidirectional 4a0 modulation, is observed between Pc1 ~ 0.58 GPa and Pc2 ~ 2.0 GPa, which explains the two-dome-like superconducting behavior under pressure. Furthermore, the nuclear spin-lattice relaxation measurement reveals evidence for pressure-independent charge fluctuations above the CDW transition temperature and unconventional superconducting pairing above Pc2. Our results not only shed new light on the interplay of superconductivity and CDW but also reveal novel electronic correlation effects in kagome superconductors AV3Sb5.

cond-mat.supr-con↗

arXiv2019

Dimension theory of Diophantine approximation related to $β$-transformations

Let $T_β$ be the $β$-transformation on $[0,1)$ defined by $$T_β(x)=βx\text{ mod }1.$$ We study the Diophantine approximation of the orbit of a point $x$ under $T_β$. Precisely, for given two positive functions $ψ_1,~ψ_2: \mathbb{N} \rightarrow \mathbb{R}^+$, define $$\mathcal{L}(ψ_1):=\left\{x\in[0,1]:T_β^n x<ψ_1(n),\text{ for infinitely many $n\in\mathbb{N}$}\right\},$$ $$\mathcal{U}(ψ_2):=\left\{x\in [0,1]:\forall~N\gg1,~\exists~n\in[0,N],\ s.t.\ T^n_βx<ψ_2(N)\right\},$$ where $\gg$ means large enough. We compute the Hausdorff dimension of the set $\mathcal{L}(ψ_1)\cap\mathcal{U}(ψ_2)$. As a corollary, we estimate the Hausdorff dimension of the set $\mathcal{U}(ψ_2)$.

math.DS↗

arXiv2019

Uniform recurrence properties for beta-transformation

For any $β> 1$, let $T_β: [0,1)\rightarrow [0,1)$ be the $β$-transformation defined by $T_βx=βx \mod 1$. We study the uniform recurrence properties of the orbit of a point under the $β$-transformation to the point itself. The size of the set of points with prescribed uniform recurrence rate is obtained. More precisely, for any $0\leq \hat{r}\leq +\infty$, the set $$\left\{x \in [0,1): \forall\ N\gg1, \exists\ 1\leq n \leq N, {\rm\ s.t.}\ |T^n_βx-x|\leq β^{-\hat{r}N}\right\}$$ is of Hausdorff dimension $\left(\frac{1-\hat{r}}{1+\hat{r}}\right)^2$ if $0\leq \hat{r}\leq 1$ and is countable if $\hat{r}>1$.

math.DS↗

arXiv2018

Diophantine approximation and run-length function on β-expansions

For any $β> 1$, denoted by $r_n(x,β)$ the maximal length of consecutive zeros amongst the first $n$ digits of the $β$-expansion of $x\in[0,1]$. The limit superior (respectively limit inferior) of $\frac{r_n(x,β)}{n}$ is linked to the classical Diophantine approximation (respectively uniform Diophantine approximation). We obtain the Hausdorff dimension of the level set $$E_{a,b}=\left\{x \in [0,1]: \liminf_{n\rightarrow \infty}\frac{r_n(x,β)}{n}=a,\ \limsup_{n\rightarrow \infty}\frac{r_n(x,β)}{n}=b\right\}\ (0\leq a\leq b\leq1).$$ Furthermore, we show that the extremely divergent set $E_{0,1}$ which is of zero Hausdorff dimension is, however, residual. The same problems in the parameter space are also examined.

math.DS↗

arXiv2017

The exceptional sets on the run-length function of beta-expansions

Let $β> 1$ and the run-length function $r_n(x,β)$ be the maximal length of consecutive zeros amongst the first n digits in the $β$-expansion of $x\in[0,1]$. The exceptional set $$E_{\max}^φ=\left\{x \in [0,1]:\liminf_{n\rightarrow \infty}\frac{r_n(x,β)}{φ(n)}=0, \limsup_{n\rightarrow \infty}\frac{r_n(x,β)}{φ(n)}=+\infty\right\}$$ is investigated, where $φ: \mathbb{N} \rightarrow \mathbb{R}^+$ is a monotonically increasing function with $\lim\limits_{n\rightarrow \infty }φ(n)=+\infty$. We prove that the set $E_{\max}^φ$ is either empty or of full Hausdorff dimension and residual in $[0,1]$ according to the increasing rate of $φ$ .

math.DS↗

arXiv2016

The topological property of the irregular sets on the lengths of basic intervals in beta-expansions

Let $β> 1$ be a real number and $(ε_1(x, β), ε_2(x, β), \ldots)$ be the $β$-expansion of a point $x \in (0, 1]$. For all $x \in (0,1]$, let $A(D(x))$ be the set of accumulation points of $\frac{-\log_β|I_n(x)|}{n}$ as $n \rightarrow \infty$, where $|I_n(x)|$ is the length of the basic interval of order $n$ containing $x \in (0, 1]$. In this paper, we prove that $A(D(x))$ is always a closed interval for any $x \in (0,1]$. Furthermore, if $λ(β)>0$, the extremely irregular set containing points $x \in [0, 1]$ whose upper limit of $\frac{-\log_β|I_n(x)|}{n}$ equals to $1+ł(β)$ is residual, where $1+ł(β)$ is a constant depending on $β$. As a consequence, the irregular set with $x\in [0, 1]$ whose limit of $\frac{-\log_β|I_n(x)|}{n}$ does not exist is residual for every $λ(β)>0$.

math.DS↗

arXiv2016

The dimension of irregular set in parameter space

For any real number $β>1$. The $n$th cylinder of $β$ in the parameter space $\{β\in \mathbb{R}: β>1\}$ is a set of real numbers in $(1,\infty)$ having the same first $n$ digits in their $β$-expansion of $1$, denote by $I^P_n(β)$. We study the quantities which describe the growth of the length of $I^P_n(β)$. The Huasdorff dimension of the set of given growth rate of the length of $I^P_n(β)$ will be determined in this paper.

math.DS↗