arXiv subjects

Xiao-Yu Yan

Publications and source records attributed to Xiao-Yu Yan.

12 recordsLinked to original sources

arXiv2026

The Beurling density of the spectrum of self-similar measure generated by Hadamard triple

Let $D\subset\Bbb Z$ with cardinality $q\ge 2$, and let $b\in \Bbb Z$ with $q<b$, and let $\mu:=\mu_{b,D}$ be the associated self-similar measure. It is well known that if there exists $L\subset \Bbb Z$ such that $(b,D,L)$ be a Hadamard triple, then the Beurling dimension of the spectrum of $\mu$ exhibits an intermediate structural property. In this paper, we establish a stronger result that both Beurling dimension and Beurling density of the spectra of $\mu$ can achieve full flexibility simultaneously. More precisely, for any $t\in(0, \frac{\log q}{\log b})$ and $s\in [0,\infty]$, there exists a spectrum $\Lambda:=\Lambda_{t,s}$ of $\mu$ such that $$\dim_{Be}(\Lambda)=t,\quad D_t^+ (\Lambda)=s.$$ Here, $\dim_{Be}$ and $D_t^+$ denote the Beurling dimension and the $t$-Beurling density, respectively. We further prove that the set of such spectrum whose Beurling dimension and Beurling density are equal to any fixed $t$ and $s$ has the cardinality of the continuum. \par This work generalizes a previous result of Lu \cite{Lu}, answers an open question raised by Dai, Fu and He \cite[Conjecture 5.3]{DaiFuHe}, and sheds new light on the fine structural properties of spectra for singularly continuous spectral measures.

math.FA↗

arXiv2026

Topological pair density waves in kagome superconductors

The pair density wave (PDW) is an unconventional superconducting state exhibiting periodic pairing modulations due to pairing with finite momentum Q. In two dimensions, multiple Q components of the PDW can have a non-trivial relative phase, breaking time-reversal symmetry and resulting in a topological electronic structure. Here we review progress on exploring such topological PDWs (TPDWs) and discuss their potential realization in kagome superconductors. We first introduce the concept of a TPDW starting from the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state and examine the challenges toward its realization. We then discuss the possibility of a TPDW in the kagome lattice, which intertwines with chiral superconductivity and loop currents, thus connecting to models describing the quantum anomalous Hall effect. Furthermore, we review the experimental signatures of a TPDW in AV3Sb5 (A = Cs, Rb, K) superconductors and highlight related quantum effects, including switchable chiral pairing modulations, Bogoliubov Fermi states, the superconducting diode effect, and the anomalous thermal Hall effect. Finally, we project the future research opportunities of this correlated topological quantum phase and discuss its broad implications for finite-momentum pairing, topological matter, and chiral superconductivity.

cond-mat.supr-con↗

arXiv2026

Josephson spectroscopy study of kagome superconductors toward the deep point-contact regime

Josephson scanning tunneling microscopy (JSTM) has emerged as an important technique for probing the superconducting order parameter at the atomic scale. However, the Josephson current in JSTM may behave quite differently when the coupling strength varies. Here, we push the junction to the deep point-contact regime, reaching a normal-state junction resistance of only 0.15 $h/2e^2 \simeq 2~{\rm k}\Omega$. We demonstrate, using kagome superconductors, that the zero-bias conductance, a key characteristic of the Josephson current, deviates strongly from the quadratic dependence on the normal-state conductance upon entering the deep point-contact regime. Furthermore, we observe a striking saturation of the zero-bias conductance, which we show arises from the series resistance in the circuit. This also serves as a cautious reminder when interpreting zero-bias conductance saturation or quantization in studies of exotic physics such as that of Majorana zero modes if the tip-sample junction resistance is extremely small. Finally, we identify an optimum regime where JSTM can be used as an atomic-scale probe for studying pair-density wave states in materials with low superconducting transition temperature, such as AV3Sb5 kagome superconductors.

cond-mat.supr-con↗

arXiv2025

Spectrality and non-spectrality of a class of Moran measures with three-element digits

A Borel probability measure $ \mu $ with compact support on $ \mathbb{R}^n $ is called spectral measure if there exists a discrete set $ \Lambda \subset \mathbb{R}^n $ such that $ E_\Lambda := \{e^{2\pi i \langle \lambda, x \rangle}: \lambda \in \Lambda\} $ forms an orthonormal basis of $ L^2(\mu) $. In this paper, we study the spectrality and non-spectrality of a class of Moran measures with three-element digits on $ \mathbb{R} $. Let $p_n\in 3\mathbb Z\setminus\{0\}$ and $\mathcal{D}_n=\{0,a_n,b_n\}$ with $\{a_n,b_n\}=\{-1,1\}\pmod 3$. It is know that the infinite convolution of uniformly discrete probability measures $$\mu_{\{p_n\},\{\mathcal D_n\}}:=\delta_{p_1^{-1}\{0,a_1,b_1\}}\ast\delta_{(p_1p_2)^{-1}\{0,a_2,b_2\}}\ast\cdots $$ is a Moran measure with compact support if and only if \begin{align*} \sum_{n=1}^{\infty}|p_{1}p_{2}\cdots p_n|^{-1}d_n<\infty,\quad \mbox{where}\;d_n=\max\{0,|a_n|, |b_n|\}. \end{align*} Without the condition $\sup_{n\geq 1}\{\frac{|a_n|+|b_n|}{|p_n|}\}<\infty$, we give two sufficient conditions under which that $\mu_{\{p_n\},\{\mathcal D_n\}}$ is a spectral measure. If $p_n=p>2$ and $\mathcal{D}_n=\{0,a_n,b_n\}$ with $\gcd(a_n,b_n)=1$, we also find an useful condition to guarantee that $\mu_{p,\{\mathcal D_n\}}$ is not a spectral measure. Our results extend some known theorems in An et al. [JFA, 2019] and Lu et al. [JFAA, 2022].

math.FA↗

arXiv2025

Many-body electronic structure in pyrochlore superconductor CsBi2 and spin liquid Pr2Ir2O7

The pyrochlore lattice materials can exhibit geometrical frustration, while the related many-body electronic states remain elusive. In this work, we performed scanning tunneling microscopy measurements on the pyrochlore superconductor CsBi2 and spin liquid Pr2Ir2O7 at 0.3 K. For the first time, we obtained atomically resolved images of their (111) surfaces, revealing a hexagonal lattice or a kagome lattice. Tunneling spectroscopy in CsBi2 reveals a nearly fully opened superconductivity gap. The ratio of 2{\Delta}/kBTC = 4.7 suggests relatively strong coupling superconductivity, as compared with that in kagome superconductors AV3Sb5 (A = K, Rb, Cs). In contrast to the previous study categorizing CsBi2 as a type-I superconductor, the applied magnetic field induces a hexagonal vortex lattice in which each vortex core exhibits an intriguing three-fold symmetry state. In Pr2Ir2O7, we observed a spatially homogeneous Kondo-lattice resonance, which is compared with that in the kagome Kondo-lattice material CsCr6Sb6. We further discover that the Kondo resonance exhibits a spatial modulation with three-fold symmetry, and the applied magnetic field induces a Zeeman splitting of the Kondo resonance with intriguing atomic site dependence. We discuss the relations of these many-body electronic phenomena with the pyrochlore lattice geometry and its charge or spin frustration. Our systematic observations offer atomic-scale insights into the many-body electronic structures of the geometrically frustrated pyrochlore superconductors and spin liquids.

cond-mat.str-el↗

arXiv2025

Switchable chiral 2x2 pair density wave in pure CsV3Sb5

We investigate electron pairing in a super clean kagome superconductor CsV3Sb5 with a residual resistivity ratio (RRR) of 290. By using the dilution-refrigerator-based scanning tunneling microscopy (STM) at the Synergetic Extreme Condition User Facility (SECUF), we find that the pairing gap exhibits chiral 2x2 modulations, and their chirality can be controlled by magnetic field training. We introduce nonmagnetic impurities to observe the complete suppression of 2x2 pairing modulations in presence of persistent 2x2 charge order. This nonmagnetic pair-breaking effect provides phase-sensitive evidence for pair-density-wave (PDW) induced pairing modulations. Our results support switchable chiral 2x2 PDW in this super clean kagome superconductor.

cond-mat.supr-con↗

arXiv2025

Phase-sensitive evidence for pair density waves in a kagome superconductor

Pair density wave (PDW) exhibits periodic amplitude and sign modulations of the superconducting order parameter. Such a pairing state has long been proposed to be highly sensitive to nonmagnetic scattering, but its experimental realization remains elusive. Here we discover a nonmagnetic PDW-breaking effect in a kagome superconductor, using designer atomic nonmagnetic impurities and high-precision scanning tunneling microscopy (STM) at a base temperature of 30mK. We detect 2x2 pair density modulations by Josephson STM with a superconducting tip and 2x2 pairing gap modulations by normal STM. We find that the pairing modulations in both cases are substantially suppressed upon doping the kagome lattice with dilute isovalent nonmagnetic impurities, whereas the charge order and uniform superconductivity remain robust. We further identify the correlation between atomic dopants and the local suppression of PDW. We attribute these findings to a nonmagnetic pair-breaking effect, arising from the phase modulation of PDW in the kagome d-orbital. Taken together with its signatures in other state-of-the-art spectroscopy and transport measurements linked by theory, our findings support the ground state of the kagome superconductor as a correlated topological phase with superconducting loop currents.

cond-mat.supr-con↗

arXiv2025

Spectral properties of a class of Sierpinski-type Moran measures on $ \mathbb{R}^n $

Let the infinite convolutions \begin{equation*} \mu_{\{R_{k}\},\{D_{k}\}}=\delta_{R_{1}^{-1}D_{1}}*\delta_{R_{1}^{-1}R_{2}^{-1}D_{2}}*\delta_{R_{1}^{-1}R_{2}^{-1}R_{3}^{-1}D_{3}}*\dotsi \end{equation*} be generated by the sequence of pairs $\{ (R_k,D_k) \}_{k=1}^{\infty} $, where $ R_k\in M_n(\mathbb{Z})$ is an expanding integer matric, $D_k$ is a finite integer digit sets that satisfies the following two conditions: (i). $ \# D_k = m $ and $ m>2 $ is a prime; (ii). $ \{x: \sum_{d\in D_{k}}e^{2\pi i\langle d,x \rangle}=0\} =\cup_{i=1}^{\phi(k)}\cup_{j=1}^{m-1}(\frac{j}{m}\nu_{k,i}+\mathbb{Z}^{n}) $ for some $ \nu_{k,i} \in \{ (l_1, \cdots, l_n)^t : l_i \in [1, m-1] \cap \mathbb{Z}, 1\leq i\leq n \} $. In this paper, we study the spectrality of $\mu_{\{R_{k}\},\{D_{k}\}}$, and some necessary and sufficient conditions for $ L^{2}(\mu_{\{R_{k}\},\{D_{k}\}}) $ to have an orthogonal exponential function basis are established. Finally, we discuss the explanations and applications of our results.

math.CA↗

arXiv2024

Evidence chain for time-reversal symmetry-breaking kagome superconductivity

Superconductivity and magnetism are antagonistic quantum matter, while their intertwining has long been considered in frustrated-lattice systems1-3. In this work, we utilize scanning tunneling microscopy and muon spin resonance to discover time-reversal symmetry-breaking superconductivity in kagome metal Cs(V,Ta)3Sb5, where the Cooper pairing exhibits magnetism and is modulated by it. In the magnetic channel, we observe spontaneous internal magnetism in a full-gap superconducting state. Under perturbations of inverse magnetic fields, we detect a time-reversal asymmetrical interference of Bogoliubov quasi-particles at a circular vector. At this vector, the pairing gap spontaneously modulates, which is distinct from pair density waves occurring at a point vector and consistent with the theoretical proposal of unusual interference effect under time-reversal symmetry-breaking. The correlation between internal magnetism, Bogoliubov quasi-particles, and pairing modulation provides a chain of experimental clues for time-reversal symmetry-breaking kagome superconductivity.

cond-mat.supr-con↗

arXiv2024

Chiral kagome superconductivity modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5

Superconductivity involving finite momentum pairing can lead to spatial gap and pair density modulations, as well as Bogoliubov Fermi states within the superconducting gap. However, the experimental realization of their intertwined relations has been challenging. Here, we detect chiral kagome superconductivity modulations with residual Fermi arcs in KV3Sb5 and CsV3Sb5 by normal and Josephson scanning tunneling microscopy down to 30mK with resolved electronic energy difference at microelectronvolt level. We observe a U-shaped superconducting gap with flat residual in-gap states. This gap exhibits chiral 2 by 2 spatial modulations with magnetic field tunable chirality, which align with the chiral 2 by 2 pair density modulations observed through Josephson tunneling. These findings demonstrate a chiral pair density wave (PDW) that breaks time-reversal symmetry. Quasiparticle interference imaging of the in-gap zero-energy states reveals segmented arcs, with high-temperature data linking them to parts of the reconstructed V d-orbital states within the charge order. The detected residual Fermi arcs can be explained by the partial suppression of these d-orbital states through an interorbital 2 by 2 PDW and thus serve as candidate Bogoliubov Fermi states. Additionally, we differentiate the observed PDW order from impurity-induced gap modulations. Our observations not only uncover a chiral PDW order with orbital-selectivity, but also illuminate the fundamental space-momentum correspondence inherent in finite momentum paired superconductivity.

cond-mat.supr-con↗

arXiv2024

Chiral pair density waves with residual Fermi arcs in RbV3Sb5

The chiral 2 by 2 charge order has been reported and confirmed in the kagome superconductor RbV3Sb5, while its interplay with superconductivity remains elusive owing to its lowest superconducting transition temperature Tc of about 0.85K among the AV3Sb5 family (A=K, Rb, Cs) that severely challenges electronic spectroscopic probes. Here, utilizing dilution-refrigerator-based scanning tunneling microscopy (STM) down to 30mK, we observe chiral 2 by 2 pair density waves with residual Fermi arcs in RbV3Sb5. We find a superconducting gap of 150{\mu}eV with substantial residual in-gap states. The spatial distribution of this gap exhibits chiral 2 by 2 modulations, signaling a chiral pair density wave (PDW). Our quasi-particle interference imaging of the zero-energy residual states further reveals arc-like patterns. We discuss the relation of the gap modulations with the residual Fermi arcs under the space-momentum correspondence between PDW and Bogoliubov Fermi states.

cond-mat.supr-con↗

arXiv2021

Degradiation of $β$-Ga$_2$O$_3$ Schottky barrier diode under swift heavy ion irradiation

The electrical characteristics and microstructures of $β$-Ga$_2$O$_3$ Schottky barrier diode (SBD) devices irradiated with swift heavy ions (2096 MeV Ta ions) have been studied. It was found that $β$-Ga$_2$O$_3$ SBD devices showed the reliability degradation after irradiation, including turn-on voltage Von, on-resistance Ron, ideality factor n and the reverse leakage current density Jr. In addition, the carrier concentration of the drift layer was decreased significantly and the calculated carrier removal rates were 5*106 - 1.3*107 cm-1. Latent tracks induced by swift heavy ions were observed visually in the whole $β$-Ga$_2$O$_3$ matrix. Furthermore, crystal structure of tracks was amorphized completely. The latent tracks induced by Ta ions bombardments were found to be the reason for the decrease in carrier mobility and carrier concentration. Eventually, these defects caused the degradation of electrical characteristics of the devices. By comparing the carrier removal rates, the $β$-Ga$_2$O$_3$ SBD devices were more sensitive to swift heavy ions irradiation than SiC and GaN devices.

cond-mat.mtrl-sci↗