arXiv subjects

Jun Ge

Publications and source records attributed to Jun Ge.

At least 37 records · Page 2Linked to original sources

arXiv2021

Some new results on bar visibility of digraphs

Visibility representation of digraphs was introduced by Axenovich, Beveridge, Hutch\-inson, and West (\emph{SIAM J. Discrete Math.} {\bf 27}(3) (2013) 1429--1449) as a natural generalization of $t$-bar visibility representation of undirected graphs. A {\it $t$-bar visibility representation} of a digraph $G$ assigns each vertex at most $t$ horizontal bars in the plane so that there is an arc $xy$ in the digraph if and only if some bar for $x$ "sees" some bar for $y$ above it along an unblocked vertical strip with positive width. The {\it visibility number} $b(G)$ is the least $t$ such that $G$ has a $t$-bar visibility representation. In this paper, we solve several problems about $b(G)$ posed by Axenovich et al.\ and prove that determining whether the bar visibility number of a digraph is $2$ is NP-complete.

math.CO↗

arXiv2021

Extrinsic and Intrinsic Anomalous Metallic States in Transition Metal Dichalcogenide Ising Superconductors

The metallic ground state in two-dimensional (2D) superconductors has attracted much attention but is still under intense scrutiny. Especially, the measurements in ultralow temperature region are challenging for 2D superconductors due to the sensitivity to external perturbations. In this work, the resistance saturation induced by external noise, named as "extrinsic anomalous metallic state", is observed in 2D transition metal dichalcogenide (TMD) superconductor 4Ha-TaSe2 nanodevices. However, with further decreasing temperature, credible evidence of intrinsic anomalous metallic state is obtained by adequately filtering external radiation. Our work indicates that at ultralow temperatures the anomalous metallic state can be experimentally revealed as the quantum ground state in 2D crystalline TMD superconductors. Besides, Ising superconductivity revealed by ultrahigh in-plane critical field (Bc2//) going beyond the Pauli paramagnetic limit (Bp) is detected in 4Ha-TaSe2, from one-unit-cell device to bulk situation, which might be due to the weak coupling between the TaSe2 sub-monolayers.

cond-mat.supr-con↗

arXiv2021

Magnetization-tuned topological quantum phase transition in MnBi2Te4 devices

Recently, the intrinsic magnetic topological insulator MnBi2Te4 has attracted enormous research interest due to the great success in realizing exotic topological quantum states, such as the quantum anomalous Hall effect (QAHE), axion insulator state, high-Chern-number and high-temperature Chern insulator states. One key issue in this field is to effectively manipulate these states and control topological phase transitions. Here, by systematic angle-dependent transport measurements, we reveal a magnetization-tuned topological quantum phase transition from Chern insulator to magnetic insulator with gapped Dirac surface states in MnBi2Te4 devices. Specifically, as the magnetic field is tilted away from the out-of-plane direction by around 40-60 degrees, the Hall resistance deviates from the quantization value and a colossal, anisotropic magnetoresistance is detected. The theoretical analyses based on modified Landauer-Buttiker formalism show that the field-tilt-driven switching from ferromagnetic state to canted antiferromagnetic state induces a topological quantum phase transition from Chern insulator to magnetic insulator with gapped Dirac surface states in MnBi2Te4 devices. Our work provides an efficient means for modulating topological quantum states and topological quantum phase transitions.

cond-mat.mes-hall↗

arXiv2021

Intrinsic magnetic topological insulators

Introducing magnetism into topological insulators breaks time-reversal symmetry, and the magnetic exchange interaction can open a gap in the otherwise gapless topological surface states. This allows various novel topological quantum states to be generated, including the quantum anomalous Hall effect (QAHE) and axion insulator states. Magnetic doping and magnetic proximity are viewed as being useful means of exploring the interaction between topology and magnetism. However, the inhomogeneity of magnetic doping leads to complicated magnetic ordering and small exchange gaps, and consequently the observed QAHE appears only at ultralow temperatures. Therefore, intrinsic magnetic topological insulators are highly desired for increasing the QAHE working temperature and for investigating topological quantum phenomena further. The realization and characterization of such systems are essential for both fundamental physics and potential technical revolutions. This review summarizes recent research progress in intrinsic magnetic topological insulators, focusing mainly on the antiferromagnetic topological insulator MnBi2Te4 and its family of materials.

cond-mat.mes-hall↗

arXiv2020

Induced anomalous Hall effect of massive Dirac fermions in ZrTe5 and HfTe5 thin flakes

Researches on anomalous Hall effect (AHE) have been lasting for a century to make clear the underlying physical mechanism. Generally, the AHE appears in magnetic materials, in which extrinsic process related to scattering effects and intrinsic contribution connected with Berry curvature are crucial. Recently, AHE has been counterintuitively observed in non-magnetic topological materials and attributed to the existence of Weyl points. However, the Weyl point scenario would lead to unsaturated AHE even in large magnetic fields and contradicts the saturation of AHE in several tesla (T) in experiments. In this work, we investigate the Hall effect of ZrTe5 and HfTe5 thin flakes in static ultrahigh magnetic fields up to 33 T. We find the AHE saturates to 55 (70) Ohm^-1*cm^-1 for ZrTe5 (HfTe5) thin flakes above ~ 10 T. Combining detailed magnetotransport experiments and Berry curvature calculations, we clarify that the splitting of massive Dirac bands without Weyl points can be responsible for AHE in non-magnetic topological materials ZrTe5 and HfTe5 thin flakes. This model can identify our thin flake samples to be weak topological insulators and serve as a new tool to probe the band structure topology in topological materials.

cond-mat.mtrl-sci↗

arXiv2020

Tunable discrete scale invariance in transition-metal pentatelluride flakes

Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials.

cond-mat.mtrl-sci↗

arXiv2020

Upper bounds on the signed edge domination number of a graph

A signed edge domination function (or SEDF) of a simple graph $G=(V,E)$ is a function $f: E\rightarrow \{1,-1\}$ such that $\sum_{e'\in N[e]}f(e')\ge 1$ holds for each edge $e\in E$, where $N[e]$ is the set of edges in $G$ that share at least one endpoint with $e$. Let $γ_s'(G)$ denote the minimum value of $f(G)$ among all SEDFs $f$, where $f(G)=\sum_{e\in E}f(e)$.In 2005, Xu conjectured that $γ_s'(G)\le n-1$, where $n$ is the order of $G$. This conjecture has been proved for the two cases $v_{odd}(G)=0$ and $v_{even}(G)=0$, where $v_{odd}(G)$ (resp. $v_{even}(G)$) is the number of odd (resp. even) vertices in $G$. This article proves Xu's conjecture for $v_{even}(G)\in \{1, 2\}$. We also show that for any simple graph $G$ of order $n$, $γ_s'(G)\le n+v_{odd}(G)/2$ and $γ_s'(G)\le n-2+v_{even}(G)$ when $v_{even}(G)>0$, and thus $γ_s'(G)\le (4n-2)/3$. Our result improves the best current upper bound of $γ_s'(G)\le \lceil 3n/2\rceil$.

math.CO↗

arXiv2020

Surface Superconductivity in the type II Weyl Semimetal TaIrTe4

The search for unconventional superconductivity in Weyl semimetal materials is currently an exciting pursuit, since such superconducting phases could potentially be topologically nontrivial and host exotic Majorana modes. The layered material TaIrTe4 is a newly predicted time-reversal invariant type II Weyl semimetal with minimum number of Weyl points. Here, we report the discovery of surface superconductivity in Weyl semimetal TaIrTe4. Our scanning tunneling microscopy/spectroscopy (STM/S) visualizes Fermi arc surface states of TaIrTe4 that are consistent with the previous angle-resolved photoemission spectroscopy (ARPES) results. By a systematic study based on STS at ultralow temperature, we observe uniform superconducting gaps on the sample surface. The superconductivity is further confirmed by electrical transport measurements at ultralow temperature, with an onset transition temperature (Tc) up to 1.54 K being observed. The normalized upper critical field h*(T/Tc) behavior and the stability of the superconductivity against the ferromagnet indicate that the discovered superconductivity is unconventional with the p-wave pairing. The systematic STS, thickness and angular dependent transport measurements reveal that the detected superconductivity is quasi-one-dimensional (quasi-1D) and occurs in the surface states. The discovery of the surface superconductivity in TaIrTe4 provides a new novel platform to explore topological superconductivity and Majorana modes.

cond-mat.supr-con↗

arXiv2020

Phase-coherent asynchronous optical sampling system

Mutual phase coherence is the most crucial factor in asynchronous optical sampling system, and its enhancement is commonly achieved by phase-locking both femtosecond lasers to a shared narrow-linewidth cavity-stabilized laser. Here we report such a system with a low residual optical phase jitter at a level of 0.04 rad in a Fourier frequency band from 1 Hz to 5 MHz around 1.55 μm, corresponding to a timing jitter of 30 as. The residual phase jitter reaches 1 rad at a Fourier frequency between 0.06 Hz and 0.1 Hz, from which the phase-coherence time is inferred at least 10 s. The multi-heterodyne beats experimentally reveal a hardware-limited phase coherence time of ~8.15 s throughout the direct lasing spectral band.

physics.optics↗

arXiv2020

Proving a conjecture on chromatic polynomials by counting the number of acyclic orientations

The chromatic polynomial $P(G,x)$ of a graph $G$ of order $n$ can be expressed as $\sum\limits_{i=1}^n(-1)^{n-i}a_{i}x^i$, where $a_i$ is interpreted as the number of broken-cycle free spanning subgraphs of $G$ with exactly $i$ components. The parameter $ε(G)=\sum\limits_{i=1}^n (n-i)a_i/\sum\limits_{i=1}^n a_i$ is the mean size of a broken-cycle-free spanning subgraph of $G$. In this article, we confirm and strengthen a conjecture proposed by Lundow and Markström in 2006 that $ε(T_n)< ε(G)<ε(K_n)$ holds for any connected graph $G$ of order $n$ which is neither the complete graph $K_n$ nor a tree $T_n$ of order $n$. The most crucial step of our proof is to obtain the interpretation of all $a_i$'s by the number of acyclic orientations of $G$.

math.CO↗

arXiv2020

Unconventional Hall Effect induced by Berry Curvature

Berry phase and Berry curvature play a key role in the development of topology in physics and do contribute to the transport properties in solid state systems. In this paper, we report the finding of novel nonzero Hall effect in topological material ZrTe5 flakes when in-plane magnetic field is parallel and perpendicular to the current. Surprisingly, both symmetric and antisymmetric components with respect to magnetic field are detected in the in-plane Hall resistivity. Further theoretical analysis suggests that the magnetotransport properties originate from the anomalous velocity induced by Berry curvature in a tilted Weyl semimetal. Our work not only enriches the Hall family but also provides new insights into the Berry phase effect in topological materials.

cond-mat.mes-hall↗

arXiv2020

Eightfold Fermionic Excitation in a Charge Density Wave Compound

Unconventional quasiparticle excitations in condensed matter systems have become one of the most important research frontiers. Beyond two- and fourfold degenerate Weyl and Dirac fermions, three-, six- and eightfold symmetry protected degeneracies have been predicted however remain challenging to realize in solid state materials. Here, charge density wave compound TaTe4 is proposed to hold eightfold fermionic excitation and Dirac point in energy bands. High quality TaTe4 single crystals are prepared, where the charge density wave is revealed by directly imaging the atomic structure and a pseudogap of about 45 meV on the surface. Shubnikov de-Haas oscillations of TaTe4 are consistent with band structure calculation. Scanning tunneling microscopy reveals atomic step edge states on the surface of TaTe4. This work uncovers that charge density wave is able to induce new topological phases and sheds new light on the novel excitations in condensed matter materials.

cond-mat.mtrl-sci↗

arXiv2020

High-Chern-Number and High-Temperature Quantum Hall Effect without Landau Levels

The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 starts the research on topological quantum states and lays the foundation of topology in physics. Afterwards, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C|=1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C>1). Here, we report the experimental discovery of high-Chern-number QHE (C=2) without Landau levels and C=1 Chern insulator state displaying nearly quantized Hall resistance plateau above the Néel temperature in MnBi2Te4 devices. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures.

cond-mat.mes-hall↗

arXiv2019

Spanning trees in complete bipartite graphs and resistance distance in nearly complete bipartite graphs

Using the theory of electrical network, we first obtain a simple formula for the number of spanning trees of a complete bipartite graph containing a certain matching or a certain tree. Then we apply the effective resistance (i.e., resistance distance in graphs) to find a formula for the number of spanning trees in the nearly complete bipartite graph $G(m,n,p)=K_{m,n}-pK_2$ $(p\leq \min\{m,n\})$, which extends a recent result by Ye and Yan who obtained the effective resistances and the number of spanning trees in $G(n,n,p)$. As a corollary, we obtain the Kirchhoff index of $G(m,n,p)$ which extends a previous result by Shi and Chen.

math.CO↗

arXiv2019

Spectral radius and Hamiltonian properties of graphs, II

In this paper, we first present spectral conditions for the existence of $C_{n-1}$ in graphs (2-connected graphs) of order $n$, which are motivated by a conjecture of Erdős. Then we prove spectral conditions for the existence of Hamilton cycles in balanced bipartite graphs. This result presents a spectral analog of Moon-Moser's theorem on Hamilton cycles in balanced bipartite graphs, and extends a previous theorem due to Li and the second author for $n$ sufficiently large. We conclude this paper with two problems on tight spectral conditions for the existence of long cycles of given lengths.

math.CO↗

arXiv2015

Spectral radius and Hamiltonian properties of graphs

Let $G$ be a graph with minimum degree $δ$. The spectral radius of $G$, denoted by $ρ(G)$, is the largest eigenvalue of the adjacency matrix of $G$. In this note we mainly prove the following two results. (1) Let $G$ be a graph on $n\geq 4$ vertices with $δ\geq 1$. If $ρ(G)> n-3$, then $G$ contains a Hamilton path unless $G\in\{K_1\vee (K_{n-3}+2K_1),K_2\vee 4K_1,K_1\vee (K_{1,3}+K_1)\}$. (2) Let $G$ be a graph on $n\geq 14$ vertices with $δ\geq 2$. If $ρ(G)\geq ρ(K_2\vee (K_{n-4}+2K_1))$, then $G$ contains a Hamilton cycle unless $G= K_2\vee (K_{n-4}+2K_1)$. As corollaries of our first result, two previous theorems due to Fiedler and Nikiforov and Lu et al. are obtained, respectively. Our second result refines another previous theorem of Fiedler and Nikiforov.

math.CO↗

arXiv2015

Minimal sufficient sets of colors and minimum number of colors

In this paper we first investigate minimal sufficient sets of colors for p=11 and 13. For odd prime p and any p-colorable link L with non-zero determinant, we give alternative proofs of mincol_p L \geq 5 for p \geq 11 and mincol_p L \geq 6 for p \geq 17. We elaborate on equivalence classes of sets of distinct colors (on a given modulus) and prove that there are two such classes of five colors modulo 11, and only one such class of five colors modulo 13. Finally, we give a positive answer to a question raised by Nakamura, Nakanishi, and Satoh concerning an inequality involving crossing numbers. We show it is an equality only for the trefoil and for the figure-eight knots.

math.GT↗

arXiv2014

Contactless Probing of the Intrinsic Carrier Transport in Single-Walled Carbon Nanotubes

Intrinsic carrier transport properties of single-walled carbon nanotubes are probed by two parallel methods on the same individual tubes: the contactless dielectric force microscopy (DFM) technique and the conventional field-effect transistor (FET) method. The dielectric responses of SWNTs are strongly correlated with electronic transport of the corresponding FETs. The DC bias voltage in DFM plays a role analogous to the gate voltage in FET. A microscopic model based on the general continuity equation and numerical simulation is built to reveal the link between intrinsic properties such as carrier concentration and mobility and the macroscopic observable, i.e. dielectric responses, in DFM experiments. Local transport barriers in nanotubes, which influence the device transport behaviors, are also detected with nanometer scale resolution.

cond-mat.mes-hall↗