arXiv subjects

Liyan Zhu

Publications and source records attributed to Liyan Zhu.

18 recordsLinked to original sources

arXiv2026

Motional-Current-Sensing Method and Simplified Closed-Loop Control Strategy for Piezoelectric-Resonator-based DC-DC Converters

Piezoelectric resonators (PRs) have been seen as a competitive alternative to magnetic components. In PR-based converters, the motional current (in the LC series branch of the equivalent circuit) is vital for control proposes but cannot be measured directly. The difficulties to detect the zero-crossing points or to measure the amplitude of the motional current has been one of the most dominating obstacles that complicates the control strategies and limits the frequency range of the PR-based converters. This work discusses a ring-dot shaped piezoelectric transformer (PT) based motional current sensing method that provides current information with low-delay, low-loss and intrinsic isolation. It is physically proven that the proposed method is robust with various non-ideal factors of the piezoceramic and circuit implementation. Based on this, an event-driven control strategy is introduced, consisting of only a finite state machine, a PI loop, a low-speed ADC and several comparators. Experiments on a step-down PR-based converter verify that the proposed approach realize ZVS for all transitions within a switching cycle with reduced hardware and software resources, enhances stability and is capable of self-startup.

physics.app-ph↗

arXiv2026

Nonlinear exceptional points in an integrated acoustic-wave oscillator for longwave infrared sensing

Exceptional points (EP) featuring enhanced responsivity and rich dynamics have attracted extensive attentions in device developments and sensing applications. However, it remains debated whether employing EP systems is beneficial in practical sensing applications. Here, we demonstrate that a nonlinear EP in our microwave-frequency acoustic-wave oscillator improves longwave infrared (LWIR) detection under practical conditions. By phase tuning the nonlinear gain, our detector can be operated at different conditions with respect to the nonlinear EP. Compared with operation away from EP, our detector at EP shows a 33-fold improvement in responsivity and an 8.75-fold extension of 3-dB bandwidth. We observe a 6-fold enhancement in signal-to-noise ratio at an input modulation frequency of 6.2 kHz. At the incident LWIR wavelength of 9.6 um, our detector at EP exhibits a noise equivalent power (NEP) of 310 pW*Hz^-1/2 at input frequency of 10 kHz, yielding a figure of merit, product of NEP and time constant, of 9.87*10^-3 pW*Hz^-3/2, a 10-fold improvement over operation away from EP. Our integrated acoustic devices offer a versatile platform for exploring noise dynamics and developing practical sensors that exploit non-Hermitian nonlinearities.

physics.optics↗

arXiv2026

Microwave-acoustic-based isolated gate driver for power electronics

Electrical isolation is critical to ensure safety and minimize electromagnetic interference (EMI), yet existing methods struggle to simultaneously transmit power and signals through a unified channel. Here we demonstrate a mechanically-isolated gate driver based on microwave-frequency surface acoustic wave (SAW) device on lithium niobate that achieves galvanic isolation of 2.75 kV with ultralow isolation capacitance (0.032 pF) over 1.25 mm mechanical propagation length, delivering 13.4 V open-circuit voltage and 44.4 mA short-circuit current. We demonstrate isolated gate driving for a gallium nitride (GaN) high-electron-mobility transistor, achieving a turn-on time of 108.8 ns comparable to commercial drivers and validate its operation in a buck converter. In addition, our SAW device operates over an ultrawide temperature range from 0.5 K (-272.6 °C) to 544 K (271 °C). The microwave-frequency SAW devices offer inherent EMI immunity and potential for heterogeneous integration on multiple semiconductor platforms, enabling compact, high-performance isolated power and signal transmission in advanced power electronics.

eess.SY↗

arXiv2026

On-chip cavity electro-acoustics using lithium niobate phononic crystal resonators

Mechanical systems are pivotal in quantum technologies because of their long coherent time and versatile coupling to qubit systems. So far, the coherent and dynamic control of gigahertz-frequency mechanical modes mostly relies on optomechanical coupling and piezoelectric coupling to superconducting qubits. Here, we demonstrate on-chip cavity electro-acoustic dynamics using our microwave-frequency electrically-modulated phononic-crystal (PnC) resonators on lithium niobate (LN). Leveraging the high dispersion of PnC, our phononic modes space unevenly in the frequency spectrum, emulating atomic energy levels. Atomic-like transitions between different phononic modes are achieved by applying electrical fields to modulate phononic modes via nonlinear piezoelectricity of LN. Among two modes, we demonstrate Autler-Townes splitting (ATS), alternating current (a.c.) Stark shift, and Rabi oscillation with a maximum cooperativity of 4.18. Extending to three modes, we achieve non-reciprocal frequency conversions with an isolation up to 20 dB. Nonreciprocity can be tuned by the time delay between the two modulating pulses. Our cavity electro-acoustic platform could find broad applications in sensing, microwave signal processing, phononic computing, and quantum acoustics.

cond-mat.mes-hall↗

arXiv2025

Inverse conductivity problem with one measurement: Uniqueness of multi-layer structures

In this paper, we study the recovery of multi-layer structures in inverse conductivity problem by using one measurement. First, we define the concept of Generalized Polarization Tensors (GPTs) for multi-layered medium and show some important properties of the proposed GPTs. With the help of GPTs, we present the perturbation formula for general multi-layered medium. Then we derive the perturbed electric potential for multi-layer concentric disks structure in terms of the so-called generalized polarization matrix, whose dimension is the same as the number of the layers. By delicate analysis, we derive an algebraic identity involving the geometric and material configurations of multi-layer concentric disks. This enables us to reconstruct the multi-layer structures by using only one partial-order measurement.

math.AP↗

arXiv2025

Spectral theory of the Neumann-Poincaré operator on multi-layer structures and analysis of plasmon mode splitting

In this paper, we develop a general mathematical framework for analyzing electostatics within multi-layered metamaterial structures. The multi-layered structure can be designed by nesting complementary negative and regular materials together, and it can be easily achieved by truncating bulk metallic material in a specific configuration. Using layer potentials and symmetrization techniques, we establish the perturbation formula in terms of Neumann-Poincaré (NP) operator for general multi-layered medium, and obtain the spectral properties of the NP operator, which demonstrates that the number of plasmon modes increases with the number of layers. Based on Fourier series, we present an exact matrix representation of the NP operator in an apparently unsymmetrical structure, exemplified by multi-layered confocal ellipses. By highly intricate and delicate analysis, we establish a handy algebraic framework for studying the splitting of the plasmon modes within multi-layered structures. Moreover, the asymptotic profiles of the plasmon modes are also obtained. This framework helps reveal the effects of material truncation and rotational symmetry breaking on the splitting of the plasmon modes, thereby inducing desired resonances and enabling the realization of customized applications.

math.AP↗

arXiv2025

Mathematical analysis of subwavelength resonant acoustic scattering in multi-layered high-contrast structures

Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in a structure of $N$-layer nested resonators. Firstly, based on the Dirichlet-to-Neumann approach, we reduce the solution of the acoustic scattering problem to an $N$-dimensional linear system, and derive the optimal asymptotic characterization of subwavelength resonant frequencies in terms of the eigenvalues of an $N\times N$ tridiagonal matrix, which we refer to as the generalized capacitance matrix. Moreover, we provide a modal decomposition formula for the scattered field, as well as a monopole approximation for the far-field pattern of the acoustic wave scattered by the $N$-layer nested resonators. Finally, some numerical results are presented to corroborate the theoretical findings.

math.AP↗

arXiv2024

Mathematical theory on multi-layer high contrast acoustic subwavelength resonators

Subwavelength resonance is a vital acoustic phenomenon in contrasting media. The narrow bandgap width of single-layer resonator has prompted the exploration of multi-layer metamaterials as an effective alternative, which consist of alternating nests of high-contrast materials, called ``resonators'', and a background media. In this paper, we develop a general mathematical framework for studying acoustics within multi-layer high-contrast structures. Firstly, by using layer potential techniques, we establish the representation formula in terms of a matrix type operator with a block tridiagonal form for multi-layer structures within general geometry. Then we prove the existence of subwavelength resonances via Gohberg-Sigal theory, which generalizes the celebrated Minnaert resonances in single-layer structures. Intriguingly, we find that the primary contribution to mode splitting lies in the fact that as the number of nested resonators increases, the degree of the corresponding characteristic polynomial also increases, while the type of resonance (consists solely of monopolar resonances) remains unchanged. Furthermore, we derive original formulas for the subwavelength resonance frequencies of concentric dual-resonator. Numerical results associated with different nested resonators are presented to corroborate the theoretical findings.

math-ph↗

arXiv2024

Optimal estimate of electromagnetic field concentration between two nearly-touching inclusions in the quasi-static regime

We investigate the electromagnetic field concentration between two nearly-touching inclusions that possess high-contrast electric permittivities in the quasi-static regime. By using layer potential techniques and asymptotic analysis in the low-frequency regime, we derive low-frequency expansions that provide integral representations for the solutions of the Maxwell equations. For the leading-order term $\bE_0$ of the asymptotic expansion of the electric field, we prove that it has the blow up order of $ε^{-1} |\ln ε|^{-1}$ within the radial geometry, where $ε$ signifies the asymptotic distance between the inclusions. By delicate analysis of the integral operators involved, we further prove the boundedness of the first-order term $\bE_1$. We also conduct extensive numerical experiments which not only corroborate the theoretical findings but also provide more discoveries on the field concentration in the general geometric setup. Our study provides the first treatment in the literature on field concentration between nearly-touching material inclusions for the full Maxwell system.

math.AP↗

arXiv2023

Elastostatics with multi-layer metamaterial structures and an algebraic framework for polariton resonances

Multi-layer structures are ubiquitous in constructing metamaterial devices to realise various frontier applications including super-resolution imaging and invisibility cloaking. In this paper, we develop a general mathematical framework for studying elastostatics within multi-layer material structures in $\mathbb{R}^d$, $d=2,3$. The multi-layer structure is formed by concentric balls and each layer is filled by either a regular elastic material or an elastic metamaterial. The number of layers can be arbitrary and the material parameters in each layer may be different from one another. In practice, the multi-layer structure can serve as the building block for various material devices. Considering the impingement of an incident field on the multi-layer structure, we first derive the exact perturbed field in terms of an elastic momentum matrix, whose dimension is the same as the number of layers. By highly intricate and delicate analysis, we derive a comprehensive study of the spectral properties of the elastic momentum matrix. This enables us to establishe a handy algebraic framework for studying polariton resonances associated with multi-layer metamaterial structures, which forms the fundamental basis for many metamaterial applications.

physics.class-ph↗

arXiv2020

Simultaneous recovery of surface heat flux and thickness of a solid structure by ultrasonic measurements

This paper is concerned with a practical inverse problem of simultaneously reconstructing the surface heat flux and the thickness of a solid structure from the associated ultrasonic measurements. In a thermoacoustic coupling model, the thermal boundary condition and the thickness of a solid structure are both unknown, while the measurements of the propagation time by ultrasonic sensors are given. We reformulate the inverse problem as a PDE-constrained optimization problem by constructing a proper objective functional. We then develop an alternating iteration scheme which combines the conjugate gradient method and the deepest decent method to solve the optimization problem. Rigorous convergence analysis is provided for the proposed numerical scheme. By using experimental real data from the lab, we conduct extensive numerical experiments to verify several promising features of the newly developed method.

math.NA↗

arXiv2019

The Strength of Mechanically-Exfoliated Monolayer Graphene

The deformation and fracture behaviour of one-atom-thick mechanically exfoliated graphene has been studied in detail. Monolayer graphene flakes with different lengths, widths and shapes were successfully prepared by mechanical exfoliation and deposited onto poly(methyl methacrylate) (PMMA) beams. The fracture behaviour of the monolayer graphene was followed by deforming the PMMA beams. Through in-situ Raman mapping at different strain levels, the distributions of strain over the graphene flakes were determined from the shift of the graphene Raman 2D band. The failure mechanisms of the exfoliated graphene were either by flake fracture or failure of the graphene/polymer interface. The fracture of the flakes was observed from the formation of cracks identified from the appearance of lines of zero strain in the strain contour maps. It was found that the strength of the monolayer graphene flakes decreased with increasing flake width. The strength dropped to less than 10 GPa for large flakes, much lower than the reported value of 130 GPa for monolayer graphene, thought to be due to the presence of defects. It is shown that a pair of topological defects in monolayer graphene will form a pseudo crack and the effect of such defects upon the strength of monolayer graphene has been modelled using molecular mechanical simulations.

cond-mat.mtrl-sci↗

arXiv2018

Monolayer Mg$_{2}$C: Negative Poisson's ratio and unconventional 2D emergent fermions

Novel two-dimensional (2D) emergent fermions and negative Poisson's ratio in 2D materials are fascinating subjects of research. Here, based on first-principles calculations and theoretical analysis, we predict that the hexacoordinated Mg$_{2}$C monolayer hosts both exotic properties. We analyze its phonon spectrum, reveal the Raman active modes, and show that it has small in-plane stiffness constants. Particularly, under the tensile strain in the zigzag direction, the Mg$_{2}$C monolayer shows an intrinsic negative Poisson's ratio $\sim -0.023$, stemming from its unique puckered hinge structure. The material is metallic at its equilibrium state. A moderate biaxial strain can induce a metal-semimetal-semiconductor phase transition, during which several novel types of 2D fermions emerge, including the anisotropic Dirac fermions around 12 tilted Dirac points in the metallic phase, the $2$D double Weyl fermions in the semimetal phase where the conduction and valence bands touch quadratically at a single Fermi point, and the 2D pseudospin-1 fermions at the critical point of the semimetal-semiconductor phase transition where three bands cross at a single point on the Fermi level. In addition, uniaxial strains along the high-symmetry directions break the three-fold rotational symmetry and reduce the number of Dirac points. Interestingly, it also generates 2D type-II Dirac points. We construct effective models to characterize the properties of these novel fermions. Our result reveals Mg$_{2}$C monolayer as an intriguing platform for the study of novel 2D fermions, and also suggests its great potential for nanoscale device applications.

cond-mat.mes-hall↗

arXiv2017

Engineering the thermal conductivity along an individual silicon nanowire by selective helium ion irradiation

The ability to engineer the thermal conductivity of materials allows us to control the flow of heat and derive novel functionalities such as thermal rectification, thermal switching, and thermal cloaking. While this could be achieved by making use of composites and metamaterials at bulk scales, engineering the thermal conductivity at micro- and nano-scale dimensions is considerably more challenging. In this work we show that the local thermal conductivity along a single Si nanowire can be tuned to a desired value (between crystalline and amorphous limits) with high spatial resolution through selective helium ion irradiation with a well-controlled dose. The underlying mechanism is understood through molecular dynamics simulations and quantitative phonon-defect scattering rate analysis, where the behavior of thermal conductivity with dose is attributed to the accumulation and agglomeration of scattering centers at lower doses. Beyond a threshold dose, a crystalline-amorphous transition was observed.

cond-mat.mtrl-sci↗

arXiv2016

Blue Phosphorene Oxide: Strain-tunable Quantum Phase Transitions and Novel 2D Emergent Fermions

Tunable quantum phase transitions and novel emergent fermions in solid state materials are fascinating subjects of research. Here, we propose a new stable two-dimensional (2D) material, the blue phosphorene oxide (BPO), which exhibits both. Based on first-principles calculations, we show that its equilibrium state is a narrow-bandgap semiconductor with three bands at low energy. Remarkably, a moderate strain can drive a semiconductor-to-semimetal quantum phase transition in BPO. At the critical transition point, the three bands cross at a single point at Fermi level, around which the quasiparticles are a novel type of 2D pseudospin-1 fermions. Going beyond the transition, the system becomes a symmetry-protected semimetal, for which the conduction and valence bands touch quadratically at a single Fermi point that is protected by symmetry, and the low-energy quasiparticles become another novel type of 2D double Weyl fermions. We construct effective models characterizing the phase transition and these novel emergent fermions, and we point out several exotic effects, including super Klein tunneling, supercollimation, and universal optical absorbance. Our result reveals BPO as an intriguing platform for the exploration of fundamental properties of quantum phase transitions and novel emergent fermions, and also suggests its great potential in nanoscale device applications.

cond-mat.mtrl-sci↗

arXiv2015

Direction dependent thermal conductivity of monolayer phosphorene: parameterization of Stillinger-Weber potential and molecular dynamics study

A Stillinger-Weber interatomic potential is parameterized for phosphorene. It well reproduces the crystal structure, cohesive energy and phonon dispersion predicted by first-principles calculations. The thermal conductivity of phosphorene is further explored by equilibrium molecular dynamics simulations adopting the optimal set of potential parameters. At room temperature, the intrinsic thermal conductivities along zigzag and armchair directions are about 152.7 and 33.0 W/mK, respectively, with a large anisotropy ratio of five. The remarkably directional dependence of thermal conductivity in phosphorene, consistent with previous reports, is mainly due to the strong anisotropy of phonon group velocities, and weak anisotropy of phonon lifetimes as revealed by lattice dynamics calculations. Moreover, the effective phonon mean free paths at zigzag and armchair directions are about 141.4 and 43.4nm, respectively.

cond-mat.mes-hall↗

arXiv2015

Electronic, Dielectric, and Plasmonic Properties of Two-Dimensional Electride Materials X$_2$N (X=Ca, Sr): A First-Principles Study

Based on first-principles calculations, we systematically study the electronic, dielectric, and plasmonic properties of two-dimensional (2D) electride materials X$_2$N (X=Ca, Sr). We show that both Ca$_2$N and Sr$_2$N are stable down to monolayer thickness. For thicknesses larger than 1-monolayer (1-ML), there are 2D anionic electron layers confined in the regions between the [X$_2$N]$^+$ layers. These electron layers are strongly trapped and have weak coupling between each other. As a result, for the thickness dependence of many properties such as the surface energy, work function, and dielectric function, the most dramatic change occurs when going from 1-ML to 2-ML. For both bulk and few-layer Ca$_2$N and Sr$_2$N, the in-plane and out-of-plane real components of their dielectric functions have different signs in an extended frequency range covering the near infrared, indicating their potential applications as indefinite media. We find that bulk Ca$_2$N and Sr$_2$N could support surface plasmon modes in the near infrared range. Moreover, tightly-bounded plasmon modes could exist in their few-layer structures. These modes have significantly shorter wavelengths (~few tens of nanometers) compared with that of conventional noble metal materials, suggesting their great potential for plasmonic devices with much smaller dimensions.

cond-mat.mtrl-sci↗

arXiv2014

Co-existence of size-dependent and size-independent thermal conductivities in single layer black phosphorus

Thermal conductivity of single layer black phosphorus (BP) is investigated by combining density functional calculations and Peierls-Boltzmann transport equation. Differing from isotropic and divergent thermal conductivities in two-dimensional graphene and MoS$_2$, an compelling co-existence of size-dependent and size-independent thermal conductivities are discovered for single layer BP along zigzag (ZZ) and armchair (AM) direction, respectively. Besides, thermal conductivities in single layer BP are found to be highly anisotropic because of orientation dependent group velocities, e.g., thermal conductivities at 300 K are 83.5 and 24.3 W/m-K along ZZ and AM directions for single layer BP with a size of 10 $μm$, respectively.

cond-mat.mtrl-sci↗