arXiv subjects

Zhiyuan Sun

Publications and source records attributed to Zhiyuan Sun.

71 records · Page 4Linked to original sources

arXiv2020

Collective modes and terahertz near-field response of superconductors

We theoretically study the low energy electromagnetic response of BCS type superconductors focusing on propagating collective modes that are observable with THz near field optics. The interesting frequency and momentum range is $ω< 2Δ$ and $q < 1/ξ$ where $Δ$ is the gap and $ξ$ is the coherence length. We show that it is possible to observe the superfluid plasmons, amplitude (Higgs) modes, Bardasis-Schrieffer modes and Carlson-Goldman modes using THz near field technique, although none of these modes couple linearly to far field radiation. Coupling of THz near field radiation to the amplitude mode requires particle-hole symmetry breaking while coupling to the Bardasis-Schrieffer mode does not and is typically stronger. For parameters appropriate to layered superconductors of current interest, the Carlson-Goldman mode appears in the near field reflection coefficient as a weak feature in the sub-THz frequency range. In a system of two superconducting layers with nanometer scale separation, an acoustic phase mode appears as the antisymmetric density fluctuation mode of the system. This mode produces well defined resonance peaks in the near-field THz response and has strong anticrossings with the Bardasis-Schrieffer and amplitude modes, enhancing their response. In a slab consisting of many layers of quasi-two dimensional superconductors, realized for example in samples of high T$_c$ cuprate compounds, many branches of propagating Josephson plasmon modes are found to couple to the THz near field radiation.

cond-mat.supr-con↗

arXiv2019

Solving Eigenvalue Problems in a Discontinuous Approximation Space by Patch Reconstruction

We adapt a symmetric interior penalty discontinuous Galerkin method using a patch reconstructed approximation space to solve elliptic eigenvalue problems, including both second and fourth order problems in 2D and 3D. It is a direct extension of the method recently proposed to solve corresponding boundary value problems, and the optimal error estimates of the approximation to eigenfunctions and eigenvalues are instant consequences from existing results. The method enjoys the advantage that it uses only one degree of freedom on each element to achieve very high order accuracy, which is highly preferred for eigenvalue problems as implied by Zhang's recent study [J. Sci. Comput. 65(2), 2015]. By numerical results, we illustrate that higher order methods can provide much more reliable eigenvalues. To justify that our method is the right one for eigenvalue problems, we show that the patch reconstructed approximation space attains the same accuracy with fewer degrees of freedom than classical discontinuous Galerkin methods. With the increasing of the polynomial order, our method can even achieve a better performance than conforming finite element methods, such methods are traditionally the methods of choice to solve problems with high regularities.

math.NA↗

arXiv2019

Photo-enhanced metastable c-axis electrodynamics in stripe ordered cuprate La$_{1.885}$Ba$_{0.115}$CuO$_{4}$

Quantum materials are amenable to non-equilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors exhibit complex interplay between spin order, charge order and superconductivity, offering the prospect of enhanced coherence by altering the balance between competing orders. We utilize terahertz time domain spectroscopy to monitor the c-axis Josephson Plasma Resonance (JPR) in La$_{2-x}$Ba$_{x}$CuO$_{4}$ (x = 0.115) as a direct probe of superconductivity dynamics following excitation with near infrared pulses. Starting from the superconducting state, c-axis polarized excitation with a fluence of 100 $μ$J/cm2 results in an increase of the far-infrared spectral weight by more than an order of magnitude as evidenced by a blueshift of the JPR, interpreted as resulting from non-thermal collapse of the charge order. The photo-induced signal persists well beyond our measurement window of 300 ps and exhibits signatures of spatial inhomogeneity. The electrodynamic response of this new metastable state is consistent with enhanced superconducting fluctuations. Our results reveal that La$_{2-x}$Ba$_{x}$CuO$_{4}$ is highly sensitive to non-equilibrium excitation over a wide fluence range, providing an unambiguous example of photo-induced modification of order-parameter competition.

cond-mat.supr-con↗

arXiv2019

A finite element method by patch reconstruction for the Stokes problem using mixed formulations

In this paper, we develop a patch reconstruction finite element method for the Stokes problem. The weak formulation of the interior penalty discontinuous Galerkin is employed. The proposed method has a great flexibility in velocity-pressure space pairs whose stability properties are confirmed by the inf-sup tests. Numerical examples show the applicability and efficiency of the proposed method.

math.NA↗

arXiv2018

A Discontinuous Galerkin Method for the Stokes Equation by Divergence-free Patch Reconstruction

A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal component penalty terms to cancel out the pressure term. Consequently, the Stokes equation can be solved as an elliptic system instead of a saddle-point problem due to such weak form. The number of degree of freedoms of our method is the same as the number of elements in the mesh for different order of accuracy. The error estimations of the proposed method are given in a classical style, which are then verified by some numerical examples.

math.NA↗

arXiv2018

Optical Signatures of Dirac Nodal-lines in NbAs$_2$

Using polarized optical and magneto-optical spectroscopy, we have demonstrated universal aspects of electrodynamics associated with Dirac nodal-lines. We investigated anisotropic electrodynamics of NbAs$_2$ where the spin-orbit interaction triggers energy gaps along the nodal-lines, which manifest as sharp steps in the optical conductivity spectra. We show experimentally and theoretically that shifted 2D Dirac nodal-lines feature linear scaling $σ_1 (ω)\simω$, similar to 3D nodal-points. Massive Dirac nature of the nodal-lines are confirmed by magneto-optical data, which may also be indicative of theoretically predicted surface states. Optical data also offer a natural explanation for the giant magneto-resistance in NbAs$_2$.

cond-mat.mtrl-sci↗

arXiv2018

A Discontinuous Galerkin Method by Patch Reconstruction for Biharmonic Problem

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

math.NA↗

arXiv2018

Charge Separation at Mixed-Dimensional Single and Multilayer MoS2/Silicon Nanowire Heterojunctions

Layered two-dimensional (2-D) semiconductors can be combined with other low-dimensional semiconductors to form non-planar mixed-dimensional van der Waals (vdW) heterojunctions whose charge transport behavior is influenced by the heterojunction geometry, providing a new degree of freedom to engineer device functions. Towards that end, we investigated the photoresponse of Si nanowire/MoS2 heterojunction diodes with scanning photocurrent microscopy and time-resolved photocurrent measurements. Comparison of n-Si/MoS2 isotype heterojunctions with p-Si/MoS2 heterojunction diodes under varying biases shows that the depletion region in the p-n heterojunction promotes exciton dissociation and carrier collection. We measure an instrument limited response time of 1 us, which is 10 times faster than previously reported response times for planar Si/MoS2 devices, highlighting the advantages of the 1-D/2-D heterojunction. Finite element simulations of device models provide a detailed understanding of how the electrostatics affect charge transport in nanowire/vdW heterojunctions and inform the design of future vdW heterojunction photodetectors and transistors.

physics.app-ph↗

arXiv2018

Template-assisted scalable nanowire networks

Topological qubits based on Majorana fermions have the potential to revolutionize the emerging field of quantum computing by making information processing significantly more robust to decoherence. Nanowires (NWs) are a promising medium for hosting these kinds of qubits, though branched NWs are needed to perform qubit manipulations. Here we report gold-free templated growth of III-V NWs by molecular beam epitaxy using an approach that enables patternable and highly regular branched NW arrays on a far greater scale than what has been reported thus far. Our approach relies on the lattice-mismatched growth of InAs on top of defect-free GaAs nanomembranes (NMs) yielding laterally-oriented, low-defect InAs and InGaAs NWs whose shapes are determined by surface and strain energy minimization. By controlling NM width and growth time, we demonstrate the formation of compositionally graded NWs with cross-sections less than 50 nm. Scaling the NWs below 20 nm leads to the formation of homogenous InGaAs NWs which exhibit phase-coherent, quasi-1D quantum transport as shown by magnetoconductance measurements. These results are an important advance towards scalable topological quantum computing.

quant-ph↗

arXiv2018

An Arbitrary-Order Discontinuous Galerkin Method with One Unknown Per Element

We propose an arbitrary-order discontinuous Galerkin method for second-order elliptic problem on general polygonal mesh with only one degree of freedom per element. This is achieved by locally solving a discrete least-squares over a neighboring element patch. Under a geometrical condition on the element patch, we prove an optimal a priori error estimates for the energy norm and for the L$^2$ norm. The accuracy and the efficiency of the method up to order six on several polygonal meshes are illustrated by a set of benchmark problems.

math.NA↗

arXiv2017

Third-order optical conductivity of an electron fluid

We derive the nonlinear optical conductivity of an isotropic electron fluid at frequencies below the interparticle collision rate. In this regime, governed by hydrodynamics, the conductivity acquires a universal form at any temperature, chemical potential, and spatial dimension. We show that the nonlinear response of the fluid to a uniform field is dominated by the third-order conductivity tensor $σ^{(3)}$ whose magnitude and temperature dependence differ qualitatively from those in the conventional kinetic regime of higher frequencies. We obtain explicit formulas for $σ^{(3)}$ for Dirac materials such as graphene and Weyl semimetals. We make predictions for the third-harmonic generation, renormalization of the collective-mode spectrum, and the third-order circular magnetic birefringence experiments.

cond-mat.mes-hall↗

arXiv2017

Nanoscale mapping and spectroscopy of non-radiative hyperbolic modes in hexagonal boron nitride nanostructures

The inherent crystal anisotropy of hexagonal boron nitride (hBN) sustains naturally hyperbolic phonon polaritons, i.e. polaritons that can propagate with very large wavevectors within the material volume, thereby enabling optical confinement to exceedingly small dimensions. Indeed, previous research has shown that nanometer-scale truncated nanocone hBN cavities, with deep subwavelength dimensions, support three-dimensionally confined optical modes in the mid-infrared. Due to optical selection rules, only a few of many such modes predicted theoretically have been observed experimentally via far-field reflection and scattering-type scanning near-field optical microscopy. The Photothermal induced resonance (PTIR) technique probes optical and vibrational resonances overcoming weak far-field emission by leveraging an atomic force microscope (AFM) probe to transduce local sample expansion due to light absorption. Here we show that PTIR enables the direct observation of previously unobserved, dark hyperbolic modes of hBN nanostructures. Leveraging these optical modes could yield a new degree of control over the electromagnetic near-field concentration, polarization and angular momentum in nanophotonic applications.

cond-mat.mes-hall↗

arXiv2017

Universal linear and nonlinear electrodynamics of the Dirac fluid

A general relation is derived between the linear and second-order nonlinear ac conductivities of an electron system in the hydrodynamic regime of frequencies below the interparticle scattering rate. The magnitude and tensorial structure of the hydrodynamic nonlinear conductivity are shown to differ from their counterparts in the more familiar kinetic regime of higher frequencies. Due to universality of the hydrodynamic equations, the obtained formulas are valid for systems with an arbitrary Dirac-like dispersion, ranging from solid-state electron gases to free-space plasmas, either massive or massless, at any temperature, chemical potential or space dimension. Predictions for photon drag and second-harmonic generation in graphene are presented as one application of this theory.

cond-mat.other↗

arXiv2017

Relative efficiency of polariton emission in two-dimensional materials

We investigated emission and propagation of polaritons in a two dimensional van der Waals material hexagonal boron nitride (hBN). Our specific emphasis in this work is on hyperbolic phonon polariton emission that we investigated by means of scattering-type scanning near-field optical microscopy. Real-space nano-images detail how the polaritons are launched in several common arrangements including: light scattering by the edges of the crystal, metallic nanostructures deposited on the surface of hBN crystals, as well as random defects and impurities. Notably, the scanned tip of the near-field microscope is itself an efficient polariton launcher. Our analysis reveals that the scanning tips are superior to other types of emitters we have investigated. Furthermore, the study of polariton emission and emission efficiency may provide insights for development of polaritonic devices and for fundamental studies of collective modes in other van der Waals materials.

cond-mat.mes-hall↗

arXiv2016

Adiabatic amplification of plasmons and demons in 2D systems

We theoretically investigate charged collective modes in a two-dimensional conductor with hot electrons where the instantaneous mode frequencies gradually increase or decrease with time. We show that the loss compensation or even amplification of the modes may occur. We apply our theory to two types of collective modes in graphene, the plasmons and the energy waves, which can be probed in optical pump-probe experiments.

cond-mat.mes-hall↗

arXiv2016

Imaging of anomalous internal reflections of hyperbolic phonon-polaritons in hexagonal boron nitride

We use scanning near-field optical microscopy to study the response of hexagonal boron nitride nanocones at infrared frequencies, where this material behaves as a hyperbolic medium. The obtained images are dominated by a series of hot rings that occur on the sloped sidewalls of the nanocones. The ring positions depend on the incident laser frequency and the nanocone shape. Both dependences are consistent with directional propagation of hyperbolic phonon polariton rays that are launched at the edges and zigzag through the interior of the nanocones, sustaining multiple internal reflections off the sidewalls. Additionally, we observe a strong overall enhancement of the near-field signal at discrete resonance frequencies. These resonances attest to low dielectric losses that permit coherent standing waves of the sub-diffractional polaritons to form. We comment on potential applications of such shape-dependent resonances and the field concentration at the hot rings.

cond-mat.mtrl-sci↗

arXiv2015

Hamiltonian optics of hyperbolic polaritons in nanogranules

Semiclassical quantization rules and numerical calculations are applied to study polariton modes of materials whose permittivity tensor has principal values of opposite sign (so-called hyperbolic materials). The spectra of volume- and surface-confined polaritons are computed for spheroidal nanogranules of hexagonal boron nitride, a natural hyperbolic crystal. The field distribution created by polaritons excited by an external dipole source is predicted to exhibit ray-like patterns due to classical periodic orbits. Near-field infrared imaging and Purcell-factor measurements are suggested to test these predictions.

cond-mat.mes-hall↗