Phonon System Research Articles

Observed quantization of anyonic heat flow.

The quantum of thermal conductance of ballistic (collisionless) one-dimensional channels is a unique fundamental constant. Although the quantization of the electrical conductance of one-dimensional ballistic conductors has long been experimentally established, demonstrating the quantization of thermal conductance has been challenging as it necessitated an accurate measurement of very small temperature increase. It has been accomplished for weakly interacting systems of phonons, photons and electronic Fermi liquids; however, it should theoretically also hold in strongly interacting systems, such as those in which the fractional quantum Hall effect is observed. This effect describes the fractionalization of electrons into anyons and chargeless quasiparticles, which in some cases can be Majorana fermions. Because the bulk is incompressible in the fractional quantum Hall regime, it is not expected to contribute substantially to the thermal conductance, which is instead determined by chiral, one-dimensional edge modes. The thermal conductance thus reflects the topological properties of the fractional quantum Hall electronic system, to which measurements of the electrical conductance give no access. Here we report measurements of thermal conductance in particle-like (Laughlin-Jain series) states and the more complex (and less studied) hole-like states in a high-mobility two-dimensional electron gas in GaAs-AlGaAs heterostructures. Hole-like states, which have fractional Landau-level fillings of 1/2 to 1, support downstream charged modes as well as upstream neutral modes, and are expected to have a thermal conductance that is determined by the net chirality of all of their downstream and upstream edge modes. Our results establish the universality of the quantization of thermal conductance for fractionally charged and neutral modes. Measurements of anyonic heat flow provide access to information that is not easily accessible from measurements of conductance.

(Invited) Phonon Coherence and Backscattering in Thermal Transport of Silicon Nanostructures

Understanding thermal transport at the nanoscale is critical for a broad range of semiconductor technologies involving nanoelectronics, phase change data storage, heat-assisted magnetic recording, solid-state lighting, and thermoelectric energy conversion. Past studies on the thermal conductivity of silicon materials have substantially contributed to establishing microscopic understanding of thermal transport. Classical theories based on the Boltzmann Transport Equation that treat phonons as incoherent particles have accurately described the size-dependent thermal conductivity in silicon thin films and high purity nanowires; these thermal conductivity reductions are due to mean free path suppression from boundary scattering. However, recent thermal conductivity measurements of silicon nanomeshes, which are thin membranes with a fabricated periodic mesh of nanoscopic holes, have called into question the validity of this particle-based Boltzmann Transport Equation approach when applied to periodic nanostructures. Phonons can display both wave-like and particle-like behavior during thermal transport. While the prospect of controlling phonon waves is attractive for potential phononic systems, experimental reports remain inconclusive on the relative importance of wave effects versus particle-based boundary scattering effects in the nanomesh. Although there are several mechanisms proposed to explain the thermal conductivity reduction in silicon nanostructures, possible phonon coherence (wave) and backscattering (particle) effects are often coupled, and previous experimental studies were unable to isolate the dominant mechanism. Here, we measure thermal conductivity of silicon nanomesh structures defined by electron-beam lithography to isolate these competing mechanisms of thermal conductivity reduction. By comparing nanomeshes with periodic and aperiodic holes of the same average dimension, our experimental design decouples the phonon coherence effect from boundary scattering effects. Similarly, by controlling the hole-to-hole pitch from 1 µm to 100 nm, our experiments evaluate the phonon backscattering effect. The thermal conductivity measurements are performed on monolithic silicon devices using an established technique that was first developed for nanowires. The measurement temperature is controlled from 325 K to 14 K; these low temperature measurements are crucial because the important phonon wavelength and the phonon mean free path are larger at low temperature, which facilitates observation of potential coherence and backscattering effects. We perform ray tracing simulations to rigorously capture the boundary scattering required for particle model thermal conductivity predictions. By comparing experimental results between samples and against particle model predictions, we show that phonon coherence effects are not necessary to describe thermal transport in the regime where the nanomesh pitch is greater than the phonon wavelength but smaller than the phonon mean free, and that the backscattering effect leads to the thermal conductivity reductions. The insights obtained from this work will be valuable in understanding phonon transport in complicated nanostructured geometries and advancing breakthroughs in silicon nanostructure-based thermoelectric devices

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(e) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.

Semiconductor‐to‐Metal Transition and Quasiparticle Renormalization in Doped Graphene Nanoribbons

A semiconductor‐to‐metal transition in N = 7 armchair graphene nanoribbons causes drastic changes in its electron and phonon system. By using angle‐resolved photoemission spectroscopy of lithium‐doped graphene nanoribbons, a quasiparticle band gap renormalization from 2.4 to 2.1 eV is observed. Reaching high doping levels (0.05 electrons per atom), it is found that the effective mass of the conduction band carriers increases to a value equal to the free electron mass. This giant increase in the effective mass by doping is a means to enhance the density of states at the Fermi level which can have palpable impact on the transport and optical properties. Electron doping also reduces the Raman intensity by one order of magnitude, and results in relatively small (4 cm−1) hardening of the G phonon and softening of the D phonon. This suggests the importance of both lattice expansion and dynamic effects. The present work highlights that doping of a semiconducting 1D system is strikingly different from its 2D or 3D counterparts and introduces doped graphene nanoribbons as a new tunable quantum material with high potential for basic research and applications.

Topological Phonon Modes in a Two-Dimensional Wigner Crystal**Supported by the National Basic Research Program of China under Grant No 2015CB921101, and the National Natural Science Foundation of China under Grant No 11325416.

We investigate the spin–orbit coupling effect in a two-dimensional (2D) Wigner crystal. It is shown that sufficiently strong spin–orbit coupling and an appropriate sign of g-factor could transform the Wigner crystal to a topological phonon system. We demonstrate the existence of chiral phonon edge modes in finite size samples, as well as the robustness of the modes in the topological phase. We explore the possibility of realizing the topological phonon system in 2D Wigner crystals confined in semiconductor quantum wells/heterostructure. It is found that the spin–orbit coupling is too weak for driving a topological phase transition in these systems. It is argued that one may look for topological phonon systems in correlated Wigner crystals with emergent effective spin–orbit coupling.

Scattering of an electronic wave packet by a one-dimensional electron-phonon-coupled structure

We investigate the scattering of an electron by phonons in a small structure between two one-dimensional tight-binding leads. This model mimics the quantum electron transport through atomic wires or molecular junctions coupled to metallic leads. The electron-phonon coupled structure is represented by the Holstein model. We observe permanent energy transfer from the electron to the phonon system (dissipation), transient self-trapping of the electron in the electron-phonon coupled structure (due to polaron formation and multiple reflections at the structure edges), and transmission resonances that depend strongly on the strength of the electron-phonon coupling and the adiabaticity ratio. A recently developed TEBD algorithm, optimized for bosonic degrees of freedom, is used to simulate the quantum dynamics of a wave packet launched against the electron-phonon coupled structure. Exact results are calculated for a single electron-phonon site using scattering theory and analytical approximations are obtained for limiting cases.

The Role of Electronic and Phononic Excitation in the Optical Response of Monolayer WS2 after Ultrafast Excitation

Transient changes of the optical response of WS2 monolayers are studied by femtosecond broadband pump-probe spectroscopy. Time-dependent absorption spectra are analyzed by tracking the line width broadening, bleaching, and energy shift of the main exciton resonance as a function of time delay after the excitation. Two main sources for the pump-induced changes of the optical response are identified. Specifically, we find an interplay between modifications induced by many-body interactions from photoexcited carriers and by the subsequent transfer of the excitation to the phonon system followed by cooling of the material through the heat transfer to the substrate.

Critical temperature of metallic hydrogen sulfide at 225-GPa pressure

The Eliashberg theory generalized for electron—phonon systems with a nonconstant density of electron states and with allowance made for the frequency behavior of the electron mass and chemical potential renormalizations is used to study T c in the SH3 phase of hydrogen sulfide under pressure. The phonon contribution to the anomalous electron Green’s function is considered. The pairing within the total width of the electron band and not only in a narrow layer near the Fermi surface is taken into account. The frequency and temperature dependences of the complex mass renormalization ReZ(ω), the density of states N(e) renormalized by the electron—phonon interactions, and the electron—phonon spectral function obtained computationally are used to calculate the anomalous electron Green’s function. A generalized Eliashberg equation with a variable density of electron states has been solved. The frequency dependence of the real and imaginary parts of the order parameter in the SH3 phase has been obtained. The value of T c ≈ 177 K in the SH3 phase of hydrogen sulfide at pressure P = 225 GPa has been determined by solving the system of Eliashberg equations.

Engineering interactions between superconducting qubits and phononic nanostructures

Nanomechanical systems made from phononic crystals can act as highly coherent microwave-frequency circuits at cryogenic temperatures. However, generating sufficient coupling between these devices and microwave superconducting quantum circuits is challenging due to the vastly different length scales of acoustic and electrical excitations. Here we demonstrate a general recipe for calculating these interactions and show that large piezoelectric coupling rates between microwave superconducting circuits containing Josephson junctions and nanoscale phononic resonances are possible, suggesting a route to phononic crystal circuits and systems that are nonlinear at the single-phonon level.

Generalized Concurrence and Negativity in Time-Dependent C 3 ⊗ C 5 = C 15 Dimensional Ionic–Phononic Systems

We investigate the entanglement of a trapped three-level ion interacting with two vibrational phonons, which form a fifteen-dimensional Hilbert space. We reveal analytic formulas describing both the concurrence and negativity. We show that, in such a system, a higher degree of entanglement with a concurrence of 0.999 and a negativity of 0.499 can be attained at a specific time of 16.9 fs. Derived expressions of concurrence and negativity include first-order terms in the interaction picture. Finally, an explicit solution for first-order terms shows that the amount of concurrence can be tuned between 0 and 1.0, while the amount of negativity changes between 0 and 0.5.

Critical temperature of metallic hydrogen at a pressure of 500 GPa

The Eliashberg theory generalized for electron–phonon systems with a variable electron density of states is used to study Tc in the I41/AMD phase of metallic hydrogen under compression taking into account the frequency behavior of the renormalization of the mass of the electron and the chemical potential. The phonon contribution to the anomalous electron Green’s function is considered. Pairing is taken into account within the entire electron band rather than in a narrow region near the Fermi surface. The frequency and temperature dependences of the complex renormalization of the mass Re Z(ω), as well as the density of states N(ω) renormalized by the electron–phonon coupling and the spectral function of the electron–phonon coupling, which are obtained in calculations, are used to calculate the anomalous electron Green’s function. The frequency dependence of the real and imaginary parts of the order parameter in the I41/AMD phase is obtained. The solution of the system of Eliashberg equations gives the value Tc = 217 K in the I41/AMD phase of hydrogen at a pressure of 500 GPa.

Persistent nonequilibrium dynamics of the thermal energies in the spin and phonon systems of an antiferromagnet.

We present a temperature and fluence dependent Ultrafast X-Ray Diffraction study of a laser-heated antiferromagnetic dysprosium thin film. The loss of antiferromagnetic order is evidenced by a pronounced lattice contraction. We devise a method to determine the energy flow between the phonon and spin system from calibrated Bragg peak positions in thermal equilibrium. Reestablishing the magnetic order is much slower than the cooling of the lattice, especially around the Néel temperature. Despite the pronounced magnetostriction, the transfer of energy from the spin system to the phonons in Dy is slow after the spin-order is lost.

Reconstruction of the conduction band in metallic hydrogen sulfide

The theory of the normal properties of a metal generalized to the case of particular properties of an electron band with a finite width for electron–phonon systems with a varying electron density of states has been used to study the normal state of the SH3 phase of hydrogen sulfide at a pressure of 225 GPa and a temperature of 200 K. The frequency dependences of the real, ReΣ(ω), and imaginary, ImΣ(ω), parts of the selfenergy part of the Green’s function of the electron Σ(ω), as well as the electron density of states N(e) of the Im–3m stable orthorhombic structure of SH3 hydrogen sulfide at a pressure of P = 225 GPa, which is renormalized by the strong electron–phonon coupling, have been calculated. It has been established that a part of the electron conduction band of the SH3 phase of hydrogen sulfide adjacent to the Fermi level undergoes renormalization-induced reconstruction in the form of a number of energy pockets with the widths equal to fractions of the characteristic phonon energies of the system.

Confining interparticle potential makes both heat transport and energy diffusion anomalous in one-dimensional phononic systems

We provide molecular dynamics simulation of heat transport and energy diffusion in one-dimensional molecular chains with different interparticle pair potentials at zero and non-zero temperature. We model the thermal conductivity (TC) and energy diffusion (ED) in the chain of coupled rotators and in the Lennard-Jones chain either without or with the confining parabolic interparticle potential. The considered chains without the confining potential have normal TC and ED at non-zero temperature, while the corresponding chains with the confining potential are characterized by anomalous (diverging with the system length) TC and superdiffusion of energy. Similar effect is produced by the anharmonic quartic confining pair potential. We confirm in such a way that, surprisingly, the confining pair potential makes both heat transport and energy diffusion anomalous in one-dimensional phononic systems. We show that the normal TC is always accompanied by the normal ED in the thermalized anharmonic chains, while the superdiffusion of energy occurs in the thermalized chains with only anomalous heat transport.

Band-edge optical transitions in a nonpolar-plane GaN substrate: exciton–phonon coupling and temperature effects

We present a detailed investigation of the band-edge optical transitions involving the interacting exciton–phonon system, especially first-order longitudinal optical (LO) phonon-assisted luminescence of bound and free excitons in m- and c-plane GaN substrates in a low temperature range from 4 K to 40 K. The main luminescence features of all of the three kinds of excitons can be well described by the theoretical models that take exciton-LO-phonon coupling into account. The effective Bohr radii of the excitons play a key role in determining the Huang–Rhys factor characterizing the exciton-LO-phonon coupling strength in GaN. An interesting oscillatory structure is found to appear in the low-temperature luminescence spectra of the nonpolar-plane GaN substrate, which needs to be clarified by further investigations.

Mapping of spin wave propagation in a one-dimensional magnonic crystal

The formation and evolution of spin wave band gaps in the transmission spectrum of a magnonic crystal have been studied. A time and space resolved magneto inductive probing system has been used to map the spin wave propagation and evolution in a geometrically structured yttrium iron garnet film. Experiments have been carried out using (1) a chemically etched magnonic crystal supporting the propagation of magnetostatic surface spin waves, (2) a short microwave pulsed excitation of the spin waves, and (3) direct spin wave detection using a movable magneto inductive probe connected to a synchronized fast oscilloscope. The results show that the periodic structure not only modifies the spectra of the transmitted spin waves but also influences the distribution of the spin wave energy inside the magnonic crystal as a function of the position and the transmitted frequency. These results comprise an experimental confirmation of Bloch′s theorem in a spin wave system and demonstrate good agreement with theoretical observations in analogue phononic and photonic systems. Theoretical prediction of the structured transmission spectra is achieved using a simple model based on microwave transmission lines theory. Here, a spin wave system illustrates in detail the evolution of a much more general physical concept: the band gap.

Topological water wave states in a one-dimensional structure.

Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems. Here we study a one-dimensional periodic resonant surface-water-wave system and demonstrate its topological transition. By selecting three different water depths, we can construct different types of water waves - shallow, intermediate and deep water waves. The periodic surface-water-wave system consists of an array of cylindrical water tanks connected with narrow water channels. As the width of connecting channel varies, the band diagram undergoes a topological transition which can be further characterized by Zak phase. This topological transition holds true for shallow, intermediate and deep water waves. However, the interface state at the boundary separating two topologically distinct arrays of water tanks can exhibit different bands for shallow, intermediate and deep water waves. Our work studies for the first time topological properties of water wave systems, and paves the way to potential management of water waves.

The manipulation of self-collimated beam in phononic crystals composed of orientated rectangular inclusions

Self-collimation is wave propagation in straight path without diffraction. The performance is evaluated by bandwidth, angular collimating range and straightness of equi-frequency contours. The present study aims to manipulate the self-collimated beam in square-array phononic crystals by means of orientated rectangular inclusions. Finite element simulations are performed to investigate the effects of the aspect ratio and orientation angle of rectangular inclusions on the self-collimated beam. The simulation results show that the proposed design successfully achieves all-angle self-collimation phenomenon. In addition, it also shows that the propagation direction of a self-collimated beam can be effectively manipulated by varying the orientation angle of inclusions. Numerical simulation result of the S-shaped bend demonstrates that acoustic collimated beam can be steered with negligible diffraction. Overall, the proposed design has significant potential for the realization of applications such as collimators, acoustic waveguides and other phononic crystals-based systems.

Helical edge states and topological phase transitions in phononic systems using bi-layered lattices

We propose a framework to realize helical edge states in phononic systems using two identical lattices with interlayer couplings between them. A methodology is presented to systematically transform a quantum mechanical lattice which exhibits edge states to a phononic lattice, thereby developing a family of lattices with edge states. Parameter spaces with topological phase boundaries in the vicinity of the transformed system are illustrated to demonstrate the robustness to mechanical imperfections. A potential realization in terms of fundamental mechanical building blocks is presented for the hexagonal and Lieb lattices. The lattices are composed of passive components and the building blocks are a set of disks and linear springs. Furthermore, by varying the spring stiffness, topological phase transitions are observed, illustrating the potential for tunability of our lattices.

Relaxation of the resistive superconducting state in boron-doped diamond films

We report a study of the relaxation time of the restoration of the resistive superconducting state in single crystalline boron-doped diamond using amplitude-modulated absorption of (sub-)THz radiation (AMAR). The films grown on an insulating diamond substrate have a low carrier density of about 2.5x10^{21} cm^{-3} and a critical temperature of about 2 K. By changing the modulation frequency we find a high-frequency rolloff which we associate with the characterstic time of energy relaxation between the electron and the phonon systems or the relaxation time for nonequilibrium superconductivity. Our main result is that the electron-phonon scattering time varies clearly as T^{-2}, over the accessible temperature range of 1.7 to 2.2 K. In addition, we find, upon approaching the critical temperature T_c, evidence for an increasing relaxation time on both sides of T_c.