Phonon Coherence Research Articles

(Invited) Phonon Heat Transport Processes and Thermal Conductivity of II-Oxide and III-V Superlattices: Wave-like Coherent Transport in CaTiO3/SrTiO3 Superlattices and Ballistic-Diffusive Transport in GaAs/Alas Superlattices

The thermal conductivity of superlattices is strongly reduced as compared to the thermal conductivity of the individual parent materials comprising these multilayered structures due to phonon-scattering and thermal boundary resistances at the superlattice period interfaces. However, given the relatively length scale of the superlattice periods compared to typical phonon wavelengths and mean free paths, the vibrational heat transport in superlattices can give rise to unique phonon scattering processes. For example, partially ballistic and partially diffusive phonon transport in superlattices in which long wavelength phonons effectively do not “see” the interfaces on the order of the superlattice period can occur if superlattice periodicity is short enough. As another example, under certain conditions in which phonon coherence is not destroyed at superlattice interfaces, the emergence of a “minimum” in the superlattice thermal conductivity as a function of interface density can be realized. In this work, we present a series of works on III-V (e.g., GaAs/AlAs) and II-oxide (CaTiO3/SrTiO3) superlattices in which we observe unique phonon thermal transport properties based on measurements of thermal conductivity of these superlattice thin films. First, we will discuss our work on CaTiO3/SrTiO3 superlattices in which we observe coherent phonon transport based on the observation of a minimum in thermal conductivity of superlattice thin films as a function of interface density. When the period thickness decreases to below the phonon coherence length of the phonons in CaTiO3 and SrTiO3, an increase in interface density leads to an increase in thermal conductivity, a phenomenon that indicates a “particle-wave-like” crossover and coherent phonon transport influencing the in phonon thermal conductivity in superlattices. This observation is enabled by the chemically and structurally abrupt nature of the CaTiO3/SrTiO3 interfaces in these superlattices. Next, we will discuss our work on GaAs/AlAs superlattices in which we observe a ballistic-diffusive cross over based on the total thickness of the superlattice. We report on the room temperature thermal conductivity of AlAs-GaAs superlattices (SLs), in which we systematically vary the period thickness and total thickness between 2–24 nm and 20.1–2,160 nm, respectively. The thermal conductivity increases with the SL thickness and plateaus at a thickness around 200 nm, showing a clear transition from a quasiballistic to a diffusive phonon transport regime. These results demonstrate the existence of classical size effects in SLs, even at the highest interface density samples. Our results reveal that the change in thermal conductivity with period thickness is dominated by incoherent (particlelike) phonons in these III-V superlattice films, whose properties are not dictated by changes in the AlAs or GaAs phonon dispersion relations. This work demonstrates the importance of studying both period and sample thickness dependencies of thermal conductivity to understand the relative contributions of coherent and incoherent phonon transport in the thermal conductivity in SLs. “Crossover from incoherent to coherent phonon scattering in epitaxial oxide superlattices,” Nature Materials, 13, 168–172 (2014).“Interplay between total thickness and period thickness in the phonon thermal conductivity of superlattices from the nanoscale to the microscale: Coherent versus incoherent phonon transport,” Physical Review B, 97, 085306 (2018).

Ground-state phase diagram of the 1-D Holstein–Hubbard model

The Holstein–Hubbard model is investigated in one-dimension at half filling employing a series of unitary transformations taking into account the coherence and correlation of phonons. To treat the phonon subsystem more accurately a new squeezing transformation is introduced to incorporate the electron-density-dependent onsite phonon correlations to lower the energy further. The effective electronic Hamiltonian is next obtained by averaging the transformed Hamiltonian with respect to the zero-phonon state and the resulting effective electronic Hamiltonian is solved exactly using the method of Bethe ansatz. Finally the ground state is obtained by minimizing the energy with respect to all the variational parameters. The present method gives better results for the ground state energy of the system and also suggests the existence of a wider intermediate metallic phase at the charge-density-wave–spin-density-wave crossover region, which was first predicted by Takada and Chatterjee and later supported by Krishna and Chatterjee.

Ab initio based investigation of thermal transport in superlattices using the Boltzmann equation: Assessing the role of phonon coherence

The role of the coherent interference of phonons on thermal transport in artificial materials such as superlattices is of intense interest. Recent experimental studies report a non-monotonic trend in thermal conductivity with interface density which is attributed to band-folding of thermal phonons. Various models have been proposed to interpret these measurements, but most make simplifying assumptions that make definitively attributing the trends to the coherent transport difficult. Here, we investigate thermal transport in superlattices in the incoherent limit using the Boltzmann equation with intrinsic phonon dispersions and lifetimes calculated from first-principles. We find that the Boltzmann equation is unable to predict the non-monotonic behavior of thermal conductivity versus superlattice period, supporting the interpretation of phonon interference in recent experiments.

Phonon coherences reveal the polaronic character of excitons in two-dimensional lead halide perovskites.

Hybrid organic-inorganic semiconductors feature complex lattice dynamics due to the ionic character of the crystal and the softness arising from non-covalent bonds between molecular moieties and the inorganic network. Here we establish that such dynamic structural complexity in a prototypical two-dimensional lead iodide perovskite gives rise to the coexistence of diverse excitonic resonances, each with a distinct degree of polaronic character. By means of high-resolution resonant impulsive stimulated Raman spectroscopy, we identify vibrational wavepacket dynamics that evolve along different configurational coordinates for distinct excitons and photocarriers. Employing density functional theory calculations, we assign the observed coherent vibrational modes to various low-frequency (≲50 cm-1) optical phonons involving motion in the lead iodide layers. We thus conclude that different excitons induce specific lattice reorganizations, which are signatures of polaronic binding. This insight into the energetic/configurational landscape involving globally neutral primary photoexcitations may be relevant to a broader class of emerging hybrid semiconductor materials.

Akhiezer mechanism limits coherent heat conduction in phononic crystals

Heat in phononic crystals (PnCs) is carried by phonons, which can behave coherently (wave-like) or incoherently (particle-like) depending on the modes, temperature, and length scales. By comparing the measured thermal conductivity of PnCs with theories, recent works suggest that thermal conductivity of PnCs can be explained by considering only surface and boundary scatterings, which not only backscatter phonons but also break their coherence. The logic here is that since average phonon wavelength at room temperature is only a few nanometers, the roughness at the surfaces and boundaries make the scattering diffusive (break the phase coherence of phonons), and thus only very long wavelength (low frequency) phonons with negligible contribution to total thermal conductivity remain coherent. Here, we theoretically show that in a thin film PnCs, the low frequency coherent phonons could significantly contribute to thermal conductivity when assuming the three-phonon scattering model for intrinsic scattering because of their extremely large density of states that result from the low dimensional nature. Yet, further analysis shows the contribution of the low frequency coherent phonons is still negligible within temperature range from 130 to 300 K due to the Akhiezer mechanism, which properly answers the question why the thermal conductivity of PnCs can be explained by considering only scattering of incoherent phonons at these temperatures.

Entanglement sudden death and revival in quantum dark-soliton qubits

We study the finite time entanglement dynamics between two dark soliton qubits due to quantum fluctuations in a quasi one dimensional Bose-Einstein condensates. Recently, dark solitons are proved to be an appealing platform for qubits due to their appreciably long life time. We explore the entanglement decay for an entangled state of two phonon coherences and the qubits to be in the diagonal basis of so called Dicke states. We observe the collapse and revival of the entanglement, depending critically on the collective damping term but independent of the qubit-qubit interaction for both the initial states. The collective behavior of the dark soliton qubits demonstrate the dependence of entanglement evolution on the interatomic distance.

Bulk crystalline optomechanics

Brillouin processes couple light and sound through optomechanical three-wave interactions. Within bulk solids, this coupling is mediated by the intrinsic photo-elastic material response yielding coherent emission of high frequency (GHz) acoustic phonons. This same interaction produces strong optical nonlinearities that overtake both Raman or Kerr nonlinearities in practically all solids. In this paper, we show that the strength and character of Brillouin interactions are radically altered at low temperatures when the phonon coherence length surpasses the system size. In this limit, the solid becomes a coherent optomechanical system with macroscopic (cm-scale) phonon modes possessing large ($60\ \mu \rm{g}$) motional masses. These phonon modes, which are formed by shaping the surfaces of the crystal into a confocal phononic resonator, yield appreciable optomechanical coupling rates (${\sim}100$ Hz), providing access to ultra-high $Q$-factor ($4.2{\times}10^7$) phonon modes at high ($12$ GHz) carrier frequencies. The single-pass nonlinear optical susceptibility is enhanced from its room temperature value by more than four orders of magnitude. Through use of bulk properties, rather than nano-structural control, this comparatively simple approach is enticing for the ability to engineer optomechanical coupling at high frequencies and with high power handling. In contrast to cavity optomechanics, we show that this system yields a unique form of dispersive symmetry breaking that enables selective phonon heating or cooling without an optical cavity (i.e., cavity-less optomechanics). Extending these results, practically any transparent crystalline material can be shaped into an optomechanical system as the basis for materials spectroscopy, new regimes of laser physics, precision metrology, quantum information processing, and for studies of macroscopic quantum coherence.

Thermal Conductivity of Graphene-hBN Superlattice Ribbons

Superlattices are ideal model systems for the realization and understanding of coherent (wave-like) and incoherent (particle-like) phonon thermal transport. Single layer heterostructures of graphene and hexagonal boron nitride have been produced recently with sharp edges and controlled domain sizes. In this study we employ nonequilibrium molecular dynamics simulations to investigate the thermal conductivity of superlattice nanoribbons with equal-sized domains of graphene and hexagonal boron nitride. We analyze the dependence of the conductivity with the domain sizes, and with the total length of the ribbons. We determine that the thermal conductivity reaches a minimum value of 89 W m−1K−1 for ribbons with a superlattice period of 3.43 nm. The effective phonon mean free path is also determined and shows a minimum value of 32 nm for the same superlattice period. Our results also reveal that a crossover from coherent to incoherent phonon transport is present at room temperature for BNC nanoribbons, as the superlattice period becomes comparable to the phonon coherence length. Analyzing phonon populations relative to the smallest superlattice period, we attribute the minimum thermal conductivity to a reduction in the population of flexural phonons when the superlattice period equals 3.43 nm. The ability to manipulate thermal conductivity using superlattice-based two-dimensional materials, such as graphene-hBN nanoribbons, opens up opportunities for application in future nanostructured thermoelectric devices.

Understanding photon sideband statistics and correlation for determining phonon coherence

Generating and detection coherent high-frequency heat-carrying phonons has been a great topic of interest in recent years. While there have been successful attempts in generating and observing coherent phonons, rigorous techniques to characterize and detect these phonon coherence in a crystalline material have been lagging compared to what has been achieved for photons. One main challenge is a lack of detailed understanding of how detection signals for phonons can be related to coherence. The quantum theory of photoelectric detection has greatly advanced the ability to characterize photon coherence in the last century and a similar theory for phonon detection is necessary. Here, we re-examine the optical sideband fluorescence technique that has been used detect high frequency phonons in materials with optically active defects. We apply the quantum theory of photodetection to the sideband technique and propose signatures in sideband photon-counting statistics and second-order correlation measurement of sideband signals that indicates the degree of phonon coherence. Our theory can be implemented in recently performed experiments to bridge the gap of determining phonon coherence to be on par with that of photons.

(Invited) Thermal Transport and Thermal Management By Silicon Nanostructures

Thermal transport in silicon nanostructures has captured the attention of scientists for understanding phonon transport at the nanoscale, and the competitive thermoelectric figure-of-merit has inspired engineers to develop efficient power generation and solid-state cooling devices. Firstly, our work focuses on identifying fundamental mechanisms of thermal transport in silicon nanostructures. The thermal transport interpretation remains unclear at the nanoscale and is often called into doubt due to the coupled effects of phonon coherence, boundary scattering, backscattering, and contact resistance. We isolate the wave-related coherence effects by comparing periodic and aperiodic nanomeshes, and quantify the particle-related backscattering effect by comparing variable-pitch nanomeshes. The lithographically-patterned silicon nanomeshes provide a unique opportunity for this progress because the relevant dimensions including the artificial periodicity, pitch, and neck were independently controlled within a monolithic measurement device. We measure identical (within 6% uncertainty) thermal conductivities for periodic and aperiodic nanomeshes of the same average pitch, and reduced thermal conductivities for nanomeshes with smaller pitches. Our simulations based on a ray tracing technique support the measurement results. We conclude phonon coherence is unimportant for thermal transport in silicon nanomeshes with periodicities of 100 nm and higher and temperatures above 14 K. In other words, the wave nature of phonons does not need to be considered to describe transport in the regime where periodicities are greater than the dominant wavelengths but smaller than inelastic mean free paths. We also show that phonon backscattering, as manifested in the classical size effect, is responsible for the thermal conductivity reduction in silicon nanomeshes. This work provides valuable insights for describing phonon transport in complex nanostructured geometries and improves a fundamental understanding of nanoscale thermal transport that is critical for a broad range of semiconductor technologies. Lastly, our work provides a novel thermal management design based on holey silicon, in which nanoscopic holes are lithographically patterned and vertical trenches are formed to offer tunable transport properties. Due to the unique thermal conductivity anisotropy including the low in-plane thermal conductivity and the high cross-plane thermal conductivity preserved by long-wavelength phonons, the holey silicon structure will provide innovative thermoelectric cooling performance even at a confined lateral space, which is unachievable by conventional isotropic materials. The thermal conductivity anisotropy is attractive for lateral thermoelectric cooling designs because the low in-plane thermal conductivity sets required temperature gradients for thermoelectric Peltier effects in the lateral direction and the high cross-plane conductivity enables effective heat dissipation from the hotspot in the vertical direction. This work investigates the role of thermal conductivity anisotropy in thermoelectric cooling through theoretical, numerical, and experimental approaches. The work bridges the gap between fundamental thermal sciences and device engineering, in which the holey silicon-based thermoelectric cooling device benefits from the unique transport phenomena at the nanoscale. The outcomes of this research present the anisotropic silicon nanostructures as efficient and effective thermoelectric materials that can offer transformative solutions to thermal management of nanoscale electronics.

Ultralow Lattice Thermal Conductivity of the Random Multilayer Structure with Lattice Imperfections

Randomizing the layer thickness of superlattices (SL) can lead to localization of coherent phonons and thereby reduces the lattice thermal conductivity κl. In this work, we propose strategies that can suppress incoherent phonon transport in the above random multilayer (RML) structure to further reduce κl. Molecular dynamics simulations are conducted to investigate phonon heat conduction in SLs and RMLs with lattice imperfections. We found that interfacial species mixing enhances thermal transport across single interfaces and few-period SLs through the phonon “bridge” mechanism, while it substantially reduces the κl of many-period SLs by breaking the phonon coherence. This is a clear manifestation of the transition from incoherent-phonon-dominated to coherent-phonon-dominated heat conduction in SLs when the number of interface increases. In contrast, interfacial species mixing always increases the κl of RMLs owing to the dominance of incoherent phonons. Moreover, we found that doping a binary RML with impurities can reduce κl significantly, especially when the impurity atom has an atomic mass lower or higher than both of the two base elements. This work reveals the critical effect of lattice imperfections on thermal transport in SLs and RMLs, and provides a unique strategy to hierachically suppress coherent and incoherent phonon transport concurrently.

Distinguishing between spatial coherence and temporal coherence of phonons

Coherent phonon transport is regarded as a promising strategy for controlling thermal properties in solids using the wave nature of phonons. However, no clear distinction between the spatial and temporal phonon coherence has been accounted for and a formalism that quantifies these two effects is still to be found. In this work, we propose a statistical approach for calculating the spatial and temporal coherence spectra using molecular dynamics simulations. We provide a microscopic assessment of these properties and we theoretically demonstrate that, while temporal and spatial coherence can be analytically related under specific conditions, they represent two characteristic lengths that set apart different physical effects. The former is associated with the phonon mean free path while the latter can be regarded as a measure of localization, representing the spatial extension of phonon wave packets. This provides a framework to engineer heat conduction in solids by quantitatively revealing the wave/particle nature of the vibrational modes.

(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

Symmetry-derived selection rules for plasmon-enhanced Raman scattering

We show how to obtain the symmetry-imposed selection rules for plasmonic enhancement in surface- (SERS) and tip-enhanced Raman scattering (TERS). Plasmon-enhanced light scattering is described as a higher-order Raman process, which introduces a series of Hamiltonians representing the interaction between light, plasmons, electrons, and phonons. Using group theory, we derive the active representations for point group symmetries of exemplary plasmonic nanostructures. The phonon representations that are enhanced by SERS and TERS are then found as induced representations for the symmetry group of the molecule or another Raman probe. The selection rules are discussed for graphene that is coupled to a nanodisk dimer as an example for SERS and coupled to a tip as a TERS example. The phonon eigenmodes that are enhanced depend on the symmetry breaking when combining the plasmonic structures with graphene. We show that the most prominent optical phonon modes $({E}_{2g}$ and ${A}_{1g})$ are allowed in all scattering configurations when using a nanodimer as a plasmonic hotspot. We predict the activation of the silent ${B}_{2g}$ as well as infrared-active ${A}_{2u}$ and ${E}_{1u}$ modes in SERS for crossed configurations of the incoming and scattered light. There is a systematic difference between spatially coherent and incoherent plasmon-enhanced Raman scattering, which is responsible for a dependence of TERS on the phonon coherence length.

Universality of Coherent Raman Gain Suppression in Gas-Filled Broadband-Guiding Photonic Crystal Fibers

As shown in the early 1960s, the gain in stimulated Raman scattering (SRS) is drastically suppressed when the rate of creation of phonons (via pump-to-Stokes conversion) is exactly balanced by the rate of phonon annihilation (via pump-to-anti-Stokes conversion). This occurs when the phonon coherence waves synchronized vibrations of a large population of molecules have identical propagation constants for both processes, i.e., they are phase-velocity matched. As recently demonstrated, hydrogen-filled photonic crystal fiber pumped in the vicinity of its zero dispersion wavelength provides an ideal system for observing this effect. Here we report that Raman gain suppression is actually a universal feature of SRS in gas-filled hollow-core fibers, and that it can strongly impair SRS even when the dephasing rate is high, particularly at high pump powers when it is normally assumed that nonlinear processes become more (not less) efficient. This counterintuitive result means that intermodal stimulated Raman scattering (for example between LP01 and LP11 core modes) begins to dominate at high power levels. The results reported have important implications for fiber-based Raman shifters, amplifiers or frequency combs, especially for operation in the ultraviolet, where the Raman gain is much higher.

Phononic Origins of Friction in Carbon Nanotube Oscillators.

Phononic coupling can have a significant role in friction between nanoscale surfaces. We find frictional dissipation per atom in carbon nanotube (CNT) oscillators to depend significantly on interface features such as contact area, commensurability, and by end-capping of the inner core. We perform large-scale phonon wavepacket MD simulations to study phonon coupling between a 250 nm long (10,10) outer tube and inner cores of four different geometries. Five different phonon polarizations known to have dominant roles in thermal transport are selected, and transmission coefficient plots for a range of phonon energies along with phonon scattering dynamics at specific energies are obtained. We find that the length of interface affects friction only through LA phonon scattering and has a significant nonlinear effect on total frictional force. Incommensurate contact does not always give rise to superlubricity: the net effect of two competing interaction mechanisms shown by longitudinal and transverse phonons decides the role of commensurability. Capping of the core has no effect on acoustic phonons but destroys the coherence of transverse optical phonons and creates diffusive scattering. In contrast, the twisting and radial breathing phonon modes have perfect transmission at all energies and can be deemed as the enablers of ultralow friction in CNT oscillators. Our work suggests that tuning of interface geometries can give rise to desirable friction properties in nanoscale devices.

Investigation of phonon coherence and backscattering using silicon nanomeshes

Phonons can display both wave-like and particle-like behaviour during thermal transport. While thermal transport in silicon nanomeshes has been previously interpreted by phonon wave effects due to interference with periodic structures, as well as phonon particle effects including backscattering, the dominant mechanism responsible for thermal conductivity reductions below classical predictions still remains unclear. Here we isolate the wave-related coherence effects by comparing periodic and aperiodic nanomeshes, and quantify the backscattering effect by comparing variable-pitch nanomeshes. We measure identical (within 6% uncertainty) thermal conductivities for periodic and aperiodic nanomeshes of the same average pitch, and reduced thermal conductivities for nanomeshes with smaller pitches. Ray tracing simulations support the measurement results. We conclude phonon coherence is unimportant for thermal transport in silicon nanomeshes with periodicities of 100 nm and higher and temperatures above 14 K, and phonon backscattering, as manifested in the classical size effect, is responsible for the thermal conductivity reduction.

Surface modification of gallium phosphide caused by swift (200 MeV) silver ions

In the present work, the effects of swift silver ion irradiation in crystalline gallium phosphide samples with various fluences ranging between 1×1011 and 2×1013ionscm−2 have been described. Atomic force microscopy images of the samples irradiated with different fluences showed the existence of hillocks at the surface, the diameter and density of these clusters were found to be depend on the ion fluence. As the ion fluence increased (⩾1×1013ionscm−2), the big size hillocks having arbitrary shapes were observed due to outflow of the molten material to the sample surface or defect induced swelling of track areas accumulated during the track overlapping. Phonon confinement model employed to first order Raman scattering from longitudinal optical phonon mode revealed the decrease in phonon coherence length from 73.0nm to 23.7nm with the increase in ion fluence from 1×1012 to 2×1013ioncm−2.

Coherent Vibrational Probes of Hydrogen Bond Structure Following Ultrafast Electron Transfer

We report measurements, ab initio calculations, and analytical models that reveal the coupling of low-frequency phonons to localized vibrations of a hydrogen-bonded organic crystal driven by ultrafast electron transfer. Fourier analysis of spectrally resolved oscillations in the transient reflectivity of mid-infrared probe pulses from single crystals of quinhydrone shows coupling between Raman- and IR-active intermolecular lattice phonons of this material. In addition, phonon coherence spectra of two of these lattice modes show that at least two qualitatively different vibrational transitions near 3000 cm–1 exist in the charge-separated state of quinhydrone. This combined experimental and theoretical approach allows us to estimate the displacement of the O–H stretching vibration of quinhydrone along its different lattice phonon normal coordinates. These results will help better understand and approach a plethora of problems in condensed phases in which electronic and vibrational coupling over vastly diffe...

Two-Dimensional Phononic Crystals: Disorder Matters.

The design and fabrication of phononic crystals (PnCs) hold the key to control the propagation of heat and sound at the nanoscale. However, there is a lack of experimental studies addressing the impact of order/disorder on the phononic properties of PnCs. Here, we present a comparative investigation of the influence of disorder on the hypersonic and thermal properties of two-dimensional PnCs. PnCs of ordered and disordered lattices are fabricated of circular holes with equal filling fractions in free-standing Si membranes. Ultrafast pump and probe spectroscopy (asynchronous optical sampling) and Raman thermometry based on a novel two-laser approach are used to study the phononic properties in the gigahertz (GHz) and terahertz (THz) regime, respectively. Finite element method simulations of the phonon dispersion relation and three-dimensional displacement fields furthermore enable the unique identification of the different hypersonic vibrations. The increase of surface roughness and the introduction of short-range disorder are shown to modify the phonon dispersion and phonon coherence in the hypersonic (GHz) range without affecting the room-temperature thermal conductivity. On the basis of these findings, we suggest a criteria for predicting phonon coherence as a function of roughness and disorder.