Coherent Phonon Negative Refraction via Interfacial Momentum Compensation

Abstract

Negative refraction of coherent phonons is crucial for thermal management and quantum information processing, but it remains unrealized because achieving the suitable dispersion for negative refraction simultaneously with long-range coherence is challenging. In this letter, we overcome this limitation by introducing a momentum compensation mechanism mediated by discrete translational symmetry. Interfacial reciprocal lattice vectors provide momentum compensation during phonon tunneling and induce asymmetric mode matching, resulting in negative refraction without requiring strong dispersion anisotropy or a negative-curvature band. Using non-equilibrium Green's function formalism, we demonstrate coherent negative refraction of isotropic acoustic phonons in graphene/hexagonal boron nitride heterostructures. This general mechanism enables active control of phonon flow via interfacial design, paving the way for applications in atomic-scale phonon lenses and directional thermal transport.

Figures (5)

• Figure 1: Schematic diagram of equifrequency contours (EFCs) analysis. The upper part shows the equifrequency surface analysis in reciprocal lattice space, where the solid lines represent EFCs at the operating frequency and the dashed lines represent EFCs at a slightly higher frequency; the lower part corresponds to the behaviour of phonon propagation in real space. (a) Positive refraction. (b) Total internal reflection. (c) Negative refraction. Here, $\mathbf{k}$ is the phonon wavevector, $\theta$ is the angle, with subscripts $i,r,t$ labeling incident, reflected, and transmitted components respectively, and $\delta$ denotes decay length.
• Figure 2: (a) Device architecture. Transport direction along x; periodicity along y. Semi-infinite left (L) and right (R) thermal leads are composed of graphene and hBN, respectively. (b) Lattice and reciprocal basis vectors. $A_{\parallel}$, $A_{\bot}$ is supercell lattice vectors; $a_{1,2}$ is primitive cell basis vectors of graphene/hBN; $G_{\parallel}$, $G_{\bot}$ is supercell reciprocal lattice vectors; $b_{1,2}$ is primitive reciprocal vectors of graphene/hBN. Corresponding BZ are shaded blue (primitive cell) and warm white (supercell). (c) Full-frequency mode-resolved transmission spectrum. $k_x<0$ and $k_x>0$ regions correspond to graphene and hBN phonon channels, respectively. (d)-(f) Phonon-branch transmission characteristics. Transmission coefficients for longitudinal(LA), transverse(TA), and out-of-plane(ZA) acoustic branches as functions of incidence angle $\theta$ and frequency $\omega$.
• Figure 3: (a) Mode-resolved transmission spectrum at 3.25 THz and (b) at 6.5 THz. The red-shaded region (left) represents the absorption spectrum in graphene, while the blue-shaded region (right) corresponds to the transmission spectrum in hBN. The gray solid line indicates the interface. The incident and transmitted wave vectors, $\mathbf{k}_i$ and $\mathbf{k}_t$, are illustrated by arrowed line segments. Phonon branches are arranged radially from inside to outside as follows: LA, TA, and ZA.
• Figure 4: Incident angle $(\theta_i)$ versus transmission angle $(\theta_t)$ for different phonon modes. (a)–(c) LA, TA, ZA modes at 6.5 THz; (d) TA mode at 16 THz. Blue and Red shading refers to positive, negative refraction regions respectively.
• Figure 5: Phonon transmission eigenchannels. (a) Positive refraction at 3.25THz. Incident angle $\theta_i = 12^\circ$, transmission angle $\theta_t = 14^\circ$. (b) Total internal reflection at 3.25THz. Incident angle $\theta_i = 60^\circ$. The propagation direction of the transmitted wave turns parallel to the interface, with its amplitude decaying exponentially with depth, exhibiting characteristics of an evanescent wave. (c) Negative refraction at 6.5THz. Incident angle $\theta_i = 60^\circ$, transmission angle $\theta_t = -49^\circ$. Phonons gradually turn their propagation direction toward the interface within the interfacial region, while their amplitude shows a decaying trend with medium depth. After crossing the interface, they resume propagation mode, achieving negative refraction.