Fluctuation-Induced Supersolidity at the Superfluid-Solid Interface

Abstract

Supersolidity, combining superfluid and crystalline orders, has been realized in dipolar Bose-Einstein condensates by tuning interatomic interactions. Here we show that supersolidity can also emerge from mode coupling at a superfluid-solid interface, without modifying bulk interactions and for a broad class of superfluids. Using an analytical and numerical treatment of the coupled superfluid and phonon fields, we derive the criterion for a density-modulation instability driven by interfacial coupling and dependent on dimensionality. In superfluid helium, the instability first appears at the roton mode, while in a Bose-Einstein condensate with contact interactions it occurs at the lowest accessible wave vector set by the system size. Beyond the threshold, the ground state acquires an interfacial density modulation while the bulk remains superfluid, forming a hybrid superfluid-supersolid phase. Our results identify interfacial mode coupling as a promising route to supersolidity, enabling the simultaneous exploitation of interfacial supersolid and bulk superfluid quantum properties.

Figures (3)

• Figure 1: Model.(a) Schematics of the system: a superfluid is deposited at a smooth solid interface. Both the superfluid and the solid have density fluctuations and they interact through an attractive coupling, but they remain uncorrelated. (b) Schematics of a supersolid phase: in order to maximize the attractive interfacial coupling the density of both the superfluid and the solid present an in-phase density modulation in space, breaking the translation symmetry.
• Figure 2: Supersolid transition in 2D.(a) Spectral function $-\frac{1}{\pi}\textnormal{Im}\left[G^{\rm R}(\textbf{q},\omega+i0^+)\right]$ of a 2D layer of He II renormalised by acoustic phonon of speed $c=250$ m/s through an interfacial coupling $\alpha= 0.02$ meV.nm$^3$. Helium has a density of $n_0=2.2\cdot 10^{28}$ /m$^3$ and we use $\theta=0.3$ nm. The solid has an atomic density $n_{\rm sol}^0=38$ /nm$^2$ and mass $m_{\rm sol}=12\;m_0$ ($m_0$ being the atomic mass). The dashed lines correspond to the energy bands of non-interacting superfluid helium and phonons. (b) Critical interfacial coupling $\alpha$ to induce the supersolid instability as a function of the wavevector of the density modulation for the same system. The minimum corresponds to the roton mode. (c) Sketch of the instability bifurcation: the uniform density state becomes instable above the interfacial coupling critical and a density modulation then becomes stable. The translation symmetry breaking results into a bifurcation. (d) Phase diagram for a 2D layer of a BEC of thickness $\theta=1$ nm over a length $L_x=50$ nm interacting with acoustic phonons of speed $c=50$ m/s: relative density modulation amplitude $\epsilon_0/\sqrt{n_0}$ as a function of the contact coupling $g$ and interfacial coupling $\alpha$. The supersolid phase corresponds to a nonzero modulation. The BEC molecular mass $m=7\; m_0$ with density $n_0=10^{23}$ /m$^3$.
• Figure 3: Supersolid transition in 3D.(a) Critical interfacial coupling $\alpha$ to induce the supersolid instability as a function of the wavevector of the density modulation for He II and acoustic phonons of speed $c=250$ m/s. The minimum corresponds to the roton mode. (b) Phase diagram of a BEC over a length $L_x=50$ nm interacting with acoustic phonons of speed $c=50$ m/s: relative density modulation amplitude $\epsilon_0/\sqrt{n_0}$ as a function of the contact coupling $g$ and interfacial coupling $\alpha$. The supersolid phase corresponds to a nonzero modulation. (c) Ground state density $n/n0$ of the BEC for $\alpha=1.1\; \alpha_c$ as a function of space. Here, $g=0.75$ meV.nm$^3$, $\alpha_c\approx 0.16$ meV.nm$^3$, $\xi\approx 6.3$ nm and $L_x=8\xi=50$ nm. (d) Ground state density $n/n0$ of the same system at the interface as a function of in-plane distance $x/\xi$. The average interfacial density is indicated as a blue dashed line, the bulk density is indicated as a black dashed line. (e) Ground state density $n/n0$ of the same system from the interface at $x=0$ as a function of the out-of-space distance $z/\xi$. The exponential decay predicted for small fluctuations is indicated as a dashed line.