Quantum cluster quasicrystals

Quasicrystals remain among the most intriguing materials in physics and chemistry. Their structure results in many unusual properties, including anomalously low friction as well as poor electrical and thermal conductivity, but it also supports superconductivity, which shows that quantum effects in quasicrystals can be quite unique. We theoretically study superfluidity in a model quantum cluster quasicrystal. Using path-integral Monte Carlo simulations, we explore a two-dimensional ensemble of bosons with the Lifshitz-Petrich-Gaussian pair potential, finding that moderate quantum fluctuations do not destroy the dodecagonal quasicrystalline order. This quasicrystal is characterized by a small yet finite superfluidity, demonstrating that particle clustering combined with the local cogwheel structure can underpin superfluidity even in the almost classical regime. This type of distributed superfluidity may also be expected in certain open crystalline lattices. Large quantum fluctuations are shown to induce transitions to cluster solids, supersolids, and superfluids, which we characterize fully quantum mechanically.

Figure 1

Quantum QC in the semiclassical regime: (a) PIMC snapshot of the dodecagonal QC at $\mathrm{\Lambda }=0.1$, reduced temperature $t=0.05$, and reduced density $\rho r_0^2=0.8$; here, $N=8192$. (b) Radial distribution function $g\left(r\right)$ for $\mathrm{\Lambda }=0.1$ (red line) and $\mathrm{\Lambda }=0$ (black line). (c) Fourier transform of the positions of world lines in (a). The parameters of the interparticle potential in Eq. (2) are $\sigma =0.770746$, $C_0=1$, $C_2=-1.09456$, $C_4=0.439744$, $C_6=-0.0492739$, and $C_8=0.00183183$ as reported in Ref. [14].

Figure 2

Quantum quasicrystal and reentrant superfluidity: (a)–(d) Dodecagonal quantum QC, cluster crystal, cluster supersolid, and superfluid at $t=0.05$, $\rho r_0^2=0.8$, and $\mathrm{\Lambda }=0.1$, 0.141, 0.632, and 1, respectively; $N=2048$. (e)–(h) Radial distribution functions of the four phases in (a)–(d). Inset in (e): Distribution functions of QC for bosons (solid line), semiclassical boltzmannons (dashed line), and classical particles (dotted-dashed line). (i)–(k) Frequency of exchange cycles of length $L$ in the QC, cluster solid, and supersolid in (a)–(c). (l) Superfluid density profile of the dodecagonal QC from (a).

Figure 3

Phase diagram of 2D Lifshitz-Petrich-Gaussian bosons featuring the dodecagonal quantum QC, supersolid, and superfluid as well as a hexagonal cluster solid and a normal fluid phase. Circles represent the $N=2048$ data points analyzed; the indicated phase boundaries are approximate. The thick black line depicts the Berezinskii-Kosterlitz-Thouless transition $t_{\text{BKT}}\approx \pi {\overline{\rho }}_s{r}_0^2{\mathrm{\Lambda }}^2/2$ (${\overline{\rho }}_s$ being the superfluid density at $t_{\text{BKT}}$) between the normal fluid (yellow) and the superfluid phase (gray).