Effective Mass of Two-Dimensional ${}^3\mathrm{H}\mathrm{e}$

We use structural information from diffusion Monte Carlo calculations for two-dimensional ${}^3\mathrm{H}\mathrm{e}$ to calculate the effective mass. Static effective interactions are constructed from the density and spin-structure functions using sum rules. We find that both spin and density fluctuations contribute about equally to the effective mass. Our results show, in agreement with recent experiments, a flattening of the single-particle self-energy with increasing density, which eventually leads to a divergent effective mass.

Figure 1

The density structure functions $S(k)$ (upper curves) and correlation part of the spin structure functions $S_{\sigma }(k)-S_F(k)$ (lower curves) are shown at the densities $\rho =0.046{\AA }^{-2}$ (solid lines) and $\rho =0.061{\AA }^{-2}$ (dashed line). The zero level (dotted line) is included as a guide to the eye.

Figure 2

The density-channel and spin-channel interactions obtained from the corresponding structure functions through the RPA relationship (3) are shown for the densities $\rho =0.046{\AA }^{-2}$ (solid lines) and $\rho =0.061{\AA }^{-2}$ (dashed lines). The interactions are given in units of ${\hslash }^2{k}_F^2/2m$.

Figure 3

The figure shows the Fock term $u(k)$ (short-dashed line), the “density” term ${\Sigma }_{\rho }\mathbf{(}k,t(k)\mathbf{)}$ (solid line), and the “spin” term ${\Sigma }_{\sigma }\mathbf{(}k,t(k)\mathbf{)}$ (long-dashed line) of the self-energy for the density $\rho =0.046{\AA }^{-2}$. All functions have been shifted to be zero at the Fermi momentum; all energies are given in units of ${\hslash }^2{k}_F^2/2m$.

Figure 4

The figure shows the full on-shell spectrum (7) for the densities $\rho =0.026{\AA }^{-2}$, $\rho =0.046{\AA }^{-2}$, and $\rho =0.061{\AA }^{-2}$. The free single-particle spectrum $t(k)$ is also shown for comparison. All functions have been shifted to be zero at the Fermi momentum; all energies are given in units of the Fermi energy of the noninteracting liquid.

Figure 5

The figure shows the density dependence of $m/m^{*}$ at the Fermi wave number $k_F$ (solid line). Also shown are the results from density fluctuations (long-dashed line) and from spin fluctuations only (short-dashed line). The dashed lines with solid markers show the experimental values of Refs. 6, 17, 18. The lines through the theoretical data are quadratic fits.