Incoherent Bragg reflection and Fermi-surface hot spots in a quasi-two-dimensional metal

We propose a mechanism whereby a finite correlation length associated with the periodicity of the crystalline lattice gives rise to incoherent Bragg reflection of quasiparticles. This introduces an additional effective scattering rate ${\tau }_{\text{hot}}^{-1}\left[{\mathbf{k}}_{\mathrm{F}}\right]$ that selectively damps quantum oscillations originating from orbits that are the product of Bragg reflection. The model is applied to the dimerization in $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{Cu}{\left(\mathrm{NCS}\right)}_2$ where we show that ${\tau }_{\text{hot}}^{-1}\left[{\mathbf{k}}_{\mathrm{F}}\right]$ is strongly dependent on the Fermi momentum ${\mathbf{k}}_{\mathrm{F}}$, being concentrated at “hot spots” located on the Brillouin zone boundary.

Figure 1

(Color online) A schematic of the Fermi surface of $\kappa \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2\mathrm{Cu}{\left(\mathrm{NCS}\right)}_2$ before (dotted lines) and after (solid lines) its reconstruction due to Bragg reflection at the Brillouin zone boundary. The red dots indicate the proposed positions of hot spots at the Brillouin zone boundary.

Figure 2

Examples of the shift in the TDO frequency due to the sample’s finite resistivity, displayed for five different samples T1 and T2, grown in Tsukuba, A1 and A2 grown in Argonne and L1 grown in London.

Figure 3

Dingle plots of $\ln A_{\alpha }$ and $\ln A_{\beta }$ versus $1∕B$ having corrected for $R\left(T\right)$ and renormalized the amplitude of the quantum oscillations by the background magnetoresistance, together with fits to Eq. (1) shown for $B_0=38\mathrm{T}$ (see text).

Figure 4

(a) Scattering rates determined from Fig. 3 as a function of $B_0$. (b) The ratio ${\tau }_{\alpha }^{-1}∕{\tau }_{\beta }^{-1}$ as a function of $B_0$. The dashed line represents ${\tau }_2^{-1}∕{\tau }_1^{-1}$ estimated using Eq. (2). (c) Plot of ${({\tau }_{\alpha }∕{\tau }_{\beta })}^2$ with the solid lines representing ${({\tau }_{\alpha }∕{\tau }_{\beta })}^2\pm \sigma$ to estimate the value of $B_0$ (dotted line) where convergence occurs.

Figure 5

(a) A plot of the Fermi surface topology in the vicinity of the Brillouin zone boundary as a consequence of Bragg reflection. (b) A plot of the calculated ratio ${\tau }_{\text{hot}}^{-1}\left[{\mathbf{k}}_{\mathrm{F}}\right]∕{\tau }_{\text{hot}}^{-1}$ according to the model as a function of the momentum vector $k_y$ parallel to $\mathbf{K}$.