Angular magnetoresistance oscillations in quasi-one-dimensional organic conductors in the presence of a crystal superstructure

We study the effect of crystal superstructures produced by orientational ordering of the ${\text{ReO}}_4$ and ${\text{ClO}}_4$ anions in the quasi-one-dimensional organic conductors, ${\left(\text{TMTSF}\right)}_2{\text{ReO}}_4$ and ${\left(\text{TMTSF}\right)}_2{\text{ClO}}_4$, on the angular magnetoresistance oscillations observed in these materials. Folding of the Brillouin zone due to anion ordering generates effective tunneling amplitudes between distant chains. These amplitudes cause multiple peaks in interlayer conductivity for the magnetic-field orientations along the rational crystallographic directions (the Lebed magic angles). Different wave vectors of the anion ordering in ${\left(\text{TMTSF}\right)}_2{\text{ReO}}_4$ and ${\left(\text{TMTSF}\right)}_2{\text{ClO}}_4$ result in the odd and even Lebed angles, as observed experimentally. When a strong magnetic field is applied parallel to the layers and perpendicular to the chains and exceeds a certain threshold, the interlayer tunneling between different branches of the folded electron spectrum becomes possible, and interlayer conductivity should increase sharply. This effect can be utilized to probe the anion ordering gaps in ${\left(\text{TMTSF}\right)}_2{\text{ClO}}_4$ and ${\left(\text{TMTSF}\right)}_2{\text{ReO}}_4$. An application of this effect to $\kappa \text{−}{\left(\text{ET}\right)}_2\text{Cu}{\left(\text{NCS}\right)}_2$ is also briefly discussed.

Figure 1

(Color online) A view along the chains of a Q1D metal with the anion ordering at a wave vector $\mathit{Q}$. The filled and open circles represent the chains with the energies $\pm E_g$. (a) ${\left(\text{TMTSF}\right)}_2{\text{ReO}}_4$ and $\mathit{Q}=\left(0,1/2,1/2\right)$. (b) ${\left(\text{TMTSF}\right)}_2{\text{ClO}}_4$ and $\mathit{Q}=\left(0,1/2,0\right)$.

Figure 2

(Color online) (a) Plot of the function $f\left(\varphi \right)$ given by Eq. (22). (b) Plot of the second term in $f\left(\varphi \right)$ given by Eq. (25). In both plots, $E_g/2t_b=0.1$.

Figure 3

(Color online) Normalized interlayer conductivity ${\sigma }_{zz}/{\sigma }_0$ calculated from Eq. (13) for ${\left(\text{TMTSF}\right)}_2{\text{ReO}}_4$ and plotted vs $B_y^{\prime }$ at $B_x^{\prime }=0$ shown in the linear (left) and logarithmic (right) scales.

Figure 4

(Color online) Contour plot of $\text{ln}\left({\sigma }_{zz}/{\sigma }_0\right)$ calculated from Eq. (13) for ${\left(\text{TMTSF}\right)}_2{\text{ReO}}_4$ at ${\omega }_c\tau =\sqrt{50}$.

Figure 5

(Color online) Plot of ${\sigma }_2/{\sigma }_0^{\prime }$ vs $B_y^{\prime }$ at $B_x^{\prime }=0$ shown in the linear (left) and logarithmic (right) scales. ${\sigma }_2$ is the contribution to ${\sigma }_{zz}$ in Eq. (13) from the second term in Eq. (25), and ${\sigma }_0^{\prime }={\sigma }_0{\left(t_c^{\prime }/t_c\right)}^2$.

Figure 6

(Color online) Fermi surfaces of two adjacent layers shifted by the vector $\mathit{q}$ of Eq. (28) due to an in-plane magnetic field. The Fermi surfaces for each layer (the solid lines and the dashed lines) consist of two bands separated by the gap $2E_g/v_F$ due to anion ordering and labeled $+$ and $-$.

Figure 7

(Color online) Phase diagram of interlayer tunneling vs the normalized in-plane magnetic-field components $B_y$ and $B_x$. Tunneling between the same and different types of bands is possible in the upper left and the lower right regions of the diagram, correspondingly, and not possible in the intermediate region. The thin curves show the interlayer conductivity ${\sigma }_{zz}$ calculated using Eq. (34) as a function of $B_y$ for several values of $B_x$ for the superstructure of ${\left(\text{TMTSF}\right)}_2{\text{ReO}}_4$.

Figure 8

(Color online) The same as in Fig. 7 but for the superstructure of ${\left(\text{TMTSF}\right)}_2{\text{ClO}}_4$.

Figure 9

(Color online) The in-plane Fermi surface of $\kappa \text{−}{\left(\text{ET}\right)}_2\text{Cu}{\left(\text{NCS}\right)}_2$. The $\alpha$ and $\beta$ branches of the Fermi surface are separated by the distance $\Delta k$ in the momentum space.