False spin zeros in the angular dependence of magnetic quantum oscillations in quasi-two-dimensional metals

The interplay between angular and quantum magnetoresistance oscillations in quasi-two-dimensional metals leads to the angular oscillations of the amplitude of quantum oscillations. This effect becomes pronounced in high magnetic field, where the simple factorization of the angular and quantum oscillations is not valid. The amplitude of quantum magnetoresistance oscillations is reduced at the Yamaji angles, i.e., at the maxima of the angular magnetoresistance oscillations. These angular beats of the amplitude of quantum oscillations resemble and may be confused with the spin-zero effect, coming from the Zeeman splitting. The proposed effect of “false spin zeros” becomes stronger in the presence of incoherent channels of interlayer electron transport and can be used to separate the different contributions to the Dingle temperature and to check for violations of the standard factorization of angular and quantum magnetoresistance oscillations.

Figure 1

Comparison of the functions $S_0\left(B_z\right)$ (solid green line) and $S_p\left(B_z\right)$ at $p=0$ (dashed red line), given by Eqs. (17) and (18) at $\left|\text{Im}\mathrm{\Sigma }\left(\varepsilon \right)\right|={\mathrm{\Gamma }}_0=\text{const}$ and $\alpha =20\gamma$. Both functions show oscillations around the same background, but the amplitude of the oscillations of $S_0\left(B_z\right)$ is much stronger at $\gamma \ll 1$. The dotted blue line gives $2S_p\left(p=1\right)$ for comparison.

Figure 2

Comparison of the new formula for conductivity ${\sigma }_{zz}^{\mathrm{new}}\left(B_z\right)$, given by Eqs. (16, 17, 18) and shown by the solid blue line, with ${\sigma }_{zz}^{\mathrm{old}}\left(B_z\right)$, given by Eqs. (4) and (2) with ${\sigma }_{zz}^{\mathrm{MQO}}\left(B\right)={\sigma }_{zz}^0{S}_0\left(B_z\right)$ and shown by the dashed red line. For this comparison we take three different values of $\kappa \equiv k_{F}dtan\theta$: (a) ${\kappa }_1=1$, (b) ${\kappa }_2=2$, and (c) ${\kappa }_3=2.405$. The latter corresponds to the first Yamaji angle. The insets show resistivity $R_{zz}\left(B_z\right)\approx 1/{\sigma }_{zz}\left(B_z\right)$.

Figure 3

The angular dependence of conductivity (main panel) and magnetoresistance (inset) at $k_{F}d=3, {\omega }_{c0}{\tau }_0=5$ and at three temperatures: $T=0.1{\mathrm{\Gamma }}_0$ (blue solid line), $T=0.5{\mathrm{\Gamma }}_0$ (red dashed line), and $T={\mathrm{\Gamma }}_0$ (green dotted line). The minima of the MQO amplitude, arising from the influence of AMROs on MQOs, may be erroneously treated as spin zeros.

Figure 4

The angular dependence of magnetoresistance in the presence of the incoherent channel of interlayer conductivity at (a) ${\sigma }_{zz}^i=0.04{\sigma }_0$ and (b) ${\sigma }_{zz}^i=0.2{\sigma }_0$ for three temperatures: $T=0.1{\mathrm{\Gamma }}_0$ (blue solid line), $T=0.5{\mathrm{\Gamma }}_0$ (red dashed line), and $T={\mathrm{\Gamma }}_0$ (green dotted line).

Figure 5

The maxima (solid blue line) and minima (dashed red line) of quantum oscillations of interlayer conductivity (main panel) and of magnetoresistance (inset) calculated in SCBA in the absence of an electron reservoir as a function of the tilt angle $\theta$ of the magnetic field at $k_{F}d=3$ and ${\gamma }_0=2$. These plots give the angular dependence of the envelope of MQOs.

Figure 6

Angular dependence of the relative amplitude $\left({\sigma }_{zz}^{max}-{\sigma }_{zz}^{min}\right)/{\sigma }_0$ of the oscillations of interlayer conductivity at $k_{F}d=3$ for various ${\gamma }_0$ calculated in SCBA in the absence of an electron reservoir.

Figure 7

Angular dependence of the relative amplitude $\left({\sigma }_{zz}^{max}-{\sigma }_{zz}^{min}\right)/{\sigma }_0$ of oscillations of interlayer conductivity for various $k_{F}d$ at ${\gamma }_0=3$ calculated in SCBA.