Weakly incoherent regime of interlayer conductivity in a magnetic field

We investigate the electronic conductivity in layered metals in magnetic field in the “weakly incoherent” limit, when the interlayer transfer integral is smaller than the Landau-level separation and broadening by impurities, but the interlayer electron tunneling conserves the intralayer momentum. It is shown that the impurity potential has much stronger effect in this regime, than in the quasi-two-dimensional metals in the coherent limit. The weakly incoherent regime has several unique qualitative features, missed in the previous theoretical approaches. The background interlayer magnetoresistance in this regime monotonically grows with the increase of magnetic field perpendicular to the conducting layers. The Dingle temperature increases with magnetic field, which damps the magnetic quantum oscillations and changes the field dependence of their amplitudes. The angular magnetoresistance oscillations become much smoother, and the positions of magnetoresistance maxima at the Yamaji angles slightly shift. The monotonic part of the angular dependence of magnetoresistance also considerably changes in the weakly incoherent regime.

Figure 1

The MQO of resistivity $R_{\mathit{zz}}(B)=1/{\sigma }_{\mathit{zz}}$, calculated using Eq. (34) with ${\Gamma }_B$ given by Eq. (20) (solid blue line) and with ${\Gamma }_B={\Gamma }_0$, which corresponds to Ref. 22 (dashed red line). The parameters used to plot (a) are $m^{*}=1.45m_e$, ${\Gamma }_0=0.58$ K, and $T=1$ K. The parameters in(b) are $m^{*}=m_e$, ${\Gamma }_0=1$ K, and $T=0.6$ K.

Figure 2

The angular dependence of conductivity ${\sigma }_{\mathit{zz}}(\theta )/{\sigma }_{\mathit{zz}}(0)$ (a) and of magnetoresistance $R_{\mathit{zz}}(\theta )/R_{\mathit{zz}}(0)$ (b), calculated using Eq. (36) with ${\tau }_B$ given by Eq. (37) (solid blue line) and with ${\tau }_B={\tau }_0$ (dotted red line). The parameters for this plot are $k_{F}d=4$, $m^{*}=m_e$, $B=3$ T, ${\Gamma }_0=1$ K, which gives ${\omega }_c\tau \approx 1.74$.

Figure 3

The same as in Fig. 2 but at a higher magnetic field value $B=15$ T, which corresponds to ${\omega }_c\tau \approx 8.7$.

Figure 4

The first diagram for the electron self-energy with the intersection of the impurity lines.

Figure 5

The set of diagrams for the irreducible self-energy, corresponding to the self-consistent single-site approximation. The double solid line symbolizes the exact electron Green’s function.