Magnetic Breakdown Induced Peierls Transition

We predict a new type of phase transition in a quasi-one-dimensional system of interacting electrons at high magnetic fields, the stabilization of a density wave which transforms a two-dimensional open Fermi surface into a periodic chain of large pockets with small distances between them. We show that quantum tunneling of electrons between the neighboring closed orbits enveloping these pockets transforms the electron spectrum into a set of extremely narrow energy bands and gaps that decreases the total electron energy, thus leading to a magnetic breakdown induced density wave ground state analogous to the well-known instability of the Peierls type.

Figure 1

Quasi one-dimensional Fermi surface, $\epsilon (\overrightarrow{p})={\epsilon }_F$, where $\epsilon (\overrightarrow{p})$ is the electron dispersion law and ${\epsilon }_F$ is the Fermi energy, with arrows denoting directions of semiclassical electron motion under a magnetic field perpendicular to the plane ($p_x$, $p_y$). $b_x^{*}$ and $b_y^{*}$ are reciprocal lattice constants.

Figure 2

(a) Periodic net of large closed orbits separated by small classically inaccessible MB arrears (thick dots). $\overrightarrow{Q}=(Q\approx 2k_F,0)$ is lattice deformation wave vector, and the distance between closed orbits is proportional to the product of electron mass and deformation potential $V(x)$. (b) Areas of closed orbits, $S_{1,2}$, and areas under open orbits, $S_{3,4}$ for the respective left and right motion of electrons, determine the phases of semiclassical electron wave functions defined in the text.

Figure 3

(a) Energy spectrum for electrons shown in Fig. 2 in the regime of strong MB ($|\tau {|}^2\ll 1$). $n$ is the MB band number and $P_{x0}$ is the conserved generalized electron momentum. The period of $E_n(P_{x0})$ is $2\pi \sigma /b_y^{*}$, while the widths of the energy bands and gaps are $\Delta E_{\mathrm{band}}\sim |\rho {|}^2\hslash {\omega }_c$ and $\Delta E_{\mathrm{gap}}\sim |\tau {|}^2\hslash {\omega }_c$ respectively (${\omega }_c$ is the cyclotron frequency). Dotted straight lines denote the electron spectrum in the absence of MB. (b) The free energy difference $\Delta F/\Delta F_0$ vs $x\equiv (\pi g^2/\sigma |v_x{v}_y|)b^2$ for $\gamma \equiv (\sigma |v_x{v}_y|/\pi g^2)(\hslash {\omega }_Q/\Delta F_0)=0.8$, showing stable minimum of DW ground state at $x_0\approx 0.22$.