Topological instability of two-dimensional conductors

Abstract

In the present paper we propose a mechanism of the structural instability with a periodic charge ordering in two-dimensional isotropic conductors with a closed Fermi surface which completely excludes the conventional nesting mechanism. We show that the structural instability in such conductors may arise as a topological reconstruction under which the initially closed Fermi surface is transformed into an open one. We have found that the order parameter of the charge ordering ground state may exceed one hundredth of the Fermi energy. Furthermore, this charge ordering is a quantum phase transition with respect to the dimensionless coupling constant λ related to the mechanism that drives the band reconstruction (e. g. electron-phonon coupling), with the critical value given by λc = (1+2/π) −1 . Preliminary estimations show that the suggested mechanism can be the origin of density waves observed in such materials as high−Tc cuprates or graphite intercalates.

Density wave and topological reconstruction of an isotropic two-dimensional electron band in external magnetic field

“…In the present paper we consider the latter situation. Extending the treatment initiated in our previous work 6 , we show that in such situation one can stabilize the DW under a strong magnetic field as well. Even more, we show that under magnetic field the DW order is additionally strengthened, and appears at lower values of the critical coupling constant.…”

“…where ω Q ≡ ω(q = Q). The comprehensive analysis of this Hamiltonian, i. e. of the band reconstruction due to the DW order, in the case of vanishing magnetic field (H = 0) is given in the work 6 . For finite magnetic fields it is more convenient to diagonalize the Hamiltonian by using the coordinate representation of electron field,…”

“…For further considerations it is convenient to use, like in Ref. 6 , the new origin in the momentum space coinciding with the touching point due to the finite DW, with corresponding electron momentum components p x = k x + Q/2, p y = k y , and the first Brillouin zone defined by −Q/2 ≤ p x ≤ Q/2 (see Fig.1 in which these coordinates are already used). Then the Hamiltonian (6) can be replaced by the Lifshitz -Onsager equation 20,21…”

“…In our recent paper 6 we have proposed a mechanism of the DW ordering based on the topological reconstruction of the highly symmetric, initially closed Fermi surface. As shown in Fig.1(a), the DW has a wave vector Q/ that brings the initial FS into the so-called touching range generated at the edge of the Brillouin zone established by the DW periodic modulation in the system.…”

“…As shown in Fig.1(a), the DW has a wave vector Q/ that brings the initial FS into the so-called touching range generated at the edge of the Brillouin zone established by the DW periodic modulation in the system. By lifting the energy degeneracy and opening the gap in that region, the band topology changes: two parabolic initial bands now form the lower band with saddle point and the upper band with parabolic minimum at the touching point 6 . The new Fermi surface then becomes open as shown in Fig.1(b), while the total band energy is decreased.…”