Suppression of Peierls-like nesting-based instabilities in solids

Understanding instabilities is of vast importance in material science. One such example is the Peierls instability of one-dimensional metals with a single band. The question is why H and Li chains behave so differently in spite of their similar electronic structure. We demonstrate that this is due to the suppression of the susceptibility for Li because of the interatomic, interorbital s-p mixing of the band crossing the Fermi energy. The influence of this on the structure-factor-like term in response functions is critical and depends on the wave function's details also in higher dimensions.

Figure 1

(a) Diagram of an undisturbed 1D configuration (upper chain) and a configuration with a nonzero dimerization (lower chain). (b) Total DFT energy change as a function of distance between neighboring atoms. The energy difference between the ground state and the undisturbed state of H is 143 meV.

Figure 2

DFT orbital-projected band structures for undisturbed chains of (a) hydrogen and (b) lithium. The dashed (solid) black line corresponds to tight-binding, nearest-neighbor purely $2s$ and ($2p$) dispersions. (c) Schematic of the real-space 1D lithium chain model considered for the tight-binding Hamiltonian in Eq. (4). $2s$ and $2p_z$ orbitals are shown (including $+$ and $-$ signs indicating phases) with their associated creation operators, along with the hopping parameters and overlap integrals that are taken into account. The hopping parameters used are discussed in the text.

Figure 3

Charge susceptibility of an undisturbed 1D chain of (a) hydrogen and (b) lithium using DFT energy data and eigenfunctions obtained from a tight-binding fit to the DFT band structure. The effect including s-p hybridization (in red at zero temperature and in blue at $T=95\mathrm{K}$) compared with enforcing a purely $2s$ state (in black at $T=0$) is shown for Li. The insets show the peaks at $q=2k_F$. (c) Ratio of the peak height of the full lithium charge susceptibility and of the susceptibility calculated with a very large charge transfer energy $\mathrm{\Delta }$ as a function of $\mathrm{\Delta }$. (d) Ratio of the charge susceptibility peak height and its value at $q=0$ as a function of temperature for both H and Li. The yellow lines correspond to the temperatures at which $\chi \left(2k_F\right)=\chi \left(0\right)$.

Figure 4

Orbital contributions to the lithium one-dimensional chain susceptibility with respect to $q$ as outlined in Eq. (5). The susceptibility $\chi \left(q\right)$ (in blue) is the sum of the three other individual plotted terms.

Figure 5

Coefficients for the lower-energy eigenstate obtained from the diagonalization of the tight-binding Hamiltonian representing the 1D infinite Li chain.