Equivalence of electronic and mechanical stresses in structural phase stabilization: A case study of indium wires on Si(111)

Abstract

It was recently proposed that the stress state of a material can also be altered via electron or hole doping, a concept termed electronic stress (ES), which is different from the traditional mechanical stress (MS) due to lattice contraction or expansion. Here we demonstrate the equivalence of ES and MS in structural stabilization, using In wires on Si(111) as a prototypical example. Our systematic density-functional theory calculations reveal that, first, for the same degrees of carrier doping into the In wires, the ES of the high-temperature metallic 4×1 structure is only slightly compressive, while that of the low-temperature insulating 8×2 structure is much larger and highly anisotropic. As a consequence, the intrinsic energy difference between the two phases is significantly reduced towards electronically phase-separated ground states. Our calculations further demonstrate quantitatively that such intriguing phase tunabilities can be achieved equivalently via lattice-contraction induced MS in the absence of charge doping. We also validate the equivalence through our detailed scanning tunneling microscopy experiments. The present findings have important implications in understanding the underlying driving forces involved in various phase transitions of simple and complex systems alike.

Two-dimensional chiral stacking orders in quasi-one-dimensional charge density waves

“…To properly predict the energetics of the In/Si(111) system, we have performed DFT calculations employing the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional 13,14 with the van der Waals (vdW) correction 15,16 (referred to as HSE+vdW) within the FHI-aims code 17 . Note that the HSE+vdW scheme has been successfully applied to predict the energetics of 4 × 1, 4 × 2, and 8 × 2 structures as well as the band gap [18][19][20][21] , which is consistent with previous experimental observations 22,23 . Since the energy differences among various phases are small, we carefully performed calculations with dense 256 k points per 4 × 1 unit cell and force criteria for optimizing the structures being set to 0.001 eV/ Å.…”

Two-dimensional chiral stacking orders in quasi-one-dimensional charge density waves

“…All the atoms except the bottom two layers were allowed to relax until all the residual force components were less than 0.02 eV/ Å. We note that SCAN functional tends to underestimate the band gap but the overall band structure and the energetics between various 8 × 2 insulating states are comparable to the previously reported HSE+vdW results of hybrid exchange-correlation functional [13,[20][21][22]24], as shown in Table S1. TABLE S1.…”

“…As expected, the magnitude of circular dichroism follows the same tendency to the degree of symmetry breaking, i.e., tensile strain enhances the circular dichroism magnitude. In addition, we expect that the circular dichroism magnitude can be enhanced when the hole doping that stabilizes CDW phase [22] is introduced.…”

“…Recently, our previous work [13] demonstrated the existence of various 2D CDW chiral stacking orders in the selfassembled quasi-one-dimensional In atomic chains on Si(111) surface [14][15][16][17][18][19][20][21][22][23][24][25]. Here, each In atomic chain is dimerized parallel to the chain generating four degenerate chiral CDW building blocks due to the spontaneous mirror symmetry breaking [23].…”

Defect-induced solitons in double Peierls chain model

“…Otherwise, one should consider the secondary interactions depending on the experimental situation. For example, to realize the suggested defect-induced soliton in the In/Si(111) system, it is necessary to consider the interwire coupling between neighboring wires [50][51][52][53][54][55], which will be an interesting future work.…”