Competing Periodicities in Fractionally Filled One-Dimensional Bands

Abstract

We present a variable temperature scanning tunneling microscopy and spectroscopy study of the Si(553)-Au atomic chain reconstruction. This quasi-one-dimensional system undergoes at least two charge density wave (CDW) transitions, which can be attributed to electronic instabilities in the fractionally filled 1D bands of the high-symmetry phase. Upon cooling, Si(553)-Au first undergoes a single-band Peierls distortion, resulting in period doubling along the chains. This Peierls state is ultimately overcome by a competing 3 CDW, which is accompanied by a 2 periodicity in between the chains. These locked-in periodicities indicate small charge transfer between the nearly 1=2-filled and 1=4-filled bands. The presence and the mobility of atomic-scale dislocations in the 3 CDW state indicates the possibility of manipulating phase solitons carrying a (spin, charge) of 1=2; e=3 or 0; 2e=3 . DOI: 10.1103/PhysRevLett.96.076801 PACS numbers: 73.20.At, 68.37.Ef, 71.10.Pm, 73.20.Mf According to the Mermin-Wagner theorem [1], thermodynamic fluctuations preclude the formation of a longrange ordered broken symmetry state in one dimension, except at T 0 K [2]. For all practical purposes, however, thermodynamic phase transitions may still be possible in finite size 1D systems. Furthermore, fluctuations are inevitably suppressed if the 1D chains are weakly coupled, or if the chains are coupled to a substrate [2,3]. Prototypical 1D metallic systems such as the transition metal trichalcogenides, organic charge transfer salts, blue bronzes, and probably all atomic Au-chain reconstructions on vicinal Si substrates exhibit symmetry breaking phase transitions at finite temperatures [4,5]. For a band filling of 1=n, the phase transition opens up a gap in the single particle excitation spectrum at wave vector k F =na, and the corresponding broken symmetry state adopts the new periodicity of =k F na, where a is the lattice parameter of the high-symmetry phase [4].Fractional band fillings other than half filling provide an interesting subset of 1D systems which often exhibit exotic physical phenomena. Depending on the relative magnitude of bandwidth and electron-electron interaction, charge density wave (CDW) states often compete with spin density waves, Mott insulating states, or a Luttinger liquid state. Atomic-scale STM observations of surface phase transitions provide important insights into the complexity of symmetry breaking phenomena in reduced dimensionality [6]. For instance, the recently reported 4 1-to-8 2 phase transition in quasi-1D indium chains on Si(111) [6] involves a gap opening in a complex triple band Peierls system, resulting in a doubling of the periodicity along the atom chains. Another recently discovered system with three fractionally filled bands is the Si(553)-Au surface. Angle-resolved photoemission spectroscopy (ARPES) [7] revealed three metallic bands, but despite theoretical efforts to understand the electronic structure [7,8], the atomic structure and real space location of the surface state orbitals remain...

Systematic investigation of the structure of the Si(553)-Au surface from first principles

“…In general, we can say that the comparison with the available experimental data is satisfactory. In agreement with the experimental images, 21,23,24 the most prominent feature is the step edge. Within the terrace, we find signals coming from the row of gold atoms and its neighboring HC structure.…”

“…40 The simulated STM images of the f2 and f4 models are in good agreement with the available experimental data. 24,41 Their band structures also reproduce the main features of the photoemission data. 17,21 In particular, the band structure of the f2 model shows two dispersive onedimensional bands and one of them, which is associated with a silicon dangling bond in the surface, has a small fractional occupation that is in agreement with the measurements.…”

“…The Si͑553͒-Au reconstruction is known to suffer several distortions that increase the size of the unit cell along the step direction as the temperature is decreased. 21,24 However, here, we only consider models that preserve the ϫ1 periodicity of the silicon substrate along the steps and, therefore, are relevant to the model of a high temperature structure.…”

“…However, these three reconstructions suffer structural distortions associated with metal-insulator transitions when the temperature is lowered. 12,21,24,25,29,30 The photoemission spectrum of the Si͑557͒-Au surface is dominated by two proximal one-dimensional bands with paraboliclike dispersions. According to ab initio calculations based on the existing structural model, 10,11 these two bands are due to the spin-orbit splitting of a band coming from the hybridization of the states of the gold chains with their silicon neighbors.…”

“…In the case of vicinal substrates, the average terrace width can be controlled by the miscut angle, which provides a route to tuning interwire distances and interactions. 3 Some examples of quasi-one-dimensional reconstructions that have attracted much attention in recent years are the Si͑111͒-͑5 ϫ 2͒-Au, [3][4][5][6][7] Si͑557͒-Au, [8][9][10][11][12][13][14][15][16] Si͑553͒-Au, [17][18][19][20][21][22][23][24] and Si͑111͒-͑4 ϫ 2͒-In ͑Refs. 25-37͒ surfaces.…”