Is the Electronic Structure of Liquid Metals Free‐Electron‐Like or Bloch‐Electron‐Like?

Abstract

The electronic density of states (EDS) are calculated for liquid Na, Hg, Ga, Pb, Sn, and Bi. Calculations are performed using two formalisms : (i) second-order perturbation theory and (ii) the Green function theory. The EDS plots resulting from these two sets of calculations reveal that the perturbation calculations give consistently more structure than the Green function calculations. However, the general features of the two sets of calculations are the same and agree within their respective theoretical limitations and basic approximations. It is concluded that the electronic structure of liquid metals is neither free-electron-like nor Bloch-electron-like.Die elektronische Zustandsdichte (EDS) wird fur flussiges Ka, Hg, Ga, Pb, Sn und Bi berechnet. Die Rechnungen werden mittels zweier Formalismen durchgefuhrt : 1) Storungstheorie zweiter Ordnung und 2) Theorie Greenscher Funktionen. Die sich &us diesen beiden Rechnungsmethoden ergebenden EDS-Kurven zeigen, daO die Storungsrechnungen konsistent mehr Strukturen als die Rechnungen mit Greenschen Funktionen ergeben. Jedoch ist der allgemeine Verlauf mit beiden Rechenmethoden derselbe und stimmt mit den entsprechenden theoretischen Grenzen und Grundnaherungen uberein. Es wird angenommen, daO die elektrische Struktur der flussigen Metalle weder der freier Elektronen noch der des Bloch-Elektrons Lhnlich ist.') Tampa, Florida 33630, USA.

Review Selected properties of simple amalgams

“…Electrons in liquid metals are neither completely free nor localized [98], therefore the use of atomic radii is less erroneous than the use of the ionic radii of metals from their crystalline chlorides or oxides. As recently determined by Schwab and Schindewolf [99] the radius of sodium (which is easily ionized) in its amalgam is 1.63 x 10-8cm, so it is nearer to the sodium atom radius of 1.91 x 10 8cm than to the Na + radius of 0.97 x 10 s cm.…”

Radial Band Structure of Electrons in Liquid Metals

“…2, which indicate that the outer and the inner FSs are electron and hole pockets, respectively. The outer band with a dominant intensity disperses following a free-electron-like parabola, and can be traced to nearly free Pb-valence electrons with limited coherence [6,7], which is a reasonable approximation for electronic states away from the band gap in the theoretical model of LMs [19][20][21]. Supporting this idea, the measured electron density of the outer band (n = 2.98 × 10 15 cm −2 ) amounts to the whole free-electron density of the Pb monolayer.…”

“…In recent years, important progresses were made to understand the atomic structure of LMs, establishing the local configurations of liquid fragments [9][10][11][12] and their global radial correlation [9][10][11][12][13][14][15][16]. In sharp contrast, while various theoretical ideas were proposed since 1960's to describe the electronic structure of LMs [17][18][19][20][21], critical experimental information to develop these ideas has been lacking. To our knowledge, there is only one experimental report to directly map out the band structure of LMs with angle-resolved photoemission (ARPES) [6].…”