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The simplecubic structure of elemental Polonium and its relation to combined charge and orbital order in other elemental chalcogens
by Ana Silva, Jasper van Wezel
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Submission summary
Authors (as registered SciPost users):  Jasper van Wezel 
Submission information  

Preprint Link:  https://arxiv.org/abs/1712.09533v2 (pdf) 
Date submitted:  20180122 01:00 
Submitted by:  van Wezel, Jasper 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
Polonium is the only element to crystallise into a simple cubic structure. Moreover, at high temperatures it undergoes a structural phase transition into a less symmetric trigonal configuration. It has long been suspected that the strong spinorbit coupling in Polonium is involved in both peculiarities, but the precise mechanism by which it operates remains controversial. Here, we introduce a single microscopic model capable of capturing the atomic structure of all chalcogen crystals: Selenium, Tellurium, and Polonium. We show that the strong spinorbit coupling in Polonium suppresses the trigonal charge and orbital ordered state known to be the ground state configuration of Selenium and Tellurium, and allows the simple cubic state to prevail instead. We also confirm a recent suggestion based on ab initio calculations that a small increase in the lattice constant may effectively decrease the role of spinorbit coupling, leading to a reemergence of the trigonal orbital ordered state at high temperatures. We conclude that Polonium is a unique element, in which spins, orbitals, electronic charges, and lattice deformations all cooperate and collectively cause the emergence of the only elemental crystal structure with the simplest possible, cubic, lattice.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2018216 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1712.09533v2, delivered 20180216, doi: 10.21468/SciPost.Report.348
Strengths
1. Identifies an interesting problem  an unusual transition in Polonium
2. Provides a simple and plausible explanation for the lattice structure of chalcogen elements
Weaknesses
1. Makes many assumptions  e.g., electronic ordering drives lattice ordering, phonons interact in a simple way with electrons
2. Does not make any testable predictions  does not suggest how the validity of this picture can be tested
Report
The authors have presented a simple model to explain an unusual lattice transition that is seen in Polonium. The unusual aspect here is the lowering of symmetry above a critical temperature, from a simple cubic to a trigonal structure. The authors argue that the trigonal structure arises from electronic degrees of freedom via simultaneous charge and orbital ordering. In Polonium, they argue that spinorbit coupling preempts this order. However, at higher temperatures, phonon softening (along with some other effects) brings back the instability to trigonal structure.
The paper represents a simple and plausible explanation for the lattice structures of chalcogens. This is interesting and worth publishing. However, there are many issues that are not clear.
1. Some key aspects of the mean field scheme are not clearly described. What is the nesting wavevector Q? Are there multiple choices for Q? How do the authors select a single Q for all the orbitals?
2. Was the mean field Hamiltonian constructed and diagonalised in momentum space or in real space? If it were a momentum space approach, it may not be possible to get a finite sized Hamiltonian matrix unless the vector Q is commensurate. If it were a real space approach, there may be strong finite size effects (the authors do not mention any finite size corrections).
3. In Eq. 4, the authors impose a fixed phase relation between orbitals. In a consistent description of the physics, this is something that should emerge out of the calculation. To show that the approach is consistent, can the authors show that any other choice of the phases increases the energy?
4. The dependence of phonon energy on temperature is, in principle, a highly nonlinear quantity. The authors have used a linear form for this. Moreover, they say they have obtained the coefficient from fits to earlier ab initio data (Kang et al., PRB 2012).
(a) The linear fit may only hold for a small temperature window. If a nonlinear form is assumed, this may lead to quantitative corrections to the phase boundary. Perhaps, the qualitative picture will not change.
(b) The authors have assumed an Einstein phonon dispersion, independent of temperature. The ab initio phonon band structures all show acoustic phonons. It is not clear how the authors managed to fit the data to extract a linear coefficient.
5. This work presents a physical picture that is broadly consistent with experimentally known facts. It makes some key assumptions — the most important one being that lattice ordering is driven by electronic order.
In order to make a concrete case, they should also propose some tests of their mechanism that can be checked by future experiments. I suggest that the authors suggest some qualitative tests. For example, they could discuss the effect of pumping in photons or a trend among isotopes of Polonium.
Requested changes
1. The mean field Hamiltonian should be given explicitly, perhaps in an appendix.
The following are minor comments about the manuscript:
2. The first line of the manuscript is an overstatement. The authors say “Polonium is unique in the periodic table, being the only element to crystallise into a simple cubic lattice structure.”
The authors perhaps intend to say that Polonium is the only element to crystallise in a simple cubic structure *in ambient conditions*. There are several other elements which order in simple cubic geometry, e.g., alphaMn, betaMn, Cr, O and F.
2. “ Moreover, we show that taking into account thermal expansion of the lattice, using parameter values that are realistic for Po, softens the phonon structure to such an extent as to effectively weaken the role of spinorbit coupling in suppressing the structural instability.” — This is a runon sentence that should be broken up into two or more sentences.
3. “The full Hamiltonian,…, can be diagonalised numerically within the mean field approximation” — This can give the impression that the Hamiltonian is solved by exact diagonalisation. It may be better to say that “..can be solved numerically within the mean field approximation”.