Peer review of: T-square resistivity without Umklapp scattering in dilute metallic Bi2O2Se (2020)

REVIEWER COMMENTS

Reviewer #1 (Remarks to the Author): 

This manuscript reported a non-trivial phenomenon that the transport of dilute metallic Bi2O2Se 
displays T-square resistivity below the degeneracy temperature caused by electron-electron scattering, 
which neither Umklapp nor interband scattering are conceivable for inducing mechanism. Overall, the 
results are interesting and a set of control experiments was carried out to verify the non-trivial T-
square resistivity proposed by the authors. However, the reviewer suspects the insufficient evidence 
cannot support this non-trivial phenomenon, at least in the present form, that can’t meet the criterion 
of Nature Communications. The main issues are listed as following: 
1) As claimed by the authors, the T-square resistivity without Umklapp and interband scattering in 
dilute metallic Bi2O2Se is caused by electron-electron scattering. Nevertheless, it lacks clear and 
sufficient evidence of transport data to further support the electron-electron scattering in dilute 
metallic Bi2O2Se. In addition, there are also need more experimental and theoretical evidence to 
demonstrate that the induced mechanism of the so-called non-trivial phenomenon is distinguished 
from Umklapp scattering. 
2) The authors claimed the case of Bi2O2Se, a layered semiconductor with hard phonons, which 
becomes a dilute metal with a small single-component Fermi surface upon doping. As we know, there 
are unavoidable defects in as-synthesized Bi2O2Se crystals, such as Se, Bi, O Vacancies and Se-Bi, Bi-
Se anti-site defects (Phys. Rev. B 2018, 97, 241203(R); Sci. Rep. 2018, 8, 10920.). The types of 
defects that led to formation of dilute metallic Bi2O2Se is not clear. It still needs further experimental 
or theoretical evidence to support the author’s claim. 
3) The authors used SrTiO3 as a reference to explain the observed phenomenon. Nevertheless, it still 
lacks sufficient analysis of the difference of the band structure or crystal structure of both SrTiO3 and 
Bi2O2Se to reveal the underlying mechanism which induced the T-square resistivity in dilute metallic 
Bi2O2Se. 
4) The order of graphs in Figure 1 and 2 need to be corrected and the description of the graphs is 
confusing in manuscript. The type of fonts in Figure 1 is different. 



Reviewer #2 (Remarks to the Author): 

The article by Wang et al. report on the observation of a T^2 resistivity in ultra low carrier density 
samples of Bi2O2Se. As stated by the authors, this is remarkable because there is no obvious 
mechanism at such low carrier densities for the electron bath to relax it’s momentum during the 
presumed electron-electron scattering responsible for the T^2 temperature dependence. This is the 
second clear observation of such phenomena, with the first being reported by some of the same 
authors in SrTiO3. I already find this fact on its own sufficient to justify publication in Nature 
Communications. However, the authors note that there are several unique features about Bi2O2Se, 
which provide new insight on trying to resolve this mystery. Due to the phonon spectrum, the lack of 
magnetic ions, and simple parabolic electronic dispersion, the authors are able to rule out three of the 
possible mechanisms, which were argued to have been possibly relevant in SrTiO3. The manuscript is 
overall, very well written and deserves to be published in Nature Communication. I provide here a few 
additional comments, which I urge the authors to consider before publication. 

- It was perhaps stated, but I certainly missed it if it was, that the carrier concentration reported in 
the paper was determined from the linear Hall resistivity measurements. 
- At the end of page 4 the authors claim “it is straight forward to estimate the Fermi energy at a given 
carrier density.” The authors need to explicitly state the expression that they use to convert the 
carrier density to a Fermi energy. Presumably it will be something like EF = hbar^2/2m* 
(3pi^2n_Hall)^2/3. There is additional subtlety in presenting Fig. 3d as a result. By my estimate of 
the numbers I found that the authors appear to have used m*~0.18 m_e, or more likely - the 
effective mass from the SdH oscillation data. Again, the authors should be explicit as to which 
effective mass they used? Using the m* from SdH would makes sense though as the Fermi energy 
then reflects the property of the electrons near EF, which contribute to transport. However, Fig. 3d, 
presents a picture that looks like an electronic dispersion (E(K) although it is correctly labeled as 
EF(k)). The quadratic dispersion that is drawn through the data further suggests such properties. If 
true, this would suggest that there is no electronic renormalization (for instance due to electron-
phonon coupling). If true, that would be a stunning result. The reality is that I don’t believe the 
authors can actually comment on the bare dispersion, since they only have the near EF effective mass. 
The parabolic dispersion is then a consequence of the constant effective mass as a function of carrier 
density. Unfortunately, I’m not sure how to rectify this figure, but the authors should state explicitly 
that the EF vs k plot is NOT a band dispersion E(k) plot. 
- On a related point, the authors might also note that the dispersion shown in Fig. 3d also appears 
consistent with the ARPES data which find m* = 0.14 m_e. This perhaps allows for an independent 
determination of the dispersion, and if one takes the numbers seriously, then one actually can 
estimate a mass renormalization by the comparison of these two effective masses. Interestingly, the 
ARPES data do not seem capable of identifying a kink or el-phonon renormalization if it exists either. I 
don’t know if there is a way to reconcile all these points. 
- I’m curious if the authors have any thoughts as to why the deviation from the T^2 behavior is in the 
positive direction and nearly at the same temperature in most samples? Phonons are the one thing 
that occur to me to have a stronger than T^2 temperature dependence, but I would not naively 
expect the strength of the electron phonon scattering to change with electron density, but clearly the 
e-e scattering strongly depends on this. The deviation is very similar to that what was found for STO, 
and at a very similar temperature scale of ~ 30 K. 
- My only other semi-significant complaint is that the authors don’t address the potential role of 
transport anisotropy in the creation of Fig. 4a. From the ratio of the cyclotron effective masses, one 
can estimate that m*_c ~ 0.37 m_e, which is twice the in-plane effective mass. Naively this would 
increase the A coefficient by a factor of 4. That doesn’t change the order of magnitude estimates in fig. 
4, but does question the matching in Fig. 4a, as a bit fortuitous. This is further emphasized by the fact 
that there is a clear break in slope between the STO data and the Bi2O2Se data, and the points where 
the data overlap are already in the multiband regime of STO, where the slope was argued to have 
already changed from single band expectations in ref. 7. 
- The inset to figure 2g: how the residual resistivity depends on carrier density, is not mentioned in 
the figure caption or elsewhere. I am happy the data is included, and I presume the data is for 
Bi2O2Se, but it should be stated. 
- I found the discussion in the SI ruling out other mechanisms very terse in general, and wouldn’t 
mind if the authors expanded a bit on this. Most significantly, the authors rule out the quantum 
interference mechanism as “not relevant to the case here”. Why is it not? An additional statement 
clarifying that would be useful. 
- Is the dashed line in Fig. 1f,g the experimental lattice parameter, or simply the computational lattice 
parameter for ambient pressure? 



Reviewer #3 (Remarks to the Author): 

The authors report a comprehensive experimental characterization of the 
transport properties of the dilute Bi2O2Se for a broad range of 
temperatures and carrier concentrations. 
These measurements reveal a quadratic dependence of the resistivity 
on temperature. 
The T-square dependence of the resistivity is a widely 
established behaviour in metals, whereby electron-electron 
scattering provides the dominant contribution to the resistitivity. 
The authors argue that Bi2O2Se may constitute an exceptional 
case for the observation of T-square resistivity, since 
the physical processes that are typically invoked to explain this 
phenomena, namely, Umklapp scattering and the coexistence 
of different electronic pockets, are excluded. 
The authors discuss at length why this is the case and 
provide compelling experimental evidence that the Umklapp scattering 
may not take place, and that other electronic mechanisms can also be excluded. 
The authors further report the observation of a universal scaling law for the 
quadratic dependence on temperature. 

The discovery of a new diluted metal exhibiting T-square resistivity 
may stimulate wide interest, and would certainly deserve publication in 
some foem. The claims and conclusions put forward in this study however 
are not entirely novel, since in Ref.[7] some of the authors report the 
observation of T-square resistivity for SrTiO3 (STO). In that paper, similar 
arguments are put forward to illustrate that the T-square behaviour cannot be 
reconducted to the usual mechanisms (Umklapp and interband scattering). 
The novelty of this manuscript rely primarily on the difference between 
Bi2O2Se and STO. The authors argue that in Bi2O2Se, the electronic origin 
of the T-square behaviour is unambiguos, whereas in STO soft-phonons may 
be considered as a possible source of this behaviour. This discussion, 
however, is not entirely convincing, and is merely based on the phonon 
calculation reported in Fig. 1 (d-e) and (g). 
To make this argument more solid the authors should truly rule out the emergence of 
soft acoustic modes, and discuss why they may underpin T-square resistivity. 
Is this also due a Umklapp scattering process? 
Can other modes acoustic modes soften upon small lattice distortion?