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\section*{Jess Brewer's comments on \\ Hassan Saadaoui's PhD thesis}
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Most of what comes below is critical, because that's how we make 
things better.  So I just want to start off by saying that this was 
a nice easy read for the most part, and obviously represents 
some excellent work!  ~ --- Jess

~

\begin{enumerate}

\item {\large\bf Chapter 1: Introduction}

\begin{enumerate}
\item Page 1 (and probably throughout the thesis): 
you can have many ``phenomen{\bf a}'', but only one ``phenomen{\bf on}''.   
\item The past tense of ``lead'' is ``led''.  
\item I am seeing a lot of grammatical errors, 
in particular the mixing of singular with plural; 
I will stop listing them after p. 1, 
as I don't have time to play copy editor.  
\item ** The problem with Fig. 1.1 is that it does not correctly predict 
the state of a field-cooled superconductor with strong flux pinning.  
As $T$ is decreased from above $T_c$ in a field $B < B_{c_1}(0)$, 
the first superconducting phase reached will be the vortex state 
at some temperature $T_v$ where the $B_{c_2}(T)$ curve crosses $B$.  
It remains in the vortex state until a lower temperature $T_M$ 
where the $B_{c_1}(T)$ curve crosses $B$.  
It is then nominally in the Meissner state, {\sl but}, 
if the pinning is strong enough at $T_M$, 
the vortices will remain ``frozen in''.  
This is how early ``decoration'' experiments were accomplished 
in fields well below $B_{c_2}$.  
So the question is, how strong is the pinning at $T_M$?  
See also p. 34 and pp. 40-41.  Also Fig. 2.4 on p. 64 
and especially on p. 66!   
\item * Pages 2 \& 29: Can you explain in simple terms why, 
{\sl in general}, 
local magnetic fields in ZF are considered evidence for 
spontaneous time-reversal symmetry breaking?  
\item Page 8: Compl{\bf e}mentary, not compl{\bf i}mentary.  
\item Page 10 (Fig. 1.5): is the angular distribution really an 
off-center circle?  What would it look like  for 100\% asymmetry?  
\item Page 11, Eq. (1.3): Any particular reason why you used the 
{\bf ratio} of L \& R to construct the asymmetry, rather than the 
more common (at least recently) form 
$$ \frac{L(t) - R(t)}{L(t) + R(t)} \; ? $$
On p. 80 you refer to $(F-B)/(F+B)$.  Did you use one form 
in the low-field spectrometer and the other in the high-field one?  
\item Page 13: The comment about $^{11}$Be development is sort of 
stapled onto the end of a paragraph comparing $\beta$-NMR and $\mu$SR.  
Why?  
\item * Page 14: You say that $\mu$SR ``only measures in the time domain, 
and a Fourier transform is needed to find the field distribution in 
the frequency domain.''  Do you recognize any {\sl advantages\/} 
of a time-domain measurement over a frequency-domain one?  
\item Page 17 (Fig. 1.8): You show a gap between the AF and SC phases 
on the hope-doped side of the phase diagram.  Do you believe this?  

\item * Page 23: Can you explain in simple terms why time reversal 
turns an order parameter into its complex conjugate?  

\item Page 27: Quasiparticle Reflection yadda yadda: do you actually 
understand this stuff?  I sure don't.  

\item Throughout: Do you know about the \verb+\boldmath+ command in \LaTeX?  

\item Page 35: ``Four{\bf n}ier components''?  

\item Page 38 (Fig. 1.15): The caption does not seem to describe 
the Figure.  There are no (a), (b) or (c) parts!  

\item * Page 44 (Fig 1.19): The third moment is related to the skewness, 
but they are not the same thing.  Can you explain the difference?  

\end{enumerate}

Subsequent Chapters: \underline{Who actually {\sl wrote\/} these papers}?  

\item {\large\bf Chapter 2: Search for TRSB in YBCO}

\begin{enumerate}

\item Page 60: Was the frequency-randomized pulsed RF technique 
your invention?  

\item Page 63 (Fig 2.3): Why does the caption refer to the open circles 
as just ``Ag film'' when the legend shows them as ``Ag/STO''?  

\item * The arguments on p. 66 for why the observed broadening 
can't be due to TRSB would seem also to argue that TRSB cannot 
be detected by this technique, even if it present.  Would you agree?  

\end{enumerate}

\item {\large\bf Chapter 3: VL in YBCO}

\begin{enumerate}
\item Page 72: Missing reference {\it re\/} NMR.  
\item * Pages 75-77: Why are you convoluting with a {\sl Lorentzian\/} 
disorder of width $\Delta_D$ rather than a {\sl Gaussian\/} 
disorder of width $\sigma_D$ (as everyone else has done, 
starting with Brandt)?  Do you have reason to believe that 
this is a better model of the effects of vortex lattice disorder?  
Have you actually modeled the $p(B)$ produced by the pattern 
shown in the inset of Fig. 3.1(b)?  This would seem to be implied 
by Fig. 3.2, but I don't see any explanation for what is meant 
exactly by $D$ in that Figure.  
\dots\ ~
Aha!  You do describe this, but not until p. 78, 3 pages after 
Fig. 3.1 is displayed.  You need to coordinate Figures and text better!  
In any case, it still is not so clear to me how $D$ translates into 
$\Delta_D$, or why the result is Lorentzian rather than Gaussian.  
\item Pages 77-78: You refer to Figs. 3.2(a) and 3.2(b) when you 
clearly mean Figs. 3.1(a) and 3.1(b).  This doesn't help 
the confusion I just mentioned.  
\item * Pages 78-79 and Fig. 3.2: You translate the extra broadening 
(due to disorder on a scale $D$) into a revised $T$-dependence, 
but I don't see any mention of the effect of {\sl depinning\/} 
as a function of increasing {\sl temperature\/} --- only of 
depinning caused by increasing {\sl field}.  We know that 
depinning sets in around $0.7 T_c$ (lower in higher field) 
so this would surely modify the $\sigma(T)$ curves in Fig. 3.2.  
I am inclined to suspect that the general conclusion is, 
``If you don't use high quality, aligned single crystals, 
you might get just about anything you can imagine!''  
\item Page 86 (Fig. 3.6):  The caption says the dashed lines are 
ideal VL lineshapes convoluted with a Lorentzian, but this appears 
to be the case only for the film sample.  
\item Page 87: ``Eq. (3.9))''?  
\item Pages 89-90 seem to make the crucial point of this paper: 
that the non-$d$-wave $T$-dependence of the linewidth can be 
explained in terms of VL disorder and is therefore not evidence 
for $s$-wave SC, as a handful of intransigent folks keep insisting.  
I believe this is correct, but I'm not convinced that the particular 
form of said disorder effects show here is by any means exhaustive.  
\end{enumerate}

\item {\large\bf Chapter 4: PCCO}

\begin{enumerate}
%% \item Page 103: ``This unexpected temperature dependence of the FWHM 
%% could be related to the fact that the $^8$Li$^+$ probes are outside 
%% the PCCO, where the intrinsic vortex lattice broadening is suppressed 
%% and $p(B)$ is more sensitive to long-range fluctuations of 
%% the vortex density [18].''  Was this possibility discussed earlier 
%% in regard to the YBCO results?  I don't remember seeing it.  
%% [Yup!  See p. 84!]
\item Pages 100-103:  The paramagnetic (positive) frequency shift in PCCO 
below $T_c$ is touted as distinctive, and so it is; but not 
necessarily unique: Fig. 3.4 on p. 83 looks to me as if the 
large diamagnetic (negative) shift in YBCO below $T_c$ 
is suppressed at the lowest $T$ (4.5 K) relative to that at 20 K.  
This would suggest a paramagnetic contribution as $T \to 0$, 
but this is never mentioned that I can recall.  
Is it just my imagination?  Obviously you have the fits, 
so you'll know for sure.  
\end{enumerate}

\item {\large\bf Chapter 5: Summary \& Conclusions}

\begin{enumerate}
\item ** Page 106: Of the reasons listed for employing $\beta$-NMR in a 
Ag overlayer, most are pragmatic issues (basically, it wouldn't work 
inside the SC) but $(ii)$ seems to me to be the central focus of 
this work: outside the SC one quickly loses the field irregularities 
due to the vortex lattice itself, leaving only those due to 
larger-scale disorder effects.  Loss of information about the VL 
itself seemed like a disadvantage to me until this sank in: 
when you can see the VL, you {\sl can't\/} see the disorder 
(or not very directly).  So this is the main {\sl strength\/} 
of this technique.  You may have said this earlier, but as I said, 
it only sank in for me on this page.  I think it deserves a 
higher profile.  You could have entitled your thesis, 
``Studies of large-scale VL disorder using $\beta$-NMR in overlayers'' 
(or something a little catchier) to emphasize this advantage.  
Modesty is rarely rewarded in science.  
\item Page 107: The caption to Fig. 2.4 on p. 64 states that the (100) 
film was measured after ZFC, giving $\Delta \propto B_0$, 
but the (110) film was only measured after FC, and only at 
two low fields, so the statements that $\Delta \propto B_0$ 
for both, and that (110) and looks the same as (100), 
are rather poorly justified, IMHO.  
\item * Pages 107-108: That you get different results with a 
poor ohmic contact between the SC and the metal overlayer 
from those with a good ohmic contact is, as you say, expected; 
however, it is an overly generous extrapolation from this to say that 
this rules out the proximity effect as an important source of your 
observed effects.  Couldn't you still have a reduced, or otherwise 
altered, proximity effect?  

\end{enumerate}

\item {\large\bf Appendix: RF Methods}

\begin{enumerate}
\item Page 113: ``\dots applied applied\dots''?  
\end{enumerate}
\end{enumerate}
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