Thursday, March 09, 2023

Room-Temperature Superconductor?

Here we go again!

Big news with the new publication out of Nature this week. A report on an observation of room-temperature superconductivity on a sample that is under pressure at only 1 GPa. That pressure is exceedingly low considering that most of the other superconductors that that has a high transition temperatures tend to be under hundreds of GPa.

Superconductivity has been observed at 20 °C (294 K) in a nitrogen-doped lutetium hydride under a pressure of 1 GPa (10 kbar). The material was made and studied by Ranga Dias and colleagues at the University of Rochester in the US, who claim that the finding raises hopes that a material that superconducts at ambient conditions may soon be found.

Not only that, this thing changes color as pressure is increased, with it turning from blue to pink at the onset of superconductivity. I'm sure doing a reflectivity measurement such as UV-VIS to look at the phonon modes would be very interesting here. 

But as with anything here, this needs to be independently verified, meaning that another group must be able to replicate the recipe and observe the same thing, before this is widely accepted. We will just have to wait.

Z.

Friday, February 17, 2023

Blackholes The Source Of Dark Energy?

Can blackholes at the center of galaxies be the source of the dark energy that we have been detecting?

That seems to be the conclusion based on two recently published papers [1,2]. Both of these are open access papers, so the full papers are available to everyone.

You may read an explanation and review of the papers at the AAS news website. The implication here is that if this is true, then dark energy is not something exotic or new since it can already be explained with General Relativity.

Now, if only we can find those pesky dark matter.... if they exist.

Zz.

[1] D. Farrah et al., Astrophy. J. Lett., v.944, p.L31 (2023).

[2] D. Farrah et al., Astrophy. J., v.943, p.133 (2023).

Tuesday, February 14, 2023

ChatGPT Does Physics

I'm guessing that most of you who are reading this have heard of ChatGPT or maybe have even tried it. I have. I had to, because I need to know what it can and cannot do in case my students are also using it. I am still playing with it and trying several different things, so I will have a lot more to say about it.

Still, when I came across this video on YouTube, I had to post it here, because it seems that we have similar general observations (not including the writing the Python code for the infinite square well problem - I've never asked ChatGPT to write a code).


It is true that ChatGPT still can't handle graphs and figures as of now. While this may be a way out for instructors to prevent students from using ChatGPT effectively, the extensive use of figures and graphs is also a hindrance to students with certain disabilities. In many cases, I have tried to make my exams and questions to be more "friendly" toward such students, especially in the spirit of making all my material accessible and moving toward conforming to the idea of Universal Design in Learning (UDL).

Of course, if my questions, including the figures, can be deciphered by text or document readers, then it should, in principle, be capable to be fully understood by ChatGPT, which then removes that barrier of using it to solve those problems. Sigh....

Like I said, there's more to come about this.

Z.

Saturday, January 14, 2023

One of the Things That I'm Keeping From My Remote Classes

I mentioned earlier that when we went remote due to the pandemic, I forced myself to be trained as an online instructor and received credentials from the school to teach online courses. While I do not intend to be an online instructor, many of the lessons and technique that I learned from such training are actually quite useful even when I eventually went back to in-person classes.

One of the aspect of online classes that I'm keeping even for my in-person classes is the discussion forum. At first, it seems that discussion forum might be a bit of a waste of time, considering that we all meet each other during classes, and can easily engage in conservation and discussion. It turns out that online discussion forum has been quite useful for me. Here's how I implement it in my in-person classes.

I always start the semester with the first discussion topic in Week 1, which is for the students to introduce themselves. I ask them to write a brief description of who they are, what their majors or intended majors are, and what career to they aspire to. I ask them about their hobbies, and anything else that may be interesting and unique about them.

What this gives me immediately is the information on what they are interested in, especially with their ares of study. I like this because I can invoke examples in my lessons that apply to what they want to do. This is something I do frequently, which is a conscious attempt at making the physics lessons relevant to their area of study. Even if it is not applicable to their major, I can also connect this to something they are into, especially if they are musicians and play a particular instruments, when we talk about sound waves, resonance, pitch, etc. Last semester, one of my students was a college tennis player, and we had a long discussion on air flow, Bernoulli principle, etc. when we were discussing fluid dynamics.

But you may ask "Yeah, ZapperZ, this is all interesting and useful, but why do you have to do this over an online discussion forum? Why can't you just ask them in person?".

The answer is, not every student is comfortable with speaking in front of a group of people. In fact, many students are terrified of being the center of attention during class. I am offering a form of engagements in which many of the introverts will be more comfortable with and are able to be more open in sharing who they are. The more extrovert ones are more than welcome to introduce themselves during class time. In the spirit of Universal Design in Learning (UDL), I am trying to provide more than just one means of engagement for the students.

This is not the only topic that I use in the online discussion forum. I'll make another post on another topic that make use of the discussion forum to get a snapshot on how the students think and analyze a particular scenario.

Zz.

Friday, January 06, 2023

Which Comes First, Energy Or Momentum?

First of all, Happy New Year! It's my first post of 2023. I'm crossing my fingers that I won't be as stressed out as I was toward the end of 2022.

As I prepare for another semester of teaching General Physics, I'm struck at trying to understand the logic in the sequence of the introduction of the topics on energy and momentum. I know that as instructors, we have the freedom to arrange the sequence that we introduce the topics that we teach, so this is not a criticism. Rather, it is just trying to understand if there is a rational reason for introducing one ahead of the other.

I'm talking in particular about the topics of momentum and energy. This is because different textbooks introduce them in different order. I'll list a few examples.

  • Serway-Jewett: "Physics for Scientists and Engineers" 10th ed. - Energy Chap. 7&8; Momentum Chap. 9.
  • Knight: "Physics for Scientists and Engineers" 4/e - Energy Chap 9&10; Momentum Chap. 11.
  • Knight-Jones-Field: "College Physics" 4e - Momentum Chap. 9; Energy Chap. 10.
  • Giancoli: "Physics - Principles with Applications" 7th ed - Energy Chap. 6; Momentum Chap. 7.
  • Hewitt: "Conceptual Physics" 13th ed - Momentum Chap. 6; Energy Chap. 7.

As you can see, different authors/textbooks introduce momentum and energy in different order. My question is, WHY?

From my view, it is more logical to introduce the concept of energy FIRST, and then introduce momentum. This is because a large part of momentum, and real-world cases of collisions, involves inelastic events in which kinetic energy is not conserved. So how does one ignore inelastic collisions when dealing with conservation of momentum? Or, if one does include inelastic collisions, how does one tip-toe around it when the concept of energy (kinetic energy) has not been introduced yet? 

Has anyone done this using the sequence of momentum first and then energy? How did you go about doing it? Is there a rational reason for introducing the topic this way?

Zz.

Saturday, December 24, 2022

2022 Nobel Prize In Physics Lectures

If you are bored over the holidays, here's something to keep you occupied for 2 hours.



Zz.

Saturday, December 17, 2022

The Semester From Hell Is Over!

Fall 2022 semester is finally over! I've turned in all the grades, and I am breathing a big sigh of relief.

I only have myself to blame, but I can't take all the "credits" either. I taught two courses that I've taught before, but they both were using new Open Educational Resources (OER) texts. This  means that I have to use all new lectures notes, set up new homework, quizzes, etc. And of course, being OER, the instructor support is barely there. I've mentioned already how unimpressed I was on what they call their "lecture notes". A dump of figures cannot be called lecture notes!

So this past semester, I had to basically do everything from scratch. And when you have two whole classes on different topics for that, I felt as if I'm behind at the beginning of each week! I'm used to producing extensive Powerpoint lecture notes with animations, videos, links, etc. I can't just use the old ones, mainly because of copyright issues, but also because I want my notes to be consistent with the notations, symbols, figures etc. that are used in their OER text. So each week, I have to produce brand new lecture notes, and since there's no support from the OER text, I have to do this from scratch. And we still haven't talk about quizzes, homework, etc. that I have to set up from scratch.

I never, ever, want to be in this situation again!

It was the closest I had come to being burnt out. I love teaching, and I gave up my career as a research physicist for this, but this past semester was the first time that I hated doing this. The joy that came from teaching did not exceed the aggravation. It didn't help that I was pissed at the dept. for shoving the OER texts and requirements on us without consulting us and asking the type of support that we would need. I was used to getting the type of instructor support from Pearson and Cengage, but this past semester, the rug was pulled from right under us and we were left with nothing.

What is actually rather amusing and funny is that the school is seriously pushing for our courses to try and adopt the Universal Design in Learning (UDL) standards, in which we accommodate students with various abilities, backgrounds, etc., and therefore, allow for our methods of delivery, assessments, etc. to be flexible and varied. The students portals at Pearson and Cengage had those, while the OER sources have practically zilch! So one part of the institution wants us to do one thing, while the other part removes the ability for us to do just that. The right hand doesn't know what the left hand is doing!

Yes, I'm venting. For my own sanity, I need to air out my frustrations at this whole silliness. I have no doubt that the standards that I set for myself for these classes suffered this past semester, and I'm not happy about it. Now I just need to figure out how to prepare way in advance for next semester. Luckily, I'm teaching only ONE class using OER text, and it is the same one that I taught this past semester. Hopefully, I'm more prepared.

Wish me luck!

Z.

Wednesday, December 14, 2022

We Have Ignition!

So the big news of the week, which was preceded by the rumors a few days before the official announcement, is the breakeven achievement in a fusion process at Lawrence Livermore's National Ignition Facility (NIF).

This is certainly a major breakthrough, and it is something that has achieved for the very first time ever in a controlled experiment (it happens all the time in our Sun and other stars). However, to me, this is more of a proof-of-principle experiment, meaning that it is a demonstration that it is possible, rather than to show that it is viable. It is certainly very, VERY far away from producing anything useful because harnessing this energy is an entirely different matter.

While you can read many sites reporting this, I kinda like the one that I read on CNET because there's a certainly level of sensibility aimed towards the general public. In particular, there is this definition of what is meant by "breakeven":

More specifically, scientists at NIF kickstarted a fusion reaction using about 2 megajoules of energy to power the lasers and were able to get about 3 megajoules out. Based on the definition of ignition used by NIF, the benchmark has been passed during this one short pulse. 

But that doesn't convey the whole thing, because this is what should also be mentioned:

"The calculation of energy gain only considers the energy that hit the target, and not the [very large] energy consumption that goes into supporting the infrastructure," said Patrick Burr, a nuclear engineer at the University of New South Wales.

What it means is that they only considered the energy of the laser hitting the target, and then finding the energy output from the ignition that subsequently resulted in fusion. Sure, that energy output is greater than the input energy of the laser, but this is not the total energy of the entire facility that created the laser. That facility would still not be self-sufficient to run just by using the output energy of the fusion it created, even assuming 100% efficiency.

This does not diminish the amazing achievement, considering that other facilities and techniques have not even reach this level. It is just that it needs to be tampered with a bit more realistic expectations so that we don't oversell ourselves to the public.

Zz.

Wednesday, November 30, 2022

How Fast is Gravity?

 Don Lincoln has produce another fun video on the speed of gravity.

SPOILER: It has the same speed as the speed of light!

But what is more interesting in this video is a brief description of LIGO and gravitational interferometry and how gravitational waves are detected.

Enjoy!

Zz.


Impact of Physics on the Economy

 It is not know if the public is aware of the economic impact of physics, not just in terms of industry to support the workings of physics, but also how new ideas and technologies have sprung new innovations and devices that made our world the way it is today. Of course, the most obvious example would be the invention of the solid state transistor, which is the heart of every modern electronic devices that we have now.

This Swiss study tries to quantify the impact of physics on the Swiss economy. One can clearly see the breath of the impact across many different disciplines and sector of the economy.

This is not that much different than the previous similar studies that were done for the US economy and for Europe. The significant conclusion one can draw out of these data is that one gets a lot of returns for the initial investment. But it is not just that. If one looks at the nature of the returns, many of them are vital to the advancement of our civilization, so these investments are important not merely for financial reasons.

BTW, I still encounter people (a few of them my students) who are surprised that physics has anything to do with their smarphones.

Zz.

Saturday, November 26, 2022

How Was the Universe Created?

 In case you want to know our current view on how we came into being, here's a brief article on how we currently understand how the universe was created.

It's too bad he doesn't go into the evidence that we have to support each stage of the formation of the universe. Of course there isn't much to go by in term of good evidence for anything less than 380,000 since the Big Bang, but the CMB is such a strong evidence that it should have been elaborated.

Zz.

Friday, November 25, 2022

Three Ways You Use Quantum Physics Everyday

Most of you know this already, but it is always helpful to remind people on how quantum physics, as esoteric of a subject as it is, is the key to understanding many of the devices that we use everyday and take for granted.

The only drawback here is that the article listed only three, when there could be plenty more.

Zz.

Saturday, August 13, 2022

OER Lecture Materials - So Far They Don't Impress Me Much!

I mentioned a while back that the dept. is migrating to using Open Educational Resources (OER) texts this coming Fall. I'm all for it because the texts are quite reasonable and it will save the students a lot of money when their textbooks are free.

I'll be teaching two different courses that use to different OER texts out of OpenStax. I'm so freaking glad that I looked at the so-called lecture materials that accompanied each of these texts early this month because I would have been in a panic mode if I were to start preparing just 2 weeks before classes start! This is because the PowerPoint lecture materials are nothing more than a collection of the figures from the texts. That's it!

My first reaction when I first opened them was "What the......?"

Then blood drained from my face because I realized that I had to produce the lecture notes from scratch for both classes! And I had 3 weeks to do that!

Now you could tell me that I can just copy the lecture presentations from the same course that I had taught previously. True, but I want to stick with the content of the texts that the students will be using, especially in going over the same examples, using the same notations and format, etc. I want to use the same symbols for the various quantities that we will be using, so that the lecture presentation is consistent with the text. So I can't just copy old lecture notes verbatim, and I certain have to change the examples to match the examples in the text.

But even that is not that easy. My PowerPoint presentations often have links, animation, and other interactive stuff that are specific to that text and course. We were using Pearson's Mastering Physics, and I used quite a number of their videos to illustrate various physics principles. I can't use that anymore because those are copyrighted to Pearson and to be used only with their material. This means that I have to redo the animation and find new videos to include in the lecture presentation.

I did a Google search online to see if there are lecture notes using these two textbooks. There are, but all the ones that I have encountered so far are in PDF, meaning that I could not modify them to suit my needs.

Ugh! This semester is going to be a nightmare! I hate not already be prepared by this time!

This is why you haven't seen a lot of blog posts from me these past few weeks. Sigh....

Zz.

Wednesday, July 27, 2022

How Classical Kinetic Energy Is Actually A Subset Of Relativistic Kinetic Energy

Many people think that Classical Physics and Relativistic Physics are two different things. Of course, anyone who has studied both can tell you that one can derive many of the classical physics equations from relativistic equations, proving that classical equations are actually special cases of the more general relativistic equations.

In this Don Lincoln's video, he shows how classical kinetic energy that many students learn in General Physics courses can actually be derived from the more general relativistic energy equation, and why we still use the classical physics equation in most cases.

Z.

Thursday, July 07, 2022

Electrons Behave Like A Fluid - Exhibit Vortices

This is a rather cool experiment.

They have a direct observation, for the first time, of electrons behaving like an ordinary fluid and exhibiting vortices  when going thorough a channel.[1]

In contrast, electrons flowing through tungsten ditelluride flowed through the channel and swirled into each side chamber, much as water would do when emptying into a bowl.

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.

“That is a very striking thing, and it is the same physics as that in ordinary fluids, but happening with electrons on the nanoscale. That’s a clear signature of electrons being in a fluid-like regime.”

So far, "ordinary" electron flow behaves like a "Fermi liquid", which is not like ordinary fluid flow. To get electrons to behave this way, they had to make sure that the electrons do not bump into the crystal lattice (the bulk material), so this is not easy since normal-state electrons usually have such interaction (non-zero resistivity).

Just to be clear, this is not the first observation of electrons exhibiting vortex flow. This is a common observation when they are in a superconducting state, where vortices form around magnetic flux lines that penetrates Type II superconductors. But in that case, these electrons are in a superfluid, and what is flowing is the paired electrons (Cooper pairs).

In this experiment, these are individual electrons not in a superconducting state, so this truly is a river of electrons.

Z.

[1] A Aharon-Steinberg et al., Nature 607, 74 (2022).

Thursday, June 30, 2022

My Favorite Web Applications - Part 6

Previous posts:

My favorite web applications - Part 1

My favorite web applications - Part 2

My favorite web applications - Part 3

My favorite web applications - Part 4

My favorite web applications - Part 5

Continuing on with my pet project here, this next web application is actually another one of those that closely mimics an actual experiment. This time, it is on specific heat, and the goal here is to measure the specific heat of an unknown liquid. You do this by measuring the mass and temperature of the unknown liquid, and then mixing it with hot water of known mass and temperate. By finding the final equilibrium temperature, you then calculate the specific heat of the unknown liquid.

Like I said, this web experiment is done step by step just like a real experiment. In fact, you could use this as the lab instruction and get the students to follow each step of the experiment. But what I like the most is that each student will be given a different set of numbers to work with. The masses will be different, and so will the starting temperatures of the liquid, resulting in different final temperature as well. I don't remember if the specific heat of the unknown liquid is also different for different students. Please let me know if you've used this app or if you discover this later on.

I used this as one of my virtual labs when we went remote. But I continue to use this after we gone back to face-to-face classes as part of my in-class problem solving exercises. I've also given this as a take-home homework problem, and they have to show the final acknowledgement page that they got this correct if they want to receive credit for it. If the students have done the actual experiment itself, this web application will be quite familiar and they should have a good clue on how to correctly find the unknown specific heat.

Zz.

Friday, June 24, 2022

Share It, Don't Split It - Is It Working?

I'm teaching a physics course with labs over the summer. And if you've taught Summer courses, you know that they go very fast and furious, so I'm not sure if there's any chance for any evaluation on the effectiveness of anything.

I mentioned a study a while back that seems to imply that it is better for students, especially minorities and marginalized students, to share lab work and have equal access to every part of the experiment, rather than splitting responsibilities and have each students just do one part of it. I am still unsure of how effective it is or whether I can tell if it is working, but I've made sure that the students know that no one is to do just one part of the experiment, that everyone must take turns doing different parts of the experiment.

Much to my surprise, the students seem to be amicable about it. So far, I've seen everyone taking turns and rotating themselves to different tasks as they perform the experiment. Better yet, I've seen students helping and teaching other students on what they just learned about doing certain parts of the experiment or in performing the analysis of the data.

One direct result that I've seen so far is that everyone in the group knows how to work and setup the computer interface to connect to the various sensors, whereas in previous classes, I've noticed that the same students had the responsibility of setting up the sensors. Already, I can tell that the students are learning about conducting the whole experiment rather than only certain parts of it.

I did not plan on doing any form of assessment on how beneficial or effective this is, because I had not run any control study before. Besides, it is a summer session, and "rushing" is the most common theme for a physics summer class.

I don't know if this will boost the students' "self-efficacy" but from simply a superficial observation, I can see the benefit of requiring that the lab work be shared rather than split.

Zz.

Thursday, May 05, 2022

My Favorite Web Applications - Part 5

Previous posts:

My favorite web applications - Part 1

My favorite web applications - Part 2

My favorite web applications - Part 3

My favorite web applications - Part 4

This time, it is an experiment that mimics the fabled Archimedes experiment where he supposedly determined for the "king" whether the crown was made of pure gold or not. This web application basically allows a student to perform a similar virtual experiment to determine the density of the object being investigated.

There are two reasons why I like this app. The first reason is that if you change the default settings for the mass and the volume, you will given rather random values. This means that each student will have different values for the mass and volume, resulting in each student having a unique set of data and calculation.

The second reason why I like this "experiment" is that it actually is the same experiment that we would do in a f2f lab. We use PASCO's Capstone system, and one of the experiments that we do is practically identical to what is shown in this virtual experiment, where a student has connected a weight sensor to a hanging mass, and then he/she slowly lowers it into a beaker of liquid. The sensor sends a reading of the hanging weight value to a data collection system that plots the value of the weight in real time. As the weight is lowered into the liquid, the data being plotted looks almost exactly as what is shown in the virtual experiment in this app. The weight changes due to the buoyant force of the liquid.

The analysis of the experiment and the extraction of the value of the object's density are similar for both the f2f lab and this virtual lab. So in that sense, the student is not being deprived of much of the physics. There are, of course, more errors involved in the real experiment because often the object isn't hanging still, and the movement adds more noise to the data. The app doesn't allow the data to be extracted directly, so no curve fitting or calculation of average value can be made for a range of the data points, something the students in the f2f lab are asked to do to be able to determined the weight before and after immersion.

Still, it is an adequate virtual experiment, especially since each student will have to do his/her own analysis on a unique set of measurement. I actually have used this as part of an assessment where this app was part of an exam for a f2f class (before the pandemic). The student had already done the actual experiment, so they should be familiar with how to find the density of the object using this app since things should look rather familiar.

Zz.


 

Friday, April 22, 2022

The Migration to OER

For the past couple of years, the school has been pushing various departments to start adopting Open Educational Resources (OER) for various courses to help reduce educational costs to students. It has finally trickled down to our department where, starting this coming Fall, the General Physics courses will start using OER texts for the first time.

I have zero problem with doing this. I remember when I was a student, textbooks were hugely expensive. Adopting OER texts for General Physics courses will save students quite a chunk of change, especially if they, or their parents, are footing the costs.

The only issue I have is that, using texts from various publishers doesn't stop just at the textbook itself. I've been using Pearson and Cengage for General Physics texts, and they come with their online services consisting of the e-text and homework/quizzes capabilities.

But even that does not convey everything. Both Cengage and Pearson's website offers rather substantial student support that I have made used of, especially when we went remote. When I assign homework on Pearson's Mastering website, for example, I often select one or two "tutorial" items. These are questions in which, if the students are stuck, there are guided hints and prompts to help students overcome the barrier or difficulty at that stage. I find these types of tutorial very useful for the students and often had the students attempt one of them during class session.

The other thing that I find useful is the "adaptive learning" feature. I can set it up so that if a student struggled with one problem and finally thinks that he/she understood how to solve it, it will prompt the student to solve a similar problem to that one to see if the understanding can be nailed down. The student then has the chance to really test his/her understanding in solving the similar problem, and I can see for certain of the student's progress.

Unfortunately, none of these extensive feature are available in any of the OER sources. These features were extremely useful during remote learning where I'm not there to help the students in person. Yet, these features gave real-time feedback on how the students are doing and assisting the students in solving the problem, all done automatically without needing my intervention. These are what I will miss when I start using OER texts because so far, from what I can see, they only provide the text and maybe a set of homework questions, and that's it. It is no different than the old-fashioned way when I was in college, except that these are in electronic form.

It is still months away from the start of the Fall semester, but I'm already thinking and planning ahead on how to approach this. We will definitely be back to in-person instructions, so maybe the need for all the bells and whistles of online capabilities might not be as great as it is now. Still, I'm anticipating a few hiccups as I dive into a new set of challenges in running a class.

Stay tuned....

Zz.

Wednesday, April 06, 2022

Signature of Tc Inside the ARPES Pseudogap?

The physics of high-Tc superconductors (or the cuprate superconductors) continues to be elusive. After its first discovery in mid 1980's, a coherent and consistent theory on why this family of material becomes superconducting is still up for debate. There are candidate theories, but we do not have an accepted consensus as of yet.

One of the main reason for this is that this is such a rich and complex material, exhibiting so many different characteristics and puzzles. As a result, different versions of theories are competing to describe as many of the experimental results as possible. But the target is also moving. As our instrumentation improves, we are discovering new, more subtle, and more refined behavior of these material that we haven't seen before.

The existence of the so-called pseudogap in the cuprates is well-known. I've posted several articles on them. This is the gap in the single-particle spectral function that opens up well above the transition temperature Tc. In conventional superconductors, the formation of this gap coincides with Tc, below which the material becomes superconducting. However, in the cuprates, and especially in the underdoped cuprates (less oxygen doping than the optimally-doped), a gap opens up well above the Tc. The material doesn't become superconducting yet even as you lower the temperature even more. It is only when the temperature gets to Tc will the material becomes superconducting.

The origin of this pseudogap has long been debated. The posts that I had made discussed all this. However, in this new paper published in Nature (the article I linked too erroneously wrote "Science" at the time of this citation), the Z-X Shen group out of Stanford has detected the signature of Tc in the pseudogap region from ARPES measurement. But what is interesting here is that it was detected in the overdoped cuprate Bi2212.

Typically, the overdoped regime of the cuprates does not exhibit clear pseudogap signatures. When I studied a highly-overdopped Bi2212 using ARPES a long time ago, we did not detect any pseudogap at all since we saw the opening of the gap only at the bulk Tc value. Of course, this does not mean it wasn't there because it depends on the temperature resolution of our experiment. So it is rather interesting that this study decided to focus on the overdoped region where the pseudogap is more difficult to detect, as opposed to the optimally-doped or underdoped region where the pseudogap is much more obvious.

In any case, they apparently saw spectroscopic signatures of Tc within the pseudogap as the material cools down through Tc. According to them, this seems to be a strong evidence in support of a phase fluctuation (spin fluctuation?) model as the driving mechanism for superconductivity in these materials.

I tell ya, almost 40 years since its discovery, the cuprates continue to amaze and surprise us!

Zz.