Great video! As a graphene researcher, I would say this provides an intriguing aspect for layman! Also in the field today, this even-odd effect is more pronouced as few groups found the Bernal stacked graphene exhbits also flatbands, superconductors... which previously is only found in twist graphene systems. Welcome all to join the graphene research for fantastic observations!
Yo I just found this channel and it's really cool! Condensed matter physics explained by a VTuber is exactly what I needed in my life :D Joined the Discord, can't wait to chat there!
typically, many people probablay say they understand material better from youtube because its the second time they get exposed to it, the first time being in class. However, i must say that i can use your videos to either step ahead of course work or touch on stuff and take informed research steps for projects in our working group in order to keep up with people ahead of me in their studies. To sum up, gj on your explanations, probably simple enough for even laymen to grasp the basics and for students like me to recap and get a boost in studying speed. Thank you!
thanks for the detailed explanation. I`m still processing, for many piece of info I have to rewind and listen over and over , but at least I start getting the full picture, magic graphene
At 8:25, this is attributed to Haldane, who showed that graphene respect time-reversal symmetry, but topological features cannot be extracted until you break this time reversal symmetry (By distinguishing these two sets of triangular atoms). One can also also add a magnetic field to break this time-reversal symmetry as well.
Well, distinguishing the two sets of atoms as in 8:25 would only break inversion symmetry.. time reversal symmetry should remain intact. It's a good point about the topology though.. in this context, it certainly wouldn't be a Chern insulator (QHE), since TRS is preserved, but maybe there's some finite Berry curvature around the K and KPrime points that make it topological. shrug
Thanks for clarifying. Indeed I was under the mistaken assumption that introducing complex opposite phases to both sets of atoms is similar to differentiating both sets of atoms by a potential difference or onsite energy leads to the same symmetry breaking. And breaking of either symmetry will lead to a gap state. For the Haldane model that breaks time symmetry, there is no protecting symmetry class and the corresponding physics is similar to that of the Quantum Hall Effect (Basically Berry Phases and Chern numbers). The inversion symmetry does not play a part in this topological invariant. Correct me if I am wrong. Not really active in this field XD. Edit: I have checked further on Physics Stack Exchange and it seems that breaking either of these two symmetries will induce a gap state, which is good: mattermodeling.stackexchange.com/questions/1598/how-to-understand-time-reversal-symmetry-in-graphene As to which class that graphene exhibits when inversion symmetry is broken, I don't know either. I will need to ask my topological insulator prof for this. The tenfold way says that it can either be A or C or D class. Without a wide literature search, I personally suspect that time inversion symmetry will not be involved and we have the same A class (which will be similar to the QHE model that we have) Edit 2: Wait a moment: My lecture notes said that both symmetries need to be broken simultaneously in order to induce a gap and hence create a topological insulator of A class. Maybe this could be clarified in your discord T.T
@@ianyap8941 Yeah, I've mentioned the AZ classification scheme in another vod ( th-cam.com/video/UF8r9zdC9Ko/w-d-xo.html ), which is similar to what you're getting at I think? Class A is the first row, which has neither TRS nor PHS, and you are right that they both need to be broken in order to belong to that class (in d=2 dimension you would get a Z/integer topological invariant for this class, corresponding the the filling factor or Chern number in the QHE). However, there are other possibilities, for example the third row (class AII) preserves TRS but breaks PHS, and in d=2 dimensions you still get a Z2 topological invariant, meaning its a nontrivial topological insulator. I'm not sure if this is what's happening here, but it's a possibility. :)
Thanks for the great video! But can you explain why bilayer graphene should have a gap opening like TMD? I don't understand because graphene has the same sublattice, unlike TMD which could give different potentials on each sublattice.
That gap is a spontaneous gap induced by Coulomb interactions. The Fermi surface of bilayer graphene is just one band touching point, and it is suscepitible to electron interactions, which spontaneously leads to a gapped phase.
At 8:00 min of the video, you mentioned that if inversion symmetry is broken, the band structure at the k and k' point will no longer look similar. But next you showed that breaking inversion symmetry in graphene using two different potentials at two different sublattices of graphene leads to a band gap opening, And the band structure you showed is similar at both k and k' points. So, i am a bit confused at that point.
there is no mass term for monolayer graphene with a constant density of electrons, but there is a mass term for bilayer graphene if each of its layers has a different electron density value. that's what i'm saying there
Great video! As a graphene researcher, I would say this provides an intriguing aspect for layman! Also in the field today, this even-odd effect is more pronouced as few groups found the Bernal stacked graphene exhbits also flatbands, superconductors... which previously is only found in twist graphene systems. Welcome all to join the graphene research for fantastic observations!
I have never been so pleased by a VTuber Physicist. Then again, you are the first one I've seen. Great content mate
ty
Theres others?
@@Mew178 I don't think so. This is the first one I've seen.
@@Mew178yes, but you need to search them out
I'm showing this to all of my students, thank you so much
thanku :D
i hope your students like it ^^
Yo I just found this channel and it's really cool! Condensed matter physics explained by a VTuber is exactly what I needed in my life :D
Joined the Discord, can't wait to chat there!
typically, many people probablay say they understand material better from youtube because its the second time they get exposed to it, the first time being in class. However, i must say that i can use your videos to either step ahead of course work or touch on stuff and take informed research steps for projects in our working group in order to keep up with people ahead of me in their studies.
To sum up, gj on your explanations, probably simple enough for even laymen to grasp the basics and for students like me to recap and get a boost in studying speed. Thank you!
Thank you so much for helping me understand a lil bit of BLG QDs...
Nice to see your video after a long time. Your videos are awesome. Please do upload such videos on a regular basis.
Good to see catboi physicist back! Nice content as usual ^_^
thanks :D
Super high quality dude. Nice work :)
thanku ^^
thanks for the detailed explanation. I`m still processing, for many piece of info I have to rewind and listen over and over , but at least I start getting the full picture, magic graphene
At 8:25, this is attributed to Haldane, who showed that graphene respect time-reversal symmetry, but topological features cannot be extracted until you break this time reversal symmetry (By distinguishing these two sets of triangular atoms). One can also also add a magnetic field to break this time-reversal symmetry as well.
Well, distinguishing the two sets of atoms as in 8:25 would only break inversion symmetry.. time reversal symmetry should remain intact.
It's a good point about the topology though.. in this context, it certainly wouldn't be a Chern insulator (QHE), since TRS is preserved, but maybe there's some finite Berry curvature around the K and KPrime points that make it topological. shrug
Thanks for clarifying. Indeed I was under the mistaken assumption that introducing complex opposite phases to both sets of atoms is similar to differentiating both sets of atoms by a potential difference or onsite energy leads to the same symmetry breaking.
And breaking of either symmetry will lead to a gap state. For the Haldane model that breaks time symmetry, there is no protecting symmetry class and the corresponding physics is similar to that of the Quantum Hall Effect (Basically Berry Phases and Chern numbers). The inversion symmetry does not play a part in this topological invariant.
Correct me if I am wrong. Not really active in this field XD.
Edit: I have checked further on Physics Stack Exchange and it seems that breaking either of these two symmetries will induce a gap state, which is good:
mattermodeling.stackexchange.com/questions/1598/how-to-understand-time-reversal-symmetry-in-graphene
As to which class that graphene exhibits when inversion symmetry is broken, I don't know either. I will need to ask my topological insulator prof for this. The tenfold way says that it can either be A or C or D class. Without a wide literature search, I personally suspect that time inversion symmetry will not be involved and we have the same A class (which will be similar to the QHE model that we have)
Edit 2: Wait a moment: My lecture notes said that both symmetries need to be broken simultaneously in order to induce a gap and hence create a topological insulator of A class. Maybe this could be clarified in your discord T.T
@@ianyap8941 Yeah, I've mentioned the AZ classification scheme in another vod ( th-cam.com/video/UF8r9zdC9Ko/w-d-xo.html ), which is similar to what you're getting at I think? Class A is the first row, which has neither TRS nor PHS, and you are right that they both need to be broken in order to belong to that class (in d=2 dimension you would get a Z/integer topological invariant for this class, corresponding the the filling factor or Chern number in the QHE). However, there are other possibilities, for example the third row (class AII) preserves TRS but breaks PHS, and in d=2 dimensions you still get a Z2 topological invariant, meaning its a nontrivial topological insulator. I'm not sure if this is what's happening here, but it's a possibility. :)
Excellent content!!
this is so cool.
Thanks for the great video! But can you explain why bilayer graphene should have a gap opening like TMD? I don't understand because graphene has the same sublattice, unlike TMD which could give different potentials on each sublattice.
That gap is a spontaneous gap induced by Coulomb interactions. The Fermi surface of bilayer graphene is just one band touching point, and it is suscepitible to electron interactions, which spontaneously leads to a gapped phase.
This is why more introductory textbooks need to talk about electron-electron interactions outside of the Hartree approximation
And also another reason why quantum fluids are super cool
你做的好！做的好口牙！
You are the best :)
no u c:
As soon as you said coulomb force I got "no game no life" flashbacks.
😎
Yummy graphene sandwich~
get in my belly mr graphene >:3
I am confused but amazed
Love physics from catboi.
At 8:00 min of the video, you mentioned that if inversion symmetry is broken, the band structure at the k and k' point will no longer look similar. But next you showed that breaking inversion symmetry in graphene using two different potentials at two different sublattices of graphene leads to a band gap opening, And the band structure you showed is similar at both k and k' points. So, i am a bit confused at that point.
loved it
@9:00 i still don't get how you get a gapless band structure even after adding a mass term for a mono-layer graphene?
there is no mass term for monolayer graphene with a constant density of electrons, but there is a mass term for bilayer graphene if each of its layers has a different electron density value. that's what i'm saying there
Nice channel
My quantum condensed matter lecturer is really boring to watch I'm so glad of all the topics to have explained to me by a catboy it's this
1k subscriber, pretty cool
more
yos >:3
i am an idiot so i didn't understand anything, but hey an anime catboi talking about physics is cool.
no jokes keep up the good work ^_^
thanks fren :3
wtf did u call Schrödinger? skreudinjer? OMEGALUL
i sowie :C
REE AM NOT FIRST
what you are first xD :0