topocm / topocm_content Goto Github PK
View Code? Open in Web Editor NEWCourse on topology in condensed matter
Home Page: http://topocondmat.org
License: Other
Course on topology in condensed matter
Home Page: http://topocondmat.org
License: Other
The sentence
"The value k=0 is always present in the chain with boundary conditions "
is crucially missing periodic.
It's a minor thing, but the graphs that show the Trivial and the topological band stucture are somewhere between cells that don't mention the figure.
It should be below: "The effective electron mass m is just the coefficient of the expansion. Let's take a look at the band structure in this regime, both in the topological regime and in the trivial regime:"
So far we have consider a uniform superconducting pairing Δ, with constant amplitude and phase. This is an idealized situation, which would correspond to a perfect superconductor with no defects.
Derivation of Q = sgn Pf[H(0)]*Pf[H(π)] would benefit from more details.
In 8.1 add a remark that D, DIII, C, CI appear naturally, while AIII, BDI, CII require fine-tuning.
Sometimes you write counter-propagating and other times counterpropagating.
The same question has been posted in the Disusion group part of the edx.
I found a typo under the Bulk-edge correspondence, section "Bulk topological Invariant", the paragraph start with "This means that for these two Hamiltonians we should compute a Pfaffian.":
Should μ=−2t corresponding to a gap closing at k=0, and μ=2t with k=π?
I mean there is a minus sign difference when the original text referring to different situations.
In the unit "Topological phases from the bulk spectrum", the title of the paragraph "Band structure" is lost in markdown and is not displayed correctly.
Jay's ending video at 4:21, subtitle: particle whole symmetry -> particle hole symmetry
4:26, subtitle: i while --> While
Following a remark by zhongweizi, in 1.2 the solution of the Dirac equation with a domain wall should be expanded to explain the spinor structure.
The graph is above the text and immediately after the title.
The more natural position would be after the text:
"Let's calculate the gap as a function of all of the relevant parameters.
Here the vertical line denotes the critical value of Zeeman field at which the wire becomes topological."
As mentioned by christophe debeule on the forum:
In the section "Majorana zero modes in nanowire networks". In the equation underneath
We can obtain the total fermion parity by multiplying all the operators Pn…
there should be an i instead of −i according to the convention of pairing Majoranas in the text.
The two quizes in 6.2 seem to have disappeared
As you heard in the video, there might be zero energy states for some specific termination of the lattice, but these are not particularly interested
In From Kitaev chain to a nanowire, The need for spin.
First is says: "The simplest thing which we can do is to ...", then that's not the way to go, because: "Just kidding, this would be very bad!"
Then it says: "What's the next best thing to do?", while it's not a next best thing, but mere the best thing or a correct thing to do.
Next best would imply there was already a thing that worked.
The first unit in 6.1 states that
Also the product rule is confusing because we multiply 0 and 1.
topocm_content/w1_topointro/0d.ipynb
"This immediately means that if
should possibly read
"... eigenvector..."
We want to consider the case that the system is in equilibrium, and we want to ask what are the current flowing in the system as a consequence of the small applied voltage V.
Is the current or are the currents.
The relation between superconducting phase difference and flux is missing a factor of
Explain how to keep track of momentum structure.
by adding a secind vortex, so the edge has no Majoranas now
and add a space between: Majorana.And
Indeed, for these values of μ the two bands at negative and positive energy touch at E=0, for k=π and k=0 respectiely.
The fact that the surface of the cylinder is subject to a radial field is not mentioned in text or drawings. See https://courses.edx.org/courses/DelftX/TOPOCMx/1T2015/discussion/forum/274a4f6a5ece6fa10cf0c5e3d8ca2085/threads/54eb5cbe78f733e0ea000a84.
"Following the procedure that we learned the previous week, we can therefore put H(0) and H(π) in antisymmetric form."
"we must encounter a zero-energy level crossing in the energy spectrum, what last week we called a fermion parity switch."
Previous week the course did not even start yet...
There is an
Typo in first question:
Consider an isolated system with N=7 pairs of Majorana, and whose that total fermion parity is evenWhat is the ground state degeneracy of the system?
Second question:
Consider a system with only one pair of Majorana modes, thus with just two degenerate states with different fermion parity.What happens when we exchange the pair of Majorana modes, starting from a given fermion parity eigenstate?
It is probably set incorrectly in the stored jsons.
And the only other possible place where we could have a zero-energy soltuion is the core of the vortex.
Fig. 1 of the nanowire notebook has labels interchanged.
Not sure if this is intentionally or a bug (depends on the grading policy), but the correct solutions for the selfchecks are cleary accessible in the ipython notebooks.
topocm_content/w1_topointro/0d.ipynb
CHPT: The concept of a topological invariant
Below, we plot the energy levels along our path from H to H′ again, together with our topological invariant, the number of filled energy levels. You can see that this number changes from 2 to 3. Hence we can say that H and H′ are not topologically equivalent.
should probably state "...changes from 5 to 6."
In the equation in the text:
Now let us make this formal by first labeling the chains by an index ny, which takes integer values. Let us also replace k→kx to denote the wave-vector along a chain. Hence a single chain has a Hamiltonian [−(2tcosk+μ)τz+Δsinkxτy]⊗∣∣ny⟩⟨ny∣∣. The projector ∣∣ny⟩⟨ny∣∣ is needed to single out one chain out of the stack.
The (2tcosk+μ) needs to be (2t cos(k_x)+μ)
The Berry curvature and momentum change sign under time-reversal, so that the Berry curvatureat one momentum becomes opposite to the Berry curvature at opposite momentum.
add a space before "at one.....
In the intro and the summery videos by Michael, there is only sound from the right speaker which makes it a bit uncomfortable to listen to on headphones.
Typo in the question:
"Suppose that in your topological nanowire junction, positive energy quasiparticles can escapeinto a reservoir very quickly ..."
In w4, w5, w6 the sign of the mass corresponding to the topological phase in the effective Dirac Hamiltonian and in the BHZ Hamiltonian changes from being positive to negative. It would be nice to have this consistent.
As christophedebeule noticed answering a question on the forum, the logical structure of the following sentence should be fixed:
"We should just keep the Hamiltonian the same and change the sign of all terms that break time reversal symmetry, for instance the term proportional to the magnetic field B."
In fact it's the reverse: all terms change sign, except those that change sign under T.
In 2.1 "Putting everything together" Delta is formatted as %1.2f, while it has three digits.
Also alpha misses a prefactor of 1/2 to match continuum.
First question:
Consider the simple case where spin is conserved.In the quantum spin Hall bar system above, what happens if, instead of applying a voltage between terminals 1 and 2, you manage to apply a spin-polarized current between terminals 1 and 2?
Reported by SamMugel
the cylinder geometry is really equvalent to the Corbino disk, except that it easier to study.
The first question in sec 1.1 extremely hard and confusing, which is especially bad since it's the first encounter of the questions. It should be formulated clearer and/or simplified.
(In the Hall cylinder, this can be done by threading a time-dependent flux through the cylinder, as you have seen in the previou spart of the lecture).
A declarative, efficient, and flexible JavaScript library for building user interfaces.
🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.
TypeScript is a superset of JavaScript that compiles to clean JavaScript output.
An Open Source Machine Learning Framework for Everyone
The Web framework for perfectionists with deadlines.
A PHP framework for web artisans
Bring data to life with SVG, Canvas and HTML. 📊📈🎉
JavaScript (JS) is a lightweight interpreted programming language with first-class functions.
Some thing interesting about web. New door for the world.
A server is a program made to process requests and deliver data to clients.
Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.
Some thing interesting about visualization, use data art
Some thing interesting about game, make everyone happy.
We are working to build community through open source technology. NB: members must have two-factor auth.
Open source projects and samples from Microsoft.
Google ❤️ Open Source for everyone.
Alibaba Open Source for everyone
Data-Driven Documents codes.
China tencent open source team.