Timeline for Anomaly for Majorana fermion?
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10 events
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| Apr 15, 2019 at 6:00 | history | tweeted | twitter.com/StackPhysics/status/1117669045929742336 | ||
| Apr 2, 2015 at 7:01 | comment | added | Meng Cheng | @qc2014 There is no gravitational anomaly for the surface states of 3D topological superconductor, since the Majorana fermion there is only protected when there is time-reversal symmetry. In fact, you can realize exactly the same field theory in purely 2D systems but breaking time-reversal symmetry. | |
| Apr 2, 2015 at 6:59 | comment | added | Meng Cheng | @FraSchelle For chiral Majorana modes on the edge of p+ip, you can take a look at Read and Green arxiv.org/abs/cond-mat/9906453. The non-chiral one at the critical point of transverse Ising model should be covered in many textbooks, such as Subir Sachdev's "Quantum phase transitions". | |
| Mar 31, 2015 at 21:02 | comment | added | qc2014 | @FraSchelle Thanks for your comment! I am also interested in examples. I also have a followup question: does gravitational anomaly appears in 3D topological superconductor? If it exists, is it related to Majorana fermions on 2D surface? | |
| Mar 31, 2015 at 5:34 | comment | added | FraSchelle | @MengCheng Thanks a lot, and sorry to disturb you one more time, but could you give me references for these exemples ? Thanks in advance ! | |
| Mar 29, 2015 at 21:25 | comment | added | Meng Cheng | @FraSchelle Majorana fermion (not zero modes) can show up in two ways: 1. Non-chiral version can arise as a critical theory, for example the critical point of the transverse Ising model in 1+1. 2. Chiral version shows up on the edge of 2d p+ip superconductor, which has gravitational anomaly. | |
| Mar 29, 2015 at 10:08 | comment | added | FraSchelle | @MengCheng I'm not sure this question has something to do with condensed-matter, does it ? In matter, there is no Majorana fermions, only Majorana mode (in short, the Majorana-staff exists only at zero energy, so it's not a particle as usual). I would naively guess there is no anomaly in condensed matter associated to the Majorana's physics, am I correct ? | |
| Mar 27, 2015 at 21:23 | comment | added | qc2014 | Thanks for the comment! Could you please also give me a clue or reference about what should the functional integral measure look like in the Majorana case? @Meng Cheng | |
| Mar 27, 2015 at 21:15 | comment | added | Meng Cheng | The $1/2$ difference in the perturbative gravitational anomaly is true in $1+1$ dimensions. The mathematical reason is probably that Grassmann integral for Majorana fermions gives a Pfaffian while for Dirac fermions you get a Determinant, and $\text{Det}=\text{Pf}^2$. Basically Majorana fermions have "half" degrees of freedom compared to Dirac fermions. | |
| Mar 27, 2015 at 20:40 | history | asked | qc2014 | CC BY-SA 3.0 |