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Triplet character of 2Dfermion dimers arising from $s$wave attraction via spinorbit coupling and Zeeman splitting
by Ulrich Ebling, Ulrich Zülicke, Joachim Brand
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Submission summary
Authors (as registered SciPost users):  Joachim Brand · Ulrich Ebling 
Submission information  

Preprint Link:  https://arxiv.org/abs/2112.09336v1 (pdf) 
Date submitted:  20211220 23:01 
Submitted by:  Brand, Joachim 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We theoretically study spin$\frac{1}{2}$ fermions confined to two spatial dimensions and experiencing isotropic shortrange attraction in the presence of both spinorbit coupling and Zeeman spin splitting  a prototypical system for developing topological superfluidity in the manybody sector. Exact solutions for twoparticle bound states are found to have a triplet character that can become dominant in the regime of weak attractive $s$wave interaction when the energy scale of spinorbit coupling is comparable to a combination of the Zeeman and centerofmass kinetic energies. The centerofmass momentum is one of the parameters determining the existence of bound states, which we map out for both two and onedimensional types of spinorbit coupling. Distinctive features emerging in the orbital part of the boundstate wave function, including but not limited to its $p$wave character, provide observable signatures of unconventional pairing.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022322 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2112.09336v1, delivered 20220322, doi: 10.21468/SciPost.Report.4743
Strengths
1. This study is wellmotivated and timely.
2. Interesting new results on twobody bound states of spinorbit coupled fermions.
3. The results will be useful as a starting point for developing manybody theories of SOinteracting fermions.
Weaknesses
Presentation lack sufficient detail (see requested changes below).
Report
This manuscript presents a theoretical study of interacting spin1/2 fermions in two dimensions. The interactions are composed of isotropic shortrange attraction and the spinorbit coupling, and the Zeeman interactions. The authors find triplet bound states which could be observed in the regime of sufficiently strong spinorbit (SO) coupling, which leads to interesting unconventional pairing mechanisms. These mechanisms could give rise to topological superfluidity with Majoranafermion excitations. This study is therefore wellmotivated and timely.
The major new aspect of this work is the inclusion of the Zeeman splitting on the same footing as centerofmass momentum, which has apparently not been done before. In addition, the authors examine the spin properties of the bound state in detail and consider a usefully wide range of SO couplings, such as Dirac, Rashba, and Dresselhaus in 2D and the p_x \sigma_x coupling in 1D. They first solve the twobody problem with a general SO coupling to obtain the wavefunction \psi_b(p)> and then project the solution onto the total spin states of the twoparticle system (Eqs. 25). They finally consider the different types of SO couplings and analyze the properties of the bound states obtained with each type of coupling.
Some of the interesting results obtained by the authors include: (i) the COM momentum acts as an effective magnetic field and (ii) the twobody bound states disappear when the COM momentum exceeds a certain threshold.
Perhaps even more importantly, the results obtained in this manuscript will be useful as a starting point for developing manybody theories of SOinteracting fermions. Thus, in my opinion, the Expectation “Open a new pathway in an existing or a new research direction, with clear potential for multipronged followup work” is satisfied.
It should also be noted that the manuscript is clearly and concisely written. The general acceptance criteria will also be satisfied after the authors address my comments below.
As such, I recommend this manuscript for publication in SciPost Physics.
Requested changes
1. The parameter b defined below Eq. (5) gives the relative strength of the Zeeman and SO interaction seems to have the dimension of momentum. Does this parameter then adequately reflects the relative strength of these Zeeman and SO interactions. Would it not be better to use a dimensionless ratio of interaction strengths?
2. Equations (9) establish that the relative motion of two particles in the COM frame depends on the COM momentum P. This is an unusual situation because the reason one introduces the COM and relative coordinates in the first place is to decouple the Hamiltonian into two commuting parts (the COM and internal Hamiltonians).
Hence, two points should be clarified. First, is there really any practical advantage to using the coordinates in Eq. (6)? Second, it would be helpful to mention exactly which interactions are responsible for the coupling between the external and internal degrees of freedom. Are these the SO coupling terms of the kind \sigma_x p_y?
3. In Section 2.2 the authors use the Green function approach to obtain the bound states of swave interacting particles. Is this the only approach that can be used?
It would also be helpful for the general reader to understand how this approach works using a simple example. A reference to the approach being applied to, e.g., two interacting particles in the absence of the SO interaction, would be helpful.
Report #1 by Peter Schmelcher (Referee 1) on 202227 (Invited Report)
 Cite as: Peter Schmelcher, Report on arXiv:2112.09336v1, delivered 20220207, doi: 10.21468/SciPost.Report.4334
Strengths
See my referee report
Weaknesses
See my referee report
Report
See attached file.
Requested changes
See attached file.