Pis’ma v ZhETF, vol. 109, iss. 9, pp. 641 - 641
© 2019
May 10
Reply to comment on “Noise in the helical edge channel anisotropically
coupled to a local spin”
(Pis’ma v ZhETF 108, 700 (2018))
K.E.Nagaev+1), S.V.Remizov+∗, D.S.Shapiro+∗
+Kotelnikov Institute of Radioengineering and Electronics, 125009 Moscow, Russia
∗Dukhov Research Institute of Automatics (VNIIA), 127055 Moscow, Russia
Submitted 19 March 2019
Resubmitted 19 March 2019
Accepted 21 March 2019
DOI: 10.1134/S0370274X19090157
The authors of comment [1] claim that our recent
its large value does not impose any restrictions on the
results [2] on the noise in the helical edge channel of
relations between these quantities.
a 2D topological insulator coupled to a spin-1/2 impu-
The authors of the comment admit that in this ap-
rity are incorrect. Their argument is that the expression
proximation, their Eq. (5) crosses over to Eq. (7) of our
for the average backscattering current that follows from
paper [2] written for J2 = Ja = 0. In addition, it is
our Eq. (7) differs from Eq. (22) of their own paper [3].
clearly seen that the voltage-proportional current in the
They state that it is illegal to assume that the density
limit of J2 = J1 = 0 and eV ≫ T , Eq. (3) of the com-
matrix of the impurity spin is diagonal in the basis of
ment, vanishes in this case. Hence there is no contradic-
Sz, which is the cornerstone of our calculations and the
tion between papers [2] and [3].
calculations of a previous paper [4].
To summarize, our results are correct within the lim-
The authors of the comment reason that the de-
its of applicability of our model, and their critique by
phasing of the impurity spin arises not only from the
the authors of the comment is irrelevant.
term JzSzsz in the Hamiltonian, but also from the term
2JaSxsz. However this depends on the relative mag-
1. I. S. Burmistrov, P. D. Kurilovich, and V. D. Kurilovich,
nitude of the parameters Jz and Ja. In our paper we
Pis’ma v ZhETF 109, 639 (2019).
clearly state that the dephasing of the impurity spin is
2. K. E. Nagaev, S. V. Remizov, and D. S. Shapiro, JETP
due to the term JzSzsz, and this implies that Jz is large.
Lett. 108, 664 (2018); arXiv:1810.05831.
This does not mean that the exchange matrix is diago-
3. P. D. Kurilovich, V. D. Kurilovich, I. S. Burmistrov, and
nal as stated in [1], but only means that J33 in Eq. (1) of
M. Goldstein, Pis’ma v ZhETF 106, 575 (2017) [JETP
the comment is much larger than all the other elements
Lett. 106, 593 (2017)].
of the matrix. Note that this parameter does not enter
4. L. Kimme, B. Rosenow, and A. Brataas, Phys. Rev. B
into any of the transition rates Γ±0, Γa, Γ1, or Γ2 and
93, 081301 (2016).
1)e-mail: knagaev@inbox.ru
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