Pis’ma v ZhETF, vol. 113, iss. 11, pp. 729 - 730
© 2021
June 10
Aharonov-Bohm interferometry based on helical edge states1)
(Mini-review)
R. A. Niyazov+∗2), D. N. Aristov+∗, V. Yu. Kachorovskii×
+Department of Physics, St. Petersburg State University, 198504 St. Petersburg, Russia
∗National Research Centre “Kurchatov Institute”, Petersburg Nuclear Physics Institute, 188300 Gatchina, Russia
×Ioffe Institute, 194021 St. Petersburg, Russia
Submitted 21 April 2021
Resubmitted 21 April 2021
Accepted 23
April 2021
DOI: 10.31857/S1234567821110033
The Aharonov-Bohm interferometers (ABI) made
for interferometers based on superconducting SQUIDs
of quantum wires with single or few ballistic quantum
or the requirement of very strong magnetic fields for in-
channels are very attractive as prime devices to probe
terferometers based on the edge states of Quantum Hall
quantum coherent phenomena and in view of possi-
Effect systems. Moreover, the antiresonances arising in
ble applications as miniature and very sensitive sensors
the usual ABIs at T ≫ Δ, are very sensitive to the
of magnetic field. The underlying physics is related to
geometry of the problem [6-9].
Aharonov-Bohm (AB) oscillations of conductance. The
shape and amplitude of these oscillations depend essen-
tially on the strength of the tunneling coupling and on
the relation between temperature, T, and level spacing,
Δ. For T ≪ Δ and weak tunneling coupling there are
narrow resonant peaks in the dependence of conduc-
tance, G, on the magnetic flux Φ [1-3]. The positions of
the peaks depend on the electron Fermi energy [1] and
on the strength of the electron-electron interaction [4].
Remarkably, the interference effects are not entirely sup-
pressed with increasing the temperature, and the reso-
nant behavior of G(Φ) survives for the case T ≫ Δ.
Specifically, the high-temperature conductance of the
noninteracting ring weakly coupled to the contacts ex-
hibits sharp antiresonances at φ = Φ/Φ0 = 1/2 + n,
Fig. 1. (Color online) Helical ABI with the magnetic im-
purities
where Φ0 = hc/e is the flux quantum and n is an arbi-
trary integer number [5, 6]. The antiresonances acquire
A promising opportunity for a technological break-
a fine structure due to the electron-electron interaction
through in this direction is associated with the discovery
[5-8] and are broadened by the weak disorder [9].
of topological insulators, which are materials insulating
The complexity of creating ballistic single- or few-
in the bulk, but exhibiting conducting one-dimensional
channel interferometers based on conventional semicon-
helical channels at the surface or at the boundaries (see
ductors, such as GaAs or Si, is connected with tech-
Fig. 1).
nological problems of manufacturing one-dimensional
The electron transport via helical edge states is
clean systems. The efficiency of practically used quan-
ideal, in the sense that electrons do not experience
tum electronic interferometers is limited by rather strin-
backscattering from conventional non-magnetic impu-
gent requirements, for example, very low temperature
rities. Hence, in the absence of magnetic disorder, the
boundary states are ballistic and the intereferometers
1)Supplementary materials are available for this article at DOI:
constructed on such states are topologically protected
10.1134/S0021364021110035 and are accessible for authorized
users.
from external perturbations. Due to this key advantage
2)e-mail: r.niyazov@spbu.ru
the helical edge states (HES) are very promising candi-
Письма в ЖЭТФ том 113 вып. 11 - 12
2021
729
730
R. A. Niyazov, D. N. Aristov, V. Yu. Kachorovskii
dates for building blocks in quantum spin-sensitive in-
Importantly, the tunneling interferometer can be de-
terferometry. HES-based interferometers were already
scribed in terms of ensemble of flux-tunable qubits giv-
studied theoretically at zero temperature for normal
ing equal contributions both to conductance and spin
[10-12] and ferromagnetic [13] leads.
polarization. The number of active qubits participat-
In this review, we focus on the case of relatively
ing in the charge and spin transport is given by the
high temperature, T ≫ Δ. We discuss recent studies
ratio of the temperature to the level spacing. Such an
of spin dependent transport through HES-based ABI
ensemble of qubits can effectively operate at high tem-
(see Fig. 1) and formulate essential steps towards solving
perature and can be used for quantum calculations [18].
several critical problems of quantum information pro-
This opens a wide avenue for high-temperature quan-
cessing: spin filtering, long-distance spin transfer, and
tum computing.
effective spin manipulation. We start by discussing the
The work was funded by Russian Foundation for
tunneling conductance of the interferometer. We show
Basic Research, grants 19-32-60077 (R.Niyazov) and
that G is structureless in ballistic case but reveals sharp
20-02-00490 (D.Aristov and V.Kachorovskii), and
antiresonances, as a function of dimensionless flux φ in
by Foundation for the Advancement of Theoretical
the presence of magnetic impurities. Although similar
Physics and Mathematics “BASIS” (R.Niyazov and
antiresonances are known to arise in the single-channel
V. Kachorovskii).
rings made of conventional materials, the helical ABI
Full text of the paper is published in JETP Letters
shows essentially different behavior due to specific prop-
journal. DOI: 10.1134/S0021364021110035
erties of the HES. Most importantly, the effect is more
universal and robust to details of the setup, in par-
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Письма в ЖЭТФ том 113 вып. 11 - 12
2021
