Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire
Electron transport through Majorana nanowire with strongly asymmetric couplings to normal metal leads is
 considered. In three terminal geometry (electrically grounded nanowire) it is shown that the presence of unbiased
 electrode restores zero-bias anomaly even for strong Majorana e...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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| Cite this: | Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire / A.D. Shkop, A.V. Parafilo, I.V. Krive, R.I. Shekhter // Физика низких температур. — 2016. — Т. 42, № 4. — С. 398–402. — Бібліогр.: 12 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860124197349490688 |
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| author | Shkop, A.D. Parafilo, A.V. Krive, I.V. Shekhter, R.I. |
| author_facet | Shkop, A.D. Parafilo, A.V. Krive, I.V. Shekhter, R.I. |
| citation_txt | Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire / A.D. Shkop, A.V. Parafilo, I.V. Krive, R.I. Shekhter // Физика низких температур. — 2016. — Т. 42, № 4. — С. 398–402. — Бібліогр.: 12 назв. — англ. |
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| container_title | Физика низких температур |
| description | Electron transport through Majorana nanowire with strongly asymmetric couplings to normal metal leads is
considered. In three terminal geometry (electrically grounded nanowire) it is shown that the presence of unbiased
electrode restores zero-bias anomaly even for strong Majorana energy splitting. For effectively two-terminal
geometry we show that electrical current through asymmetric Majorana junction is qualitatively different from
the analogous current through a resonant (Breit–Wigner) level.
|
| first_indexed | 2025-12-07T17:41:01Z |
| format | Article |
| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 4, pp. 398–402
Low-energy anomalies in electron tunneling through
strongly asymmetric Majorana nanowire
A.D. Shkop1, A.V. Parafilo2, I.V. Krive1,3, and R.I. Shekhter4
1B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine
47 Prospekt Nauky, Kharkiv 61103, Ukraine
E-mail: Shkop@ilt.kharkov.ua
2The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151 Trieste, Italy
3Ukraine Physical Department, V. N. Karazin National University, Kharkiv 61077, Ukraine
4Department of Physics, University of Gothenburg, SE-412 96 Göteborg, Sweden
Received January 14, 2016, published online February 24, 2016
Electron transport through Majorana nanowire with strongly asymmetric couplings to normal metal leads is
considered. In three terminal geometry (electrically grounded nanowire) it is shown that the presence of unbiased
electrode restores zero-bias anomaly even for strong Majorana energy splitting. For effectively two-terminal
geometry we show that electrical current through asymmetric Majorana junction is qualitatively different from
the analogous current through a resonant (Breit–Wigner) level.
PACS: 74.25.F– Transport properties;
73.23.–b Electronic transport in mesoscopic systems;
74.78.Na Mesoscopic and nanoscale systems.
Keywords: electron tunneling, Majorana fermions, experimental setup.
1. Introduction
Last years Majorana fermions attract a great attention in
solid state physics. Firstly predicted by E. Majorana as a
fermion particle that coincides with its own antiparticle,
Majorana fermions reappeared in condensed matter in the
form of Majorana bound states (MBS)-spinless zero-ener-
gy subgap edge states in topological superconductors (see,
e.g., [1] or review [2]), useful for fault-tolerant quantum
computation [3]. By definition the creation and annihilation
operators of MBS coincide, † = jjγ γ . Being a «half» of
a Dirac fermion (its hermitian and anti-hermitian parts),
Majorana fermions obey a Clifford algebra, { , } = 2 .i k kiγ γ δ
Two MBS localized on the opposite sides of topological
superconductor form a highly nonlocal Dirac fermion,
2 † 2
1 2= ( ) / 2, = ( ) = 0c i c cγ + γ . This nonlocality leads to
unusual electron transport through Majorana bound states.
In particular, electron tunneling in Majorana systems could
be very different from resonant level electron tunneling
even in the case when Majorana hybridization 1 2Mε γ γ ( Mε
is Majorana splitting energy) is taken into account and
MBS are splitted into two fermion levels. The presence of
substrate superconductor introduces additional (Andreev)
channel of electron tunneling and supports electron hole
symmetry. Both those properties result in electron tunnel-
ing through MBS which strongly differs from ordinary re-
sonant electron tunneling described by Breit–Wigner trans-
mision probability.
Many efforts were spent to theoretically treat these to-
pological modes and distinguish them from «ordinary»
excitations in experiment which could mimic the properties
of MBS (see, e.g., review [2]). A promising venue in expe-
rimental observation of Majorana fermion is the tunneling
experiments where electrons tunnel through MBS which
provides the only possible channel for a subgap electrical
current at low bias voltages.
It is already known that Majorana fermions lead to a new
transport phenomena — resonant Andreev reflection which
manifested in zero-bias peak in differential conductance
for normal metal/topological superconductor junction [5].
Although various properties of electron tunnel transport
through Majorana bound states have been already studied
for two-terminal [6–8] and three-terminal [9–11] devices,
we can add to this knowledge new results concerning
© A.D. Shkop, A.V. Parafilo, I.V. Krive, and R.I. Shekhter, 2016
Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire
specific properties of asymmetric Majorana tunnel junction
with strongly different coupling strengths to the normal
metal leads.
For this reasons we consider experimental setup (see
Fig. 1) where an electrically grounded nanowire (i.e., 1D
wire on top of s-wave superconductor) is tunnelly coupled
to a fixed normal metal electrode (L-electrode) and to
a movable tip of scanning microscope (R-electrode). In
real experiment Majorana bound states are supposed to be
hosted at the ends of semiconducting wire on a top of
ordinary s-wave superconductor when proximity effect,
strong spin-orbit interaction and external magnetic field
work together to form effectively spinless regime of elec-
tron transport deep inside the superconducting gap. Our
purpose here is to study transmission properties of topo-
logical superconductor with two Majorana modes weakly
coupled to the normal metal leads. For electrically grounded
superconductor the currents through left (L) and right (R)
tunnel contacts in the general case of asymmetric junction
,( ,L R L RΓ ≠ Γ Γ are the coupling energies) are different
even for equal biases L Rµ = µ << ∆ (∆ is the supercon-
ducting gap). Each current depends both on LΓ and RΓ if
Majorana splitting energy 0Mε ≠ . For this junction the
linear conductances Gα ( = ,L Rα ) at low temperatures and
= 0Mε reach maximum value 22 /e h , exhibiting zero-bias
anomaly in the differential conductance (factor 2 is due to
the contribution of Andreev tunneling) just like when
( ) 0L RΓ → (see Ref. 7). For 0Mε ≠ linear conductances
are always finite 0Gα ≠ when both coupling energies
,L RΓ Γ are finite. In the limit ( ) 0,L RΓ → 0Mε ≠ the linear
conductance vanishes, ( ) 0R LG → . We show that for strong-
ly asymmetric junction <<L RΓ Γ and for finite Majorana
energy splitting Mε in the range << <<L M RΓ ε Γ the pre-
sence of the second MBS at the right end of the Majorana
nanowire coupled to the unbiased R-electrode restores
zero-bias anomaly in the differential conductance of the
left contact.
In the transport regime when Majorana nanowire is
electrically isolated it is shown that electron current through
a strongly asymmetric Majorana junction qualitatively dif-
fers from the analogous current through Breit–Wigner
resonant level.
2. Equations of motion and partial currents
At first we calculate electric currents at three terminal
system consisted of two metal leads and an electrically
grounded Majorana nanowire. The full Hamiltonian is
given by three terms = M tH H H Hα
α
+ +∑ , where
†= k kk
k
H c cα α ααε∑ is the Hamiltonian of normal leads
with †( )k kc cα α being the electron annihilation (creation)
operator for the α lead (L or R), quantum wire with
Majorana edge states is described by effective low-energy
Hamiltonian 1 2= ( / 2) ,M MH i ε γ γ which follows from Kitaev
toy model [3], here 0exp ( / )M Lε ∝ − ξ is the splitting be-
tween two zero-energy states (L is the length of the Majora-
na quantum wire and 0ξ is the superconducting coherence
length), and tH is the tunnel Hamiltonian.
The tunnel Hamiltonian describing coupling between
= /L Rα lead and topological superconductor is
,
= h.c.,t k k
k
H V cα α α
α
γ +∑ (1)
here ( ) 1(2)=L Rγ γ , kVα is the effective amplitude of tunnel-
ing which appears due to projection of superconductor
electron-field operator onto the manifold of Majorana
states, thus tunnel couplings are characterized by energy
level width (see [2,7])
2= 2 ( ) | |k k
k
Vα α αΓ πδ ε − ε∑ .
The current operator in the α lead reads ( = 1 )
( )
†
( ) = = 2 Im .kk
k k
k k
dc c
I t e e V c
dt
αα
α α α α− γ∑ ∑ (2)
By solving the Heisenberg equation of motion for
( )kc tα one finds
( )( ) = e e ( )
t
i t i t tk kk k kc t c iV t dt′− ε − ε −∗α α
α α α α
−∞
′ ′− γ∫ . (3)
Then after substitution it into Heisenberg equation for
Majorana operators
( ) = [ , ]t i Hα αγ γ (4)
we obtain matrix equation for them
( ) 2 ( ) ( )
= ,
( ) 2 ( ) ( )
L L M L L
R M R R R
t t t
t t t
γ − Γ ε γ ξ
+ γ −ε − Γ γ ξ
(5)
Fig. 1. A schematic picture of Majorana nanowire with control-
lable coupling to the leads. Tip of scanning tunneling microscope
(STM) at the right end of nanowire enables one to vary the coupl-
ing strenght RΓ . Electrical potentials of the leads = ,eVα αµ
= ,L Rα are counted from the electrical potential 0µ = of the
electrically grounded topological superconductor.
UL
ΓL
µL
µ = 0
ΓR
µRMBS
STM
UR
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 4 399
A.D. Shkop, A.V. Parafilo, I.V. Krive, and R.I. Shekhter
where
( ) = 2 e h.c.i tkk k
k
t i V c − εα
α α αξ − +∑
After straightforward calculation one finds Majorana ope-
rators
2
( ) = e i t Lk RLkL Lk Lk
Lk
i
t V c − ε ε + Γ
γ +
∆∑
e h.c.i t MRkRk Rk
Rk
i V c − ε ε
+ +
∆∑ , (6)
2
( ) = e i t Rk LRkR Rk Rk
Rk
i
t V c − ε ε + Γ
γ +
∆∑
e h.c.i t MLkLk Lk
Lk
i V c − ε ε
+ +
∆∑ (7)
Here 2 2 22 = [ ( )] ( )k L R L R Miα α∆ ε + Γ + Γ + Γ − Γ − ε . Now
with the help of Eqs. (2), (3), (6), (7) it is easy to get
desired expression for the average currents ( )I I tα α= 〈 〉 ,
where ...〈 〉 is the thermodynamic average with the Hamil-
tonian of noninteracting electrons in the leads. The average
current = ( , )I I Tα αµ reads ( = 2h π)
2= ( ) tanh .
2 B
eI d T
h k T
+∞
α
α α
−∞
µ − ω
ω ω
∫ (8)
Here T is the temperature, = eVα αµ is the electric poten-
tial counted from the Fermi energy and the transmission
coefficient 2( )Tα ω takes the form
2 2 2 2 2
2
2
4(4 )
( ) = ,
( )
L R L R MT α
α
Γ Γ + Γ ω + Γ Γ ε
ω
∆ ω
(9)
where
2 4 2 2 2 2( ) = 4 ( ) (4 )L R L R∆ ω ω + ω Γ + Γ + Γ Γ +
2 2 22( 4 ) .M M L R + ε ε − ω − Γ Γ (10)
3. Differential conductance. Zero-bias anomaly
Differential conductance in the low-temperature limit
for each equally biased lead reads
22e= ( = )G T eV
hα α ω (11)
and when = 0, = 0MV ε it becomes 2
02 / = 2e h G . We see
that ( , = 0) 0I T αµ ≡ for arbitrary tunneling rates LΓ and
RΓ as it should be when the leads are not biased with
respect to the ground. Notice the appearance for spinless
electrons an extra overall factor 2 in Eq. (11) and hyper-
bolic tangent in the current dependence on temperature and
chemical potential instead of difference of Fermi distri-
bution functions in the ordinary situation (Landauer–But-
tiker formula). Both these features are related to the pre-
sence of the substrate superconductor in electron transport
through Majorana quantum wire. Factor 2 is due to appear-
ance of addition channel (Andreev tunneling) in electron
transport through MBS. Characteristic temperature and
chemical potential dependence in Eq. (8) is usual for nor-
mal metal–superconductor (MS) junctions. In the limiting
case of a single MS contact ( = 0LΓ or = 0, = 0R MΓ ε )
our formulae for current and conductance are reduced to
the corresponding expression in Ref. 7. In general case of
asymmetric junction ( L RΓ ≠ Γ ) the currents in the left and
right contacts are not equal, L RI I≠ (see also Ref. 11). It is
reasonable to consider the limit when the total current to
the ground vanishes, = = 0G L RI I I+ . Then one can speak
about definite current from the left to right lead induced by
voltage bias eV . With the help of our general formulae
(8)–(10) we reproduce the expression for the current
= LI I through a symmetric Majorana nanowire derived
also in Refs. 9, 10. For asymmetric junction and/or asym-
metric bias | | | |L Rµ ≠ µ the total current to the ground GI
is not zero. Here we consider the dependence of dif-
ferential conductance on =L eVµ in the case when = 0Rµ
( = 0, = = ( )R G LI I I I V , see also Ref. 11). It is straightfor-
ward to find from our basic equations (8)–(10) the depen-
dence of differential conductance on bias voltage at low
temperatures 0( ) = 2 ( = )LG V G T eVω . In terms of dimension-
less variables = / 2 L RV V Γ Γ and / 2M M L Rε = ε Γ Γ dif-
ferential conductance ( )G V takes the form
22 2
22 2 2 2 2 20
1 ( / )( ) =
2 (1 ) [( ) / ]
M L R
M L R L R M
e VG V
G e V
+ ε + Γ Γ
+ ε + Γ + Γ Γ Γ − ε
. (12)
Particularly in the linear response 0V → Eq. (12) is simpl-
ified
2
0
4
= .
2 4
L R
L R M
G
G
Γ Γ
Γ Γ + ε
(13)
Thus for <<M L Rε Γ Γ differential conductance is
0/ 2 1G G → , while (0) = 0,G when = 0, >>R M LΓ ε Γ .
It means that zero-bias Majorana signature 0(0) = 2G G
disappears in a single contact junction if Majorana energy
splitting >>M Lε Γ . Zero-bias peak is re-established for
strongly asymmetric double contact junction >>R LΓ Γ
and <<M L Rε Γ Γ when the total width of splitted
Majorana levels exceeds the level splitting. In general the
presence of even unbiased second contact enhances the
current at low energies (temperature, bias voltage).
4. Electrically isolated Majorana nanowire
Now we consider experimental setup when the super-
conductor which supports Majorana nanowire is electric-
ally isolated and the current through MBS is induced
by the bias voltage =L R eVµ − µ . For a symmetric junc-
tion ( = =L RΓ Γ Γ) this problem was studied in Refs. 9, 10.
We have seen already that for symmetric electrically
grounded junction and for symmetrically biased leads
= = / 2L R eVµ −µ (only this case was considered in Ref. 10)
the total current to the ground = = 0G L RI I I+ . So the cur-
400 Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 4
Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire
rents through left and right contacts are equal, | | | |L RI I= .
It does not matter whether superconductor is electrically
grounded or not.
This strategy can be applied also for asymmetric junc-
tion. Now the equations
= ,
( ) = 0, =L R
L R
I eVα α
α
µ µ − µ∑ (14)
determine electrical potentials αµ of the leads as a function
of bias voltage V . It is evident that for small junction
asymmetry | |<<L R L RΓ − Γ Γ + Γ the asymmetry in elec-
trical potentials = L RV V Vδ + is small and weakly influ-
ences the current. In the opposite limit of strong junction
asymmetry (for definiteness we will assume >>L RΓ Γ ) elec-
trical potentials strongly differ, | | << | |L RV V for all biases V
and the current through the electrically isolated Majorana
nanowire could be different comparing with the analogous
current through resonant (Breit–Wigner) level.
At first we consider low-temperature limit 0T → and a
sufficiently long nanowire ( 0>>L ξ ) thus Majorana energy
splitting can be neglected. In this case the problem can be
easily solved analytically. When = 0Mε the transmission
coefficient Tα depends (as it should be) only on its coupl-
ing energy strength αΓ
2
2 2
4
=
4
T α
α
α
Γ
ω + Γ
(15)
and the corresponding currents take a simple form
2( ) = arctan .
2
e
I α α
α α
α
Γ µ
µ π Γ
(16)
For strongly asymmetric junction >>L RΓ Γ the solu-
tion of Eq. (16) is
2 arctan
2L R
R
eV
µ Γ Γ
(17)
( =R LeVµ − + µ ) and the current through electrically
isolated Majorana nanowire is determined by the cor-
responding current through the weakest link
2( ) = arctan
2
R
R
e eVI V
Γ
π Γ
. (18)
According to Eq. (18) the current is saturated at >> ReV Γ
to the value = ( ) /m RI eΓ which coincides with corres-
ponding maximum current through Breit–Wigner resonant
level ( >>L RΓ Γ ). However unlike usual transport where
saturation occurs at tot = L R LeV Γ Γ + Γ Γ (for strong-
ly asymmetric junction) in our case the current reaches its
maximum value at a much more lower energies ReV Γ
(see Fig. 2(b)).
Now we consider the influence of finite Majorana splitt-
ing Mε on current voltage characteristics. Our calculations
show (see Fig. 2(b)) that «small» values of splitting energy
<<M Lε Γ weakly influence I–V curves evaluated for = 0.Mε
When Mε is of the order of LΓ the saturation of current
curves occurs at energy scale s MeV ε end this I –V
characteristic resembles the well-known ( )I V -dependence
for electron tunneling through an asymmetric single-level
quantum dot. Specific features of Majorana tunneling dis-
appear.
One can see the characteristic properties of Majorana
tunneling also by analyzing the temperature dependence of
conductance ( )G T . As it is well known (see, e.g., review [12])
the conductance at resonant tunneling at high temperatures
Fig. 2. (a) Differential conductance for electrically grounded
Majorana nanowire in units 2
0 = /G e h as a function of bias
voltage normalized by the total width L RΓ + Γ : (i) solid curve
demonstrates the zero-bias anomaly ( = 0RΓ , STM tip is moved
to infinity, = 0Mε ); (ii) dotted curve corresponds to the case
of strong splitting energy = 2M Lε Γ . Majorana signature
0( = 0) = 2G V G disappears and conductance peak shifts to non-
zero voltages. When the second contact (right) with high trans-
parency >>R LΓ Γ is introduced one can observe Majorana
signature again, line for current dependence in this case coincides
with solid line. (b) Current–voltage characteristics of electrically
isolated strongly asymmetric Majorana nanowire / =R LΓ Γ
= 0.001, = 0Mε (dash-dot), =M Lε Γ (solid), = 2M Lε Γ (dot).
In strongly asymmetric system ( >>L RΓ Γ ) without level split-
ting ( = 0Mε ), the current saturates at voltages of order of the
smallest tunnel width RΓ , in contrast to conventional resonant
tunneling, thus this dependence is highly nonlinear.
/ LeV Γ/ ( )L ReV Γ + Γ
1.0
0.5
10 2 3 4 5
(a) (b)
0 5 10
G
G/
0
2
1
/(e
/
)
R
I
Γ
Fig. 3. Temperature dependence of dimensionless conductance
2
0( = /G e h) of electrically isolated Majorana nanowire ( = 0)Mε :
(i) dashed curve corresponds to symmetric junction =L RΓ Γ ,
(ii) solid curve describes strongly asymmetric junction
3/ = 10R L
−Γ Γ .
/ ( )B L Rk T Γ + Γ
2
1
100 20
G
G/
0
Low Temperature Physics/Fizika Nizkikh Temperatur, 2016, v. 42, No. 4 401
A.D. Shkop, A.V. Parafilo, I.V. Krive, and R.I. Shekhter
scales as ~ /G TΓ (where / ( )L R L RΓ = Γ Γ Γ + Γ ) and
the crossover temperature from T-independent regime of
transport to 1/ T -scaling is determined by the total level
width t L RΓ = Γ + Γ . Our calculations show (see Fig. 3)
that for strongly asymmetric electrically isolated Majorana
nanowire crossover temperature is determined by the
weakest coupling and therefore the conductance is strongly
suppressed by temperature even at a low temperatures.
5. Conclusions
In summary we calculated electrical current through
Majorana bound states for electrically grounded system
end effectively electrically isolated Majorana nanowire.
Our aim was to find specific features of electron tunneling
in this system in the presence of finite Majorana energy
splitting Mε which suppresses zero-bias anomaly in dif-
ferential conductance. We show that the fingerprints of
Majorana states can be easily revealed in tunneling experi-
ments with strongly asymmetric Majorana junction.
We suggested experimental setup where the strenght of
MBS coupling to the leads can be controlled with the help
of scanning tunneling microscope (STM). For three-ter-
minal geometry (electrically grounded Majorana nanowire)
it was shown that the presence of unbiased extra electrode
strongly coupled to the nanowire increases electric current
through Majorana bound states at low bias voltages. In
particular in the case when Majorana energy splitting is in
the range << <<L M RΓ ε Γ zero-bias anomaly in differ-
ential conductance which is suppressed for two-terminal
device ( = 0RΓ ) is restored when RΓ exceeds Mε .
Unusual tunneling characteristics of Majorana bound
states (MBS) can be observed even in the limit of vanish-
ingly small Majorana energy splitting 0Mε → . It is known
(see, e.g., [7]) that in this case transmission coefficient of
electron tunneling through MBS takes the form of Breit–
Wigner resonant tunneling probability. Therefore the pre-
sence in the system resonant levels at Fermi energy
(in particular, Kondo resonance) can mimic the properties
of Majorana fermions. We showed that the tunneling cur-
rent through electrically isolated Majorana nanowire (two-
terminal device) with strongly different couplings to the
leads is qualitatively distinct from the analogous current
through resonant (Breit–Wigner) level. For sufficiently
strong asymmetry the current is saturated at low bias volt-
ages and the measured –I V characteristics will look like
a step-function.
The authors thanks S.I. Kulinich for fruitful discus-
sions. A.S. and I.K. acknowledge financial support from
the NAS of Ukraine (grant No. 4/15-H). A.P. thanks the
Abdus Salam ICTP (Trieste, Italy) for financial support
and hospitality.
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1. Introduction
2. Equations of motion and partial currents
3. Differential conductance. Zero-bias anomaly
4. Electrically isolated Majorana nanowire
5. Conclusions
|
| id | nasplib_isofts_kiev_ua-123456789-128507 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-07T17:41:01Z |
| publishDate | 2016 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Shkop, A.D. Parafilo, A.V. Krive, I.V. Shekhter, R.I. 2018-01-10T15:00:19Z 2018-01-10T15:00:19Z 2016 Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire / A.D. Shkop, A.V. Parafilo, I.V. Krive, R.I. Shekhter // Физика низких температур. — 2016. — Т. 42, № 4. — С. 398–402. — Бібліогр.: 12 назв. — англ. 0132-6414 PACS: 74.25.F–, 73.23.–b, 74.78.Na https://nasplib.isofts.kiev.ua/handle/123456789/128507 Electron transport through Majorana nanowire with strongly asymmetric couplings to normal metal leads is
 considered. In three terminal geometry (electrically grounded nanowire) it is shown that the presence of unbiased
 electrode restores zero-bias anomaly even for strong Majorana energy splitting. For effectively two-terminal
 geometry we show that electrical current through asymmetric Majorana junction is qualitatively different from
 the analogous current through a resonant (Breit–Wigner) level. The authors thanks S.I. Kulinich for fruitful discussions.
 A.S. and I.K. acknowledge financial support from
 the NAS of Ukraine (grant No. 4/15-H). A.P. thanks the
 Abdus Salam ICTP (Trieste, Italy) for financial support
 and hospitality. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Электронные свойства проводящих систем Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire Article published earlier |
| spellingShingle | Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire Shkop, A.D. Parafilo, A.V. Krive, I.V. Shekhter, R.I. Электронные свойства проводящих систем |
| title | Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire |
| title_full | Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire |
| title_fullStr | Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire |
| title_full_unstemmed | Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire |
| title_short | Low-energy anomalies in electron tunneling through strongly asymmetric Majorana nanowire |
| title_sort | low-energy anomalies in electron tunneling through strongly asymmetric majorana nanowire |
| topic | Электронные свойства проводящих систем |
| topic_facet | Электронные свойства проводящих систем |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/128507 |
| work_keys_str_mv | AT shkopad lowenergyanomaliesinelectrontunnelingthroughstronglyasymmetricmajoranananowire AT parafiloav lowenergyanomaliesinelectrontunnelingthroughstronglyasymmetricmajoranananowire AT kriveiv lowenergyanomaliesinelectrontunnelingthroughstronglyasymmetricmajoranananowire AT shekhterri lowenergyanomaliesinelectrontunnelingthroughstronglyasymmetricmajoranananowire |