Atomristor Mott Theory of Sn Adatom Adlayer on a Si Surface
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript by L. Craco, E. E. Chagas and S. S. Carara discusses the results of a computational study on a Sn adatom adlayer on a Si (111) surface. The work aims at verifying the ability of this system to represent a non volatile atomristor, i.e. a system whose electric resistivity can be tuned between well defined and stable values through an external electric field that, shifting the energy of conductive electronic states near the surface, changes their occupation and their contribution to conduction.
The study employs the DFT+DMFT method based on a multi-orbital Hubbard Hamiltonian that is meant to capture the Mott-like character of the 5p orbitals of the Sn adatoms. The authors use this technique to study how the electronic structure of the system reorganizes in dependence of an on-site energy term which acts like a Zeeman field on the orbital sector. The manuscript focuses in particular on the changes in the spectral function (density of states) and the consequent shift of population between in-plane (xy) and out-of-plane (z) 5p states that, being around the edge of valence and conduction bands, are the ones responsible for the conduction properties. The latter are explicitly
considered in this paper through the calculation of the I-V characteristics.
The manuscript is written very clearly and is well organized. I appreciated in particular the introduction where the authors make a significant effort to frame the topic of their work within the existing literature and provide a good discussion of the problem they tackle in their manuscript. The results they present seem solid and I think they would be of interest for the scientific community.
There are, however, a few problematic aspects I would like to highlight.
1) I don't completely understand the reason why Sn 5p states should be treated within DMFT or why they should exhibit Mott-Hubbard physics. 5p states are not the most typical states to be treated as correlated ones, to show evidence of Mott physics or to require DMFT for a more accurate description (they are typically quite spread in space and give rise to disperse bands). Is all this motivated by the fact that Sn atoms are quite far apart from each other, thus inducing a pronounced localization of valence electrons on these atomic orbitals? If this is the case, wouldn't a simpler (and probably cheaper) approach like hybrid functional of DFT+U be able to capture most of the effects?
2) Related to the previous question: How where the Hubbard parameters (U and J) chosen? Were they taken from existing literature or determined some other way? If they were determined semi-empirically, what properties where they fitted on?
3) While it sounds reasonable that a bias electric field can make electrons localize on the z or xy (in-plane) states, it is not really clear to me how the on-site orbital Zeeman potential can in fact represent the effects of an external electric field. Could authors comment on this point and add a few sentences to clarify this specific aspect? Is it a standard way of representing the effect of electric fields in this type of simulations? How big should a realistic electric field be to induce orbital polarization effects like the ones described in this paper? How should it be oriented with respect to the normal of the Si surface?
4) I find the discussion of results a little bit too fast and superficial. As for the density of states, I can appreciate a significant readjustment of various peaks in dependence of Delta in the z and/or xy channels. However, it is quite hard to visualize what is going on in reality. A 3D plot of the charge density readjustment would help the reader quite much in this respect. Also, authors could complete their results by reporting the total number of electrons localized on z and x-y 5p orbitals (i.e. the integral of their curves). Is there a complete transfer of charge from one type of orbital to the other or do electron rather leak to some extent to other states (e.g., of the Si substrate)?
Concerning the I-V characteristics I also think that the discussion should be extended and completed. For example, how pronounced should the derivative shift in the I-V curves be for this characteristic to represent
a memory effect (hence the memristor behavior)? Also, what is the relation between the knees observable in the I-V curves and the readjustment of the density of states around the Fermi level (presence of peaks, etc) presented in Figs 3 and 4? In particular, what is the reason for the change in the I-V curves to be more pronounced for negative
delta shifts while the corresponding spectral function exhibits relatively minor readjustments?
5) Are there experimental proofs of authors' results on this or similar systems? How well in agreement with this manuscript outcomes are they, in case? Could authors comment on this point possibly adding a few lines to the their manuscript?
In summary, the paper contains a good work and I think it should be published on the journal after the authors have addressed the relatively minor points raised above.
Comments on the Quality of English LanguageThere are some typos and mistypings that need to be fixed. Otherwise I found the language appropriate
Author Response
Reviewer 1
----------
"The manuscript by L. Craco, E. E. Chagas and S. S. Carara discusses the
results of a computational study on a Sn adatom adlayer on a Si (111)
surface. The work aims at verifying the ability of this system to
represent a non volatile atomristor, i.e. a system whose electric
resistivity can be tuned between well defined and stable values through
an external electric field that, shifting the energy of conductive
electronic states near the surface, changes their occupation and their
contribution to conduction.
The study employs the DFT+DMFT method based on a multi-orbital Hubbard
Hamiltonian that is meant to capture the Mott-like character of the 5p
orbitals of the Sn adatoms. The authors use this technique to study how
the electronic structure of the system reorganizes in dependence of an
on-site energy term which acts like a Zeeman field on the orbital sector.
The manuscript focuses in particular on the changes in the spectral function
(density of states) and the consequent shift of population between in-plane
(xy) and out-of-plane (z) 5p states that, being around the edge of valence
and conduction bands, are the ones responsible for the conduction properties.
The latter are explicitly considered in this paper through the calculation
of the I-V characteristics.
The manuscript is written very clearly and is well organized. I appreciated
in particular the introduction where the authors make a significant effort
to frame the topic of their work within the existing literature and provide
a good discussion of the problem they tackle in their manuscript. The results
they present seem solid and I think they would be of interest for the
scientific community.
There are, however, a few problematic aspects I would like to highlight."
Reply:
We would like to thank the First Referee of Condensed Matter for the
invested time in reading and evaluating our manuscript as well as for
the constructive comments and suggestions he/she sets out below. In what
follows we will answer his/her comments and questions.
"1) I don't completely understand the reason why Sn 5p states should be
treated within DMFT or why they should exhibit Mott-Hubbard physics.
5p states are not the most typical states to be treated as correlated ones,
to show evidence of Mott physics or to require DMFT for a more accurate
description (they are typically quite spread in space and give rise to
disperse bands). Is all this motivated by the fact that Sn atoms are
quite far apart from each other, thus inducing a pronounced localization
of valence electrons on these atomic orbitals? If this is the case,
wouldn't a simpler (and probably cheaper) approach like hybrid functional
of DFT+U be able to capture most of the effects?"
Reply:
We agree with the Referee that Sn 5p states are "quite spread in space
and give rise to disperse bands", an intrinsic broadband behavior which
has been shown in an earlier study of two of us on alpha-Sn (Ref. [32])
as well as in the work by Schuwalow et al. (Ref. [28]). Interestingly,
correlation effects beyond the local density approximation (LDA) and the
generalized gradient approximation (GGA) have been investigated by
Profeta and Tosatti (Ref. [20a]) within the LDA+U method, establishing
a Hubbard U for the Sn(5pz) orbital. In these DFT+U study, the Mott
insulating state of alpha-Sn has been obtained assuming ferro- and
ferrimagnetic orders which was reached for U \approx 2.0 eV, but the
authors of Ref. [20a] have also found an Hubbard U of 4 eV from
constrained calculations. Taken together with order Hubbard model-based
studies, this suggests that the apart from intrinsic Coulomb correlation
effects the Mott physics of non-magnetic (or paramagnetic) alpha-Sn can
not be properly "captured" using static DFT+U schemes, and this together
with intrinsic dynamical transfer of spectral weight are the reasons why
we have used the many-particle DFT+FMFT scheme for the multi-orbital
problem of alpha-Sn.
2) Related to the previous question: How where the Hubbard parameters
(U and J) chosen? Were they taken from existing literature or determined
some other way? If they were determined semi-empirically, what properties
where they fitted on?
Reply:
In our opinion, Ref. [32]) can be considered as an extension of Profeta
and Tosatti's work (Ref. [20a]), which treats the effect of on-site
electron-electron interactions at Hartree mean-field level. Ref. [32]
and our present theory study takes into account the intrinsic broadband
or the delocalized nature of the Sn-5p shell as in Ref. [20a], however
in addition to Hartree correction to DFT we are providing a realistic
DFT+DMFT description of dynamical many-particle interactions hidden in
the multi-orbital problem of alpha-Sn. Ref. [32] reports the evolution
of the one-particle spectral function of alpha-Sn upon increasing the
on-site Coulomb interaction from 2.0 to 8.0 eV, showing good
theory-experiment comparison between the DFT+DMFT result obtained for
8.0 eV and extant photoemission and angle-resolved photoemission
spectroscopy data. Motivated thereby in this present work we use this
on-site Coulomb interaction parameter value to unveil the effect of the
orbital-field on the electronic structure reconstruction of alpha-Sn.
3) While it sounds reasonable that a bias electric field can make electrons
localize on the z or xy (in-plane) states, it is not really clear to me how
the on-site orbital Zeeman potential can in fact represent the effects of
an external electric field. Could authors comment on this point and add a
few sentences to clarify this specific aspect? Is it a standard way of
representing the effect of electric fields in this type of simulations?
How big should a realistic electric field be to induce orbital polarization
effects like the ones described in this paper? How should it be oriented
with respect to the normal of the Si surface?
Reply:
The use of the orbital Zeeman field was partially motivated by the work
of F. Ming et al. (Ref. [16]) which reveals a "tip-assisted phase
switching" and "tunnelling polarity effects" on Sn-double layer grown on
Si(111) surface. Our proposal is also inspired by the photoresistive
switching of MoS2 memristor study by W. Wang et al. (Scientific Reports
6, 31224 (2016)), showing that the MoS2 memristor can be switched by an
electric field in the dark or under illumination with white light through
charge polarization or modulation of charge in an electric field. Moreover,
our proposal has also been motivated by the DFT-based study of Belviso et
al. (Ref. [40]) which reports the effect of the electric field in low
dimensional material, considering as in our work the role played by
polarition effects on the p-orbitals of transition-metal chalcogenides
like Mo(Se,Te)2 and WSe2. Also interesting in this context is the work
by Preziosi et al. (Ref. [41]) reporting an electric-field control of
the orbital occupancy and switching on the 3d orbital anisotropy in a
Mn-based transition-metal oxide. These earlier proposals provide, in our
opinion, support to our theory and results.
Concerning "How big should a realistic electric field be to induce
orbital polarization effects like the ones described in this paper?"
in the revised manuscript we are now writing that a "Delta=0.2 eV
corresponds to a perpendicular electric field of 2.0 V/nm". Ref. ([54])
has been added in this context. Finally, following the seminal work by
Ming et al.Ref. {[16]) among other STM studies, the external electric
field should, in our opinion, be "oriented with respect to the normal
of the Si surface".
4) I find the discussion of results a little bit too fast and superficial.
As for the density of states, I can appreciate a significant readjustment
of various peaks in dependence of Delta in the z and/or xy channels. However,
it is quite hard to visualize what is going on in reality. A 3D plot of the
charge density readjustment would help the reader quite much in this respect.
Also, authors could complete their results by reporting the total number of
electrons localized on z and x-y 5p orbitals (i.e. the integral of their
curves). Is there a complete transfer of charge from one type of orbital
to the other or do electron rather leak to some extent to other states
(e.g., of the Si substrate)? Concerning the I-V characteristics I also
think that the discussion should be extended and completed. For example,
how pronounced should the derivative shift in the I-V curves be for this
characteristic to represent a memory effect (hence the memristor behavior)?
Also, what is the relation between the knees observable in the I-V curves
and the readjustment of the density of states around the Fermi level
(presence of peaks, etc) presented in Figs 3 and 4? In particular, what
is the reason for the change in the I-V curves to be more pronounced for
negative delta shifts while the corresponding spectral function exhibits
relatively minor readjustments?
Reply:
We would like to thank Referee's suggestion but unfortunately computation
of "charge density readjustment" is presently unreachable with our DFT+DMFT
scheme, so we leave this problem for future studies. However, in view of
the constructive suggestion above, we have added a new figure (Fig. 5 in
the revised manuscript) showing the 5p orbital occupancies of alpha-Sn.
(A new paragraph "To give additional insights ..." was added on pages 6
and 7.) This new figure shows the changes in orbital polarization as
function of Delta and the change in the ferro-orbital order at Delta
close to 0.43 eV. We shall notice here that we have not considered the
"Si substrate" in our study, therefore changes of orbital occupancies
as function of the orbital-field Delta is restricted to the 5p-chanell
of alpha-Sn.
Extant theory and experimental studies of memristors and atomristors
have shown very different "derivative shift in the I-V curves" so it is
difficult in the current stage of the research to provide a conclusive
answer "for this characteristic to represent a memory effect" to be
used in future memristive devices. We believe that our results in the
right-upper panel of Fig. 4 is the best representative example for
the memristive behavior of alpha-Sn to be seen in future experimental
studies. It shows that the current-voltage(I-V) characteristic curves
exhibit minimal memristive behavior which goes over to a memristive
switching where the resistance steady-state value exhibits an ON/OFF
ratio of 20% assisted by orbital polarization effects. This behavior
indicates that alpha-Sn atomristor exhibits resistive memory with a
bipolar low resistance state (LRS) and high resistance state (HRS).
According to our DFT+DMFT results, this intrinsic bipolar switching
is due to the selective orbital reconstruction, thus proving an
atomristive functionality for future memory-based, brain-inspired
neuromorphic computing. We have added this discussion on page 8 of
the revised manuscript. We hope this suffices.
5) Are there experimental proofs of authors' results on this or similar
systems? How well in agreement with this manuscript outcomes are they,
in case? Could authors comment on this point possibly adding a few lines
to the their manuscript?
Reply:
We believe that our agreement with photoemission, inverse photoemission
and tunnelling spectrum shown in Fig. 2 is good, constituting a clear
check to our theoretical modelling for the multi-orbital correlated
electronic structure of alpha-Sn. We believe that our work offers a
consistent theoretical picture for orbital-selective electronic
reconstruction of alpha-Sn, showing the interplay between dynamical
electronic interactions and orbital-field effects relevant to complex
many-particle systems.
"In summary, the paper contains a good work and I think it should be
published on the journal after the authors have addressed the relatively
minor points raised above."
Reply:
To conclude, we would like to thank again the First Referee of Condensed
Matter for carefully reading and evaluating our manuscript as well as
for his/her constructive comments and suggestions. Wherever applicable,
we have improved our manuscript in accordance with Referee's comments
above, by adding details that make the presentation of our study and
results clearer. With these changes, we hope that our manuscript is
suitable for publication in Condensed Matter.
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors analyze spectral and transport properties of monolayer Sn system on Si(111) surface with focus on a possibility to apply this structure in memory devices using orbital selectivity and Mottness. The obtained results are rather interesting. The most original part is combined effects of the local Coulomb repulsion and parameter Delta that mimics the orbital polarization, that can be regarded as a novelty in the field of DMFT.
Within used approximation (DFT+DMFT+Delta) the results look meaningful. However, before paper can be recommended for publicatoin, more insights on the relevance of the model to real system need to be added:
1. The authors use DMFT approximation with a rather large value of U. A straighforward question - cannot DFT+U be eniugh in this case? What is the reason for using DMFT?
2. As a continuation of the previous question - DMFT is not the best option in terms of accuracy in the 2D case. How accurate are the results? Does not one need to include momentum correction to self-energy (Dynamical Vertex approximation, etc).
3. What was the reason to use IPT solver? It does not look like the system is too large for an exact numerical solver, like CT-QMC now implemented in many codes.
4. It would be also helpful to the readers give more details on the nature of parameter Delta. Obviously, it shifts the relative positions of different orbitals tuning their occupancy, i.e. polarizability. What is physical mechanism behind it? What defines its magnitude and sign?
After the authors answer these questions, the paper can be recommended for publication.
Author Response
Reviewer 2
-----------
"The authors analyze spectral and transport properties of monolayer Sn system
on Si(111) surface with focus on a possibility to apply this structure in
memory devices using orbital selectivity and Mottness. The obtained results
are rather interesting. The most original part is combined effects of the
local Coulomb repulsion and parameter Delta that mimics the orbital
polarization, that can be regarded as a novelty in the field of DMFT.
Within used approximation (DFT+DMFT+Delta) the results look meaningful.
However, before paper can be recommended for publicatoin, more insights
on the relevance of the model to real system need to be added:"
Reply:
We would like to thank the Second Referee of Condensed Matter for the
invested time in reading and evaluating our manuscript as well as for
the comments and suggestions he/she sets out below. In what follows we
will answer his/her comments and questions.
"1. The authors use DMFT approximation with a rather large value of U. A
straighforward question - cannot DFT+U be eniugh in this case? What is
the reason for using DMFT?"
Reply:
Alpha-Sn is a p-band Mott insulator, whose Mott insulating state is a
result of dynamical transfer of spectral weight from low to hight energies:
an effect which is not properly described by static (Hartree-like) DFT+U
calculations. Thus, this is one of the reasons why we are "using DMFT".
Since alpha-Sn is a broad p-band system, it implies the need of using
"a rather large value of U" to derive the correct Mott state vis-a-vis
with experiment as shown in Fig. 2. However, the U over the bare
bandwidth (U/W) ratio, which determines the effective U or the degree
of electron correlation effects on the 5p electrons of alpha-Sn, is of
the order of 0.8, which is a rather small value but enough to induce
the Mott state as we have shown in Ref. [32].
2. As a continuation of the previous question - DMFT is not the best
option in terms of accuracy in the 2D case. How accurate are the results?
Does not one need to include momentum correction to self-energy (Dynamical
Vertex approximation, etc).
Reply:
We agree with the Referee that single-site DMFT should only be taken as an
approximation for 2D-like systems, including alpha-Sn, graphene, silicene,
among other systems which one of the authors has explored in recent years.
However, apart from the LDA+U work by Profeta and Tosatti (Ref. [20a])
which should also be taken as an approximation for 2D systems like
alpha-Sn, most of extant theory studies on alpha-Sn have focused on the
effect of electronic correlations within the effective 5p_z band of
alpha-Sn close to the Fermi energy, using normal and extended one-band
Hubbard models. Although some leading grounds have analyzed the role
played by inter-site (nearest-neighbour) Coulomb interactions, to the
best of our knowledge, Ref. [32] was the first theory study which
explores the role played by intra- and inter-orbital dynamical
correlations on alpha-Sn using the many-particle DFT+DMFT scheme. Thus,
Ref. [32] and our present study should be considered as a natural
extension of Profeta and Tosatti's work, which treat the effects of
on-site electron-electron interactions at Hartree mean-field level,
meaning that ours is the only theory study which takes into account
the intrinsic delocalized nature of the Sn-5p shell, providing a
realistic DFT+DMFT description of dynamical many-particle interactions
hidden in the multi-orbital problem of alpha-Sn. The incorporation of
"momentum correction to self-energy" or inter-site short-ranged Coulomb
correlation effects, going beyond the single-site DMFT treatment, is
left for future studies.
3. What was the reason to use IPT solver? It does not look like the system
is too large for an exact numerical solver, like CT-QMC now implemented in
many codes.
Reply:
We agree with Referee that in a first glance alpha-Sn "does not look like
the system is too large for an exact numerical solver" since it mainly
contain three correlated orbitals. However in view of the intrinsic broad
band nature of alpha-Sn it might finally be a large system for numerical
exact solvers like CT-QMC. And this might be a reason why broadband
many-particle calculations for alpha-Sn have never, to the best of our
knowledge, being performed using the DFT+DMFT(Ct-QMC) framework.
We shall point here that in recent years many leading groups have used
in their DFT+DMFT studies numerical exact impurity solvers to address the
physical properties of correlated materials. However, in view of earlier
studies by the first author, showing good theory-experiment comparison
for different physical quantities at and away of half-filling, we feel
confident to use a less numerical expensive many-body treatment based
on diagrammatic second-order perturbation theory to study the electronic
structure reconstruction of correlated broadband, multi-orbital systems
like alpha-Sn and analogs. We aware of the fact that our DMFT solver is
by construction an approximate solver. However, our real frequency
perturbative ansatz has a proven record of good semiquantitative
agreement with experiment for a range of correlated materials and it
gives results in qualitatively accord with numerical exact CT-QMC
calculations in some cases. In PRB 100, 121101(R) (2019) the first author
has provided a direct comparison between our multi-orbital IPT calculation
and DFT+DMFT(CT-QMC) results by Skornyakov et al. [PRB 97, 115165 (2018)],
showing good agreement between these many-particle DFT+DMFT approaches
for tetragonal FeSe superconductor. As seen in Fig. 1 of PRB 100, 121101(R)
(2019), the orbital-resolved DFT+DMFT density of states shows good agreement
with CT-QMC results, attesting the accuracy and quality of the multi-orbital
IPT impurity solver.
"4. It would be also helpful to the readers give more details on the nature
of parameter Delta. Obviously, it shifts the relative positions of different
orbitals tuning their occupancy, i.e. polarizability. What is physical
mechanism behind it? What defines its magnitude and sign?"
Reply:
The use of the orbital Zeeman field Delta was partially motivated by the
work of F. Ming et al. (Ref. [16]) which reveals a "tip-assisted phase
switching" and "tunnelling polarity effects" on Sn-double layer grown on
Si(111) surface. Our proposal is also inspired from the photoresistive
switching of MoS2 memristor study by W. Wang et al. (Scientific Reports
6, 31224 (2016)), showing that the MoS2 memristor can be switched by an
electric field in the dark or under illumination with white light through
the charge polarization or modulation of charge in an electric field.
Moreover, our proposal has also been motivated by the DFT-based study
of Belviso et al. (Ref. [40]) which has quantified the electronic
charge distribution under the effect of the electric field, making use
as in our work of polarition effects on the p-orbitals of transition
metal chalcogenides like Mo(Se,Te)2 and WSe2. Also interesting in this
context is the work by Preziosi et al. (Ref. [41]) reporting an
electric-field control of the orbital occupancy and switching on the
3d orbital anisotropy in a Mn-based transition-metal oxide. These
earlier proposals and studies provide, in our opinion, support to our
theory and results. Thus, based on this earlier studies we address in
this work the role played by orbital polarization on the electronic
structure reconstruction on the 5p Mott localized state of alpha-Sn.
The change in "sign" of Delta is motivated by the fact that in experiment
it is possible to change the sign of the electric field true the bias
voltage as well as to the hidden particle-hole asymmetry of the bare
and correlated spectral functions of alpha-Sn: This asymmetry is clearly
manifested in the DFT-DMFT results in Figs. 2 and 3 of our manuscript.
Finally, concerning "magnitude" of Delta and the electric field in the
revised manuscript we are now writing that a "Delta=0.2 eV corresponds
to a perpendicular electric field of 2.0 V/nm". Ref. ([54]) has been
added in this context.
"After the authors answer these questions, the paper can be recommended for
publication."
Reply:
To conclude, we would like to thank again the Second Referee of Condensed
Matter for carefully reading our manuscript and for suggesting its
publication in Condensed Matter. We believe that our work offers a
consistent theoretical picture for the normal state electronic structure
reconstruction due to the interplay between dynamical electron-electron
interaction and orbital polarization effects in alpha-Sn. Based on this
and on our responses to the Referee comments above, we hope that our
manuscript is suitable for publication in Condensed Matter.
Round 2
Reviewer 2 Report
Comments and Suggestions for Authors The authors have taken into account all my comments and answered questions. I recommend the paper for publications. It would be helpful if the authors take into account the following two remarks:- I agree that IPT often gives qualitatively similar results to CT-QMC. However, DFT+DMFT at its current stage should deal with quantitative accuracy, not qualitative (which does not mean that for given system IPT fails).
- It would be helpful for readers if the authors incorporate the answer to question 4 to the manuscript.
Comments on the Quality of English Language
Minor editing of English language required
Author Response
"The authors have taken into account all my comments and answered questions. I recommend the paper for publications. It would be helpful if the authors take into account the following two remarks:"
Reply:
We would like to thank the Second Referee of Condensed Matter for his/her positive remarks that allows us to improve the presentation of our manuscript. Below we provide a response to his/her comments.
"I agree that IPT often gives qualitatively similar results to CT-QMC. However, DFT+DMFT at its current stage should deal with quantitative accuracy, not qualitative (which does not mean that for given system IPT fails)."
Reply:
In view of Referee's comment above we have replaced on page 4 "qualitative" by "good quantitative" when we refer to the outcome of the DFT+DMFT(MO-IPT) results vis a vis with CT-QMC calculations. A new reference (Ref. [48b]), where good "quantitative" agreement between MO-IPT and CT-QMC results for the 4d valence band spectral function bct NbO2 was found, has been added in this context. We hope this suffices.
"It would be helpful for readers if the authors incorporate the answer to question 4 to the manuscript."
Reply:
In view of Second Referee's and Academic Editor's suggestion we have added a new paragraph "It should be noted ..." on page 5 to "incorporate the answer to question 4" in the revised manuscript. A new reference (Ref. [54] in the revised manuscript) was added in this context.
"Besides that, it is a nice piece of research that will interesting to the community."
Reply:
To conclude, we would like to thank again the Second Referee of Condensed Matter for carefully reading and evaluating our manuscript and for his/her constructive comments and suggestions. We have improved our manuscript in accord with Referee's remarks above, adding details that make the presentation of our results and study clearer. With these changes, we hope that we have answered the comments of Second Referee and that this will now facilitate the publication of our work in Condensed Matter.
