Engineering DNA Molecule Bridge between Metal Electrodes for High

Subscriber access provided by AUSTRALIAN NATIONAL UNIV

Article

Engineering DNA Molecule Bridge between Metal Electrodes for High-Performance Molecular Transistor: An Environmental Dependent Approach Samira Fathizadeh, Sohrab Behnia, and Javid Ziaei J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b10034 • Publication Date (Web): 22 Feb 2018 Downloaded from http://pubs.acs.org on February 24, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Engineering DNA Molecule Bridge between Metal Electrodes for High–Performance Molecular Transistor: An Environmental Dependent Approach S. Fathizadeh,∗ S. Behnia, and J. Ziaei Department of Physics, Faculty of Science, Urmia University of Technology, Urmia, Iran E-mail: [email protected] Phone: +98 443 3554313

Abstract Molecule–based transistors have attracted most attention due to their exclusive properties. Creating of a molecular transistor as well as engineering its structure have become one of the greatest aims of scientists. We have focused on the environmental dependent behavior of a DNA–templated transistor. Using the statistical distribution of the energy levels, we were able to distinguish the delocalized states of charge carriers and the transition between the localized and delocalized behaviors. On the other hand, we can determine the stability conditions of our quantum dynamical system. The results is verified by the inverse participation ratio method. Therefore, the most appropriate parameters for designing the DNA transistor is chosen. The DNA sequence is an important factor on its transport properties; but, the results have shown that the in the presence of the bath, the bath parameters are important, too. As it is shown, it is possible that via the adjustment of bath parameters, one designs a conductivity

1

ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

channel for all nucleotide contents. Thus, one can engineer a DNA based transistor simply through the setting of only one parameter.

Introduction Thanks to the wide range of potential applications in nanoelectronics including use as display drivers, and in identification tags and sensors, molecular transistors have been a focus of great interest in organic devices. Realizing that a single molecular transistor, connected by metal leads (source and drain), has the potential of application in flexible electronics paved the way towards its critical role in transport. In this regard, the past two decades have witnessed considerable progress in the development of low–cost, flexible, and large– area organic electronics for consumer products over the past two decades. 1–3 In order to answer to the problem of minimizing the electronic devices as a one of the long–standing demands of nanoelectronics, biomolecules such as protein have contributed in the past efforts as promising candidates to this end. 4 As a new mechanism for this purpose, self–assembled DNA–based template nanostructures leading to a potential method for generating complex three–dimensional electronic circuitry on the scales that are not accessible by conventional Silicon based materials is recently proposed. The programmability, flexibility as well as low cost of synthesis, has made DNA a widely used material for creating the molecular structures and molecular electronics structures 5,6 such as DNA nanowires, 7 diode 8 or transistor. A basic theoretical understanding on the carrier transport mechanism is the main constituent of designing any DNA–based functional electronic device. Based on these considerations, here we try to unveil the transport properties of a DNA–based molecular transistor in finite temperatures. This made it possible to design the molecular transistor in real situations. Regarding the importance of such a design, we aim at characterizing the mechanism of charge transport in DNA transistors via developing a new method based on the quantum dynamics of the charge. To this end, we consider the DNA chain as a central molecule

2


Page 2 of 26

Page 3 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


attached to the two metal leads and in contact with a thermal bath. By considering the coupling of system to its environment, we cannot further study it as a unitary evolution. Now, the system is an open quantum system. One of the problems of this type is the effect of quantum damping, when a relatively simple system is coupled to a continuum: a large number of oscillators or a heat bath. 9 These systems are described by the density matrix and based on master equation. To overcome this problem, we apply the quantum chaos theory. Similar to the classical chaos theory where the dynamics of the system is studied in the framework of phase space and fixed point stability analysis instead of space–time framework, the quantum chaos theory regards the stability of wave functions and fluctuations of corresponding energy levels. Technically speaking, we want to use from this fact that each completely hyperbolic classical dynamics has a quantum energy spectrum with the same fluctuations as a random matrix caricature. If the underlying classical dynamics of a quantum system displays generic chaos, then the statistical spectral properties of that system are universal and depend only on the symmetries of that system. Fluctuations in spectra of individual complex quantum systems (e.g. classically chaotic (hyperbolic) systems) can be described by the ensembles of random matrix theory (RMT). 10,11 The RMT, 12,13 firstly established by Wigner, yields analytic results for correlators of the level density by averaging over suitable ensembles of random matrices. 14 We thus expect the underlying ideas to radiate beyond spectral fluctuations, like to transport and localization. In this work, we have tried to investigate the requirements for achieving to a high performance DNA based transistor in the contact of a thermal bath. We have used the nearest neighbor level distribution as well as inverse participation ratio for determining the affected factors on the transport properties of transistor.

3



Page 4 of 26

Model Let us consider molecular transistor system model as a DNA molecule coupled to two leads and in the contact with a thermal bath. We start from the transistor Hamiltonian 15,16

Htransistor = HDN A + Hlead + HDN A−lead

(1)

which includes the contributions of the molecule, electrodes and coupling. The first term describes the isolated double stranded DNA chain as a central molecule through the tight– binding simple ladder model: 17

HDN A =

N N −1 N X X X X { (εi,j + eVg )c†i,j ci,j − [ti,i+1 c†i,j ci+1,j + H.c.]} + (λc†i,1 ci,2 + H.c.) (2) j=1,2 i=1

i=1

i=1

where c†i,j (ci,j ) is creation (annihilation) operator for an electron at site (i, j), εi,j represents the on–site energy, ti,i+1 stands for the hopping integral, and λ is the inter–strand hopping parameter. Here, Vg is the gate voltage applied for each base of DNA. Hlead specifies the left and right metal contacts of the transistor represented as: 18

Hlead =

XX j=1,2

+

eVb † )a aL 2 Lk,j k,j

(εRk,j −

eVb † )a aR 2 Rk,j k,j

k

XX j=1,2

(εLk,j +

k

(3)

where a†βk,j (aβk,j ) with β = L, R is the creation (annihilation) operator of an electron in the lead β, εβk,j is the on–site energy and Vb is bias voltage. Therefore, the third term of Hamiltonian provides a DNA–lead tunneling as follows: 18

HDN A−lead =

XX j=1,2

(tL aLk,j c1,j + tR aRk,j cN,j + H.c.)

k

4


(4)

Page 5 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where tβ is tunneling matrix elements from the lead β to the DNA chain. Our main aim is studying the vibrational mode of environment on the properties of molecular transistor. To consider the environmental vibrational degree of freedom, one can write a chain of oscillators as an external quantum bath, each of them interacts with a base of DNA. Therefore, the total Hamiltonian of the system can be written as following:

H = Htransistor + HBath + Htransistor−Bath

(5)

where HBath is Hamiltonian of the oscillators chain which arises from a nearest neighbor Hooke–like coupling model as: 19

HBath =

N X

~ωi b†i bi + 2

i=1

N −1 X

~Ωi (b†i bi+1 + b†i+1 bi )

(6)

i=1

where b†i is the creation operator of an oscillation in i−th oscillator, ω and Ω are the oscillator frequency and their mutual coupling constants, respectively. The environment effect can be described via a linear coupling term between the local field of oscillators and the electrons. Htransistor−Bath term displays the coupling of the bath and DNA lattice considered as:

Htransistor−Bath =

N XX

(ti b†i ci,j + H.c.)

(7)

j=1,2 i=1

where ti is the interaction constant. In general, the bath can be described by a spectral density as

J(ω) =

X

t2i δ(ω − ωi ) = J◦ (

i

ω s −ω/ωc )e Θ(ω) ωc

where ωc is a cut–off frequency and Θ(ω) is the Heaviside function. In the following, we consider the case s = 1, which corresponds to an ohmic bath. 20,21

5



Page 6 of 26

Method We have considered an N base pairs double–stranded DNA as central molecule which each strand is connected to an N site thermal bath and double–stranded metal leads with k sites. Hamiltonian matrix corresponding to the current model would be a (4N + 4k) × (4N + 4k) matrix. The spectral fluctuations of such a matrix could be analyzed through the probability distribution of the nearest neighbor level spacings (P (s)). The terms "regular" and "irregular" are used to distinguish between near–classical quantum systems whose classical motion is respectively quasi-periodic and ergodic. In the regular spectrum, the distribution of energy eigenvalues is random where spacing between adjacent levels distributed as Poissonian. 22 It is worth mentioning that this situation corresponds to a localized phase in which energy levels are peaked at spatially distant centers. 23 On the other hand, the fluctuations of quantal spectra with irregular behavior reveal Gaussian distribution. It is said that the states of diffusive metal exhibit Wigner–Dyson level statistics. 24 Near a mobility edge, extended states show quantum critical scaling 25,26 in the overlap of wavefunction probabilities at different energies. 27,28 The statistical properties of the spectra of complex systems such as molecules, nuclei, and mesoscopic solids can be corresponded to random matrix spectra. 29 We have studied the energy levels statistics in our DNA based system using the full Hamiltonian model represented in Eq. 5. For simplicity, we have considered a reduced version of system Hamiltonian where a double stranded DNA with two base pairs is connected to the left and right leads. The leads are double–stranded with one site in each strand. On the other hand, each strand of DNA is in the contact of the bath sites. A simple sketch of such a system is schematically shown in Fig. 1. The Hamiltonian matrix for this simplified model is written as following: 



 H11 H12  H=  H21 H22

6


(8)

Page 7 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where

T H12 = H21





       =       

0 0 0 0 0 0   0 0 0 0 0 0     0 0 0 0 0 0    0 λ 0 0 0 0    0 0 λ 0 0 0    0 0 0 0 0 0

(9)

, 

 ω1

H11

       =       

2Ω1

0

2Ω2

ω2

0

0

0

εL +

t1

0

0 0

t1

0

0

0

t2

0

tL

tL

0

tL

ε1,1 + eVg

t12

tR

t2

tL

t21

ε2,1 + eVg

tR

0

0

tR

tR

eVb 2

εR −

eVb 2

              

(10)

and 

H22

 εL +   tL     tL =   0    0   0

eVb 2

 tL

tL

0

0

ε1,2 + eVg

t12

tR

t1

t21

ε2,2 + eVg

tR

0

tR

tR

εR −

t1

0

0

ω1

0

t2

0

2Ω2

eVb 2

0

0   0     t2    0    2Ω1    ω2

(11)

Level spacing distribution One of the most applied tools in the study of spectral correlations is the nearest–neighbor spacing distribution (P(s)), where, the nearest–neighbor spacing is calculated as s = Ei+1 − 7



Page 8 of 26

Ei . In the metallic phase, P(s) is very close to the random matrix theory developed by Wigner and Dyson. 30 In the insulating regime, the electron levels of the strongly localized states fluctuate like random stochastic variables and the levels are distributed according to the Poisson law. 31 When the fluctuations of randomness of the atomic and/or impurity potential are increased, a quantum system undergoes a second order phase transition. In condensed matter physics, this transition is referred to as a localization–delocalization transition. The study of the crossover between the chaotic (Wigner) and ergodic (Poisson) statistics which is induced by the phase transition was started in 29 and became the subject of several subsequent investigations. 32,33

Inverse participation ratio Studying the localization properties of system can be quantified by inverse participation ratio (IPR) defined as: 34,35

IP R(Eα ) =

X

|ψiα |4

(12)

i

where ψiα is the amplitude of the eigenstate with energy Eα on site i. We expect that IP R = 1 for a completely localized state, and IP R = 1/dim(H) for a fully extended state. The complementary information about the dynamics of spectral fluctuation could be provided via the IPR dynamics.

Results The aim of the current study is engineering a molecular transistor based on DNA bridge between the metal electrodes. The DNA ability for long range charge transport has become a challenging debate, due to the envisioned impact of charge transport in molecular (bio)electronics. 36,37 Let us consider the effect of external environment as well as DNA chain sequence on the incorporating DNA molecules into electronic devices and circuits. Here, we 8


Page 9 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


choose εA = 8.5, εC = 8.9, εG = 8.3 and εT = 9 eV for εi,j values. On the other hand, tAA = 0.22, tT T = 0.14, tCC = 0.05 and tGG = 0.11 are the tunneling elements between the identical neighboring bases (ti,j ) and λi = −0.3 with the units in eV is the tunnelling between the complementary base pairs. 38–42 These parameters are extracted from the experimental results 43,44 and first-principles calculations. 40,45 ti,j between different neighboring bases X and Y is set to tXY = (tXX + tY Y )/2, in accordance with first–principle results. 46,47 Also, εβk,j = 7.75 eV and tβ = 0.42 eV are the lead parameters. 48

Bath parameters We have studied the electronic structure of DNA transistor embedded in a bath consisting of a collection of harmonic oscillators. We elaborate on the role played by the environment by addressing signatures of the bath on charge transport of DNA channel. In the current work, we have examined the effect of bath parameters on localization/delocalization process in DNA. Figure 2 shows the effect of bath parameters (J◦ /ωc ) on the nearest neighbor level distribution. Here, we have tried to study the different states of the DNA channel via the variation of bath frequencies. This work is done for a fixed DNA sequence (100% C − G content). We have varied J◦ /ωc parameter from 1 to 40. For J◦ /ωc = [1 − 3], P(s) shows a poissonian behavior (Figs. 2-a, 2-b, 2-c). Therefore, a DNA transistor behaves as a insulator channel in these parameters. From J◦ /ωc = 4, P(s) starts to going to the transition situation (Fig. 2-d). This value is the start point of bath parameter for using in DNA transistor for transport the electrical current. We have increased J◦ /ωc up to 40 (Figs. 2-e, 2-f). It is clear from P(s) diagrams that for all values greater than J◦ /ωc = 4, DNA chain behaves in a crucial state. In the other words, P(s) is able to determine the lowest limit of J◦ /ωc for using in a DNA transistor and for engineering a conduction channel. For better characterizing the effect of bath parameters on localization of electron in DNA transistor, we have referred to the inverse participation ratio (IPR) method. Since, IPR 9



distinguishes between the localized and delocalized states. Now, we have varied J◦ /ωc and studied the dependence of IPR to this parameter. Figure 3 shows IPR decreases through the increasing J◦ /ωc . The decreasing rate of IPR for J◦ /ωc = [1 − 4] is with a steep slope and then, the slope becomes smoother. DNA channel tends to delocalized state via the increasing the parameter. Here, IPR is more powerful tool for determining the differences caused by varying bath parameters. Therefore, one could say that the higher values of J◦ /ωc is more appropriate than lower values for designing a DNA based molecular transistor in the contact of a thermal bath.

DNA sequence The nucleotide chain of DNA is an intrinsic disorder property in the DNA molecule against the charge transport. 49 The sequence dependent inhomogeneities of energetics and base–base couplings as well as the dynamical motions of the base pairs within the molecular stack, can affect the “metallic–like" molecular conduction. 50–52 The extent and efficiency of charge transport is discussed as a function of sequence dependent energetics. 53 It is well established that all the electronic states of a strictly one–dimensional system with diagonal disorder are localized. 54 The situation is confounded for not strictly one–dimensional systems, i.e., systems with more than one channel. Recent studies on electronic conductivity properties of DNA have reported the emergence of delocalized states as a result of the base pairing of DNA. 55 It was shown that the DNA molecule with different sequences could present any transport behavior: conducting, 56 semiconducting, 57 and insulating. 58 The ohmic, semiconducting, etc character depends on the base sequence, the band structure of the electrodes as well as the coupling to the electrodes. 59 Sequence variety would perform the important role in conductivity properties of DNA. The C–G content of DNA appears to strongly influence the electrical properties of DNA. DNA behaves as a broad band–gap semiconductor that which band gap energy decreases with the increasing number of C–G bases. 60 The band–gap does not necessarily reflect the total density of electronic states, but rather density of delo10


Page 10 of 26

Page 11 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


calized states, namely states through which charge can be transported coherently through the whole strand. 60 This role of the C–G is based on the fact that guanine has the lowest electro–chemical potential of all bases and therefore facilitates charge transfer along the DNA observed previously. 61 In the previous work, we have shown the sequence dependence of conductivity channel of DNA chain. 16 That work has studied a DNA based transistor in absent of any external agent such as thermal bath. The results show that a DNA chain with the high C–G content percent behaves as a good conductor. Via the decreasing the C–G content and then increasing the AT content of chain, the DNA channel shows a critical behavior. It enters to a localization-delocalization state. Via the more increasing the AT content, DNA behaves as an insulator chain. Therefore, one can choose an appropriate sequence for creating a DNA transistor. It is very crucial for the results that the electrode on–site energy was taken closer to the Guanine on–site energy. In the future, we would try to take the electrode on–site energy closer to the Adenine on–site energy and repeat the calculations. In the current study, we have examined the effect of different sequences on conductivity properties of DNA transistor embedded in a thermal bath. Figure 4 shows the variation of IPR with respect to the simultaneous changes of bath parameters and DNA sequence. Here, IPR shows similar behavior for each of sequences. In every sequence, IPR has a decreasing behavior with respect to the value J◦ /ωc . But, this behavior is almost the same for all sequences. Therefore, we can say that in the presence of a thermal bath, the effect of bath has been important, too. It is clear that via the increasing of the bath parameters, one can approach to a more appropriate channel for electron conductivity for variety of sequences. For best understanding the effect of DNA sequence on conductivity in the presence of a thermal bath, we have studied P(s) for different sequences (Figs. 5-a, 5-b, 5-c and 5-d). We have examined the sequences with N = 1000 base pairs and different C–G contents. It is clear that all of them show a critical behavior. None of them, even with the low C–G content percent, behaves as a complete insulator. While, in the absence of a bath, the se-

11



quences with low C–G percent act as an insulator. This result can show the importance of a thermal bath in molecular transistors. As we have shown in figures (5-a, 5-b, 5-c and 5-d), P(s) for different sequences is different so insignificantly. All P(s) diagrams are in localization–delocalization state and therefore, we can say that in this situation, all of them are appropriate for designing a molecular transistor.

Conclusion Concurrent with trying for minimizing the electronic devices, DNA–based nanostructures could be considered as a potential method to create fragments of electronic circuits such as wires or transistors. We have studied the transport properties of a molecular transistor based on the DNA chain. Our aim is to determine the most appropriate setup for designing DNA transistor. Using quantum chaos theory tools, we can engineer a DNA based molecular transistor. Is it possible that a thermal bath plays the significant role in designing a DNA transistor? We can show that molecular transistors can be modulated by adjustment of the bath parameters. Here, we show that by increasing the J◦ /ωc parameter of bath, one can approach to the a conductivity channel. This result has been verified through the P(s) and IPR tools. The results are in agreement completely. On the other hand, we have studied the effect of DNA sequence on transport properties of transistor. In the previous work, we had shown that the sequence type have important effect on the transport of chain. Where, the high C–G content percent sequences are more appropriate than others. Here, in the presence of a thermal bath, the result is different. Now, the different sequences show the similar behavior with respect to the charge transport. It is interesting that all sequences with different C–G contents, behave as an appropriate channel via the setting of bath parameters. P(s) diagrams for all sequences are in crucial state. The results based on P(s) method, show quasi–conductor channels of DNA. This results specifies the major impact of thermal bath. It can say that the bath parameters are

12


Page 12 of 26

Page 13 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


effective parameters in engineering a DNA transistor which through the adjustment of them, we can create the most efficient molecular transistor with DNA sequences.

13



References (1) Liu, S.; Wang, W. M.; Briseno, A. L.; Mannsfeld, S. C. B.; Bao, Z. N. Controlled Deposition of Crystalline Organic Semiconductors for Field–Effect–Transistor Applications. Adv. Mater. 2009, 21, 1217–1232 . (2) Zaumseil, Z.; Sirringhaus, H. Electron and Ambipolar Transport in Organic Field–Effect Transistors. Chem. Rev. 2007, 107, 1296–1323 . (3) Cicoira, F.; Santato, C. Organic Light Emitting Field Effect Transistors: Advances and Perspectives. Adv. Funct. Mater. 2007, 17, 3421–3434 . (4) Chen, Y. S.; Hong, M. Y.; Huang, G. S. A Protein Transistor Made of an Antibody Molecule and Two Gold Nanoparticles. Nat. Nanotechnol. 2012, 7, 197–203 . (5) Chen, Y. J.; Groves, B.; Muscat, R. A.; Seelig G. DNA Nanotechnology from the Test Tube to the Cell. Nat. Nanotechnol. 2015, 10, 748–760. (6) Carlson, R. The Changing Economics of DNA Synthesis. Nat.Biotechnol., 2009, 27, 1091–1094 . (7) Gu, Q.; Cheng, C.; Gonela, R.; Suryanarayanan, S.; Anabathula, S.; Dai, K.; Haynie, D. T. DNA Nanowire Fabrication. Nanotechnology, 2005, 17, R14 . (8) Malyshev, A. V. DNA Double Helices for Single Molecule Electronics. Phys. Rev. Lett., 2007, 98, 096801 . (9) Khidekel, V. Markovian and Rotating–Wave Approximations Versus Exact Solution of Damped Quantum Oscillator. Phys. Rev. E, 1995, 52, 2510 . (10) Bohigas, O.; Giannoni, M. J.; Schmit, C. Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws. Phys. Rev. Lett., 1984, 52, 1 .

14


Page 14 of 26

Page 15 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(11) Gnutzmann, S.; Alexander, A. Universal Spectral Statistics in Quantum Graphs. Phys. Rev. Lett., 2004, 93, 194101 . (12) Stöckmann, H. -J. Quantum Chaos: An Introduction; Cambridge University Press, Cambridge, England, 1999 . (13) Haake, F. Quantum Signatures of Chaos; Springer, Berlin, 2000 . (14) Müller, S.; Heusler, S.; Braun, P.; Haake, F.; Altland, A. Semiclassical Foundation of Universality in Quantum Chaos. Phys. Rev. Lett., 2004, 93, 014103 . (15) Raju, C. N.; Chatterjee, A. Quantum Dissipative Effects on Non–Equilibrium Transport through a Single–Molecular Transistor: The Anderson–Holstein–Caldeira–Leggett Model. Sci. Rep., 2016, 6, 18511 . (16) Behnia, S.; Fathizadeh, S.; Ziaei, J. Controlling Charge Current through a DNA Based Molecular Transistor. Phys. Lett. A, 2017, 381, 36–43 . (17) Díaz, E.; Sedrakyan, A.; Sedrakyan, D.; Domínguez-Adame, F. Absence of Extended States in a Ladder Model of DNA. Phys. Rev. B, 2007, 75, 014201 . (18) Chen, Z.-Z.; Lü, R.; Zhu, B. F. Effects of Electron–Phonon Interaction on Nonequilibrium Transport through a Single–Molecule Transistor. Phys. Rev. B, 2005, 71, 165324 . (19) Nicacio, F.; Ferraro, A.; Imparato, A.; Paternostro, M.; Semião, F. L. Thermal Transport in Out–of–Equilibrium Quantum Harmonic Chains. Phys. Rev. E, 2015, 91, 042116. (20) Gutiérrez, R.; Mandal, S.; Cuniberti, G. Quantum Transport through a DNA Wire in a Dissipative Environment. Nano Lett., 2005, 5, 1093–1097 . (21) Gutiérrez, R.; Mandal, S.; Cuniberti, G. Dissipative Effects in the Electronic Transport through DNA Molecular Wires. Phys. Rev. B, 2005, 71, 235116 . 15



(22) Herrick, D. R. Symmetry of the Quadratic Zeeman Effect for Hydrogen. Phys. Rev. A, 1982, 26, 323 . (23) Huse, D. A.; Nandkishore, R.; Oganesyan, V. Phenomenology of Fully Many–Body– Localized Systems. Phys. Rev. B, 2014, 90, 174202 . (24) Sivan, U.; Imry, Y. Energy–Level Correlation Function and Ac Conductivity of a Finite Disordered System. Phys. Rev. B, 1987, 35, 6074 . (25) Chalker, J. T.; Daniell, G. J. Scaling, Diffusion, and the Integer Quantized Hall Effect. Phys. Rev. Lett., 1988, 61, 593 . (26) Chalker, J. Scaling and Eigenfunction Correlations Near a Mobility Edge. Physica A: Stat. Mech. Appl., 1990, 167, 253 . (27) Fyodorov, Y. V.; Mirlin, A. D. Strong Eigenfunction Correlations Near the Anderson– Localization Transition. Phys. Rev. B, 1997, 55, R16001 . (28) Cuevas, E.; Kravtsov, V. E. Two–Eigenfunction Correlation in a Multifractal Metal and Insulator. Phys. Rev. B, 2007, 76, 235119 . (29) Shklovskii, B. I.; Shapiro, B.; Sears, B. R.; Lambrianides, P.; Shore, H. B. Statistics of Spectra of Disordered Systems Near the Metal–Insulator Transition. Phys. Rev. B, 1993, 47, 11487 . (30) Mehta, M. L. Random Matrices; Academic Press, Boston, 1991, 523p . (31) Zharekeshev, I. Kh.; Kramer, B. Asymptotics of Universal Probability of Neighboring Level Spacings at the Anderson Transition. Phys. Rev. Lett., 1997, 79, 717–721 . (32) Zharekeshev, I. Kh.; Kramer, B. Universal Fluctuations in Spectra of Disordered Systems at the Anderson Transition. Jpn. J. Appl. Phys., 1995, 34, 4361 .

16


Page 16 of 26

Page 17 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(33) Efetov, K. B. Supersymmetry in Disorder and Chaos, Cambridge University Press, 1999 . (34) Rodriguez, A.; Vasquez, L. J.; Römer, R. A. Multifractal Analysis of the Metal– Insulator Transition in the Three–Dimensional Anderson Model. II. Symmetry Relation under Ensemble Averaging. Phys. Rev. B, 2008, 78, 195107 . (35) Vasquez, L. J.; Rodriguez, A.; Römer, R. A. Multifractal Analysis of the Metal– Insulator Transition in the Three–Dimensional Anderson Model. I. Symmetry Relation under Typical Averaging. Phys. Rev. B, 2008, 78, 195106 . (36) Seeman, N. C. DNA Nicks and Nodes and Nanotechnology. Nano Lett., 2001, 1, 22 . (37) Braun, E.; Eichen, Y.; Sivan, U.; Ben-Yoseph, G. DNA–Templated Assembly and Electrode Attachment of a Conducting Silver Wire. Nature, 1998, 391, 775 . (38) Trofimov, A. B.; Schirmer, J.; Kobychev, V. B.; Potts, A. W.; Holland, D. M. P.; Karlsson, L. Photoelectron Spectra of the Nucleobases Cytosine, Thymine and Adenine. J. Phys. B, 2006, 39, 305 . (39) Senthilkumar, K.; Grozema, F. C.; Guerra, C. F.; Bickelhaupt, F.M.; Lewis, F. D.; Berlin, Y. A.; Ratner, M. A.; Siebbeles, L. D. A. Absolute Rates of Hole Transfer in DNA. J. Am. Chem. Soc., 2005, 127, 14894. (40) Apalkov, V.; Berashevich, J.; Chakraborty, T. Unique Magnetic Signatures of Mismatched Base Pairs in DNA. J. Chem. Phys., 2010, 132, 085102 . (41) Guo, A. M.; Sun, Q. F. Sequence–Dependent Spin–Selective Tunneling along Double– Stranded DNA. Phys. Rev. B, 2012, 86, 115441 . (42) Guo, A. M.; Sun, Q. Spin–Selective Transport of Electrons in DNA Double Helix. Phys. Rev. Lett., 2012, 108, 218102 .

17



(43) Dougherty, D.; Wittel, K.; Meeks, J.; McGlynn, S. P. Photoelectron Spectroscopy of Carbonyls, Ureas, Uracils, and Thymine. J. Am. Chem. Soc., 1976, 98, 3815 . (44) Lin, J.; Yu, C.; Peng, S.; Akiyama, I.; Li, K.; Lee, L. K.; LeBreton, P. R. Ultraviolet Photoelectron Studies of the Ground–State Electronic Structure and Gas–Phase Tautomerism of Hypoxanthine and Guanine. J. Phys. Chem., 1980, 84, 1006 . (45) Grozema, F. C.; Berlin, Y. A.; Siebbeles, L. D. Mechanism of Charge Migration through DNA: Molecular Wire Behavior, Single–Step Tunneling or Hopping? J. Am. Chem. Soc., 2000, 122, 10903 . (46) Hawke, L. G. D.; Kalosakas, G.; Simserides, C. Electronic Parameters for Charge Transfer along DNA. Eur. Phys. J. E, 2010, 32, 291 . (47) Zhang, H.; Li, X. Q.; Han, P.; Yu, X. Y.; Yan, Y. A Partially Incoherent Rate Theory of Long–Range Charge Transfer in Deoxyribose Nucleic Acid. J. Chem. Phys., 2002, 117, 4578 . (48) Malakooti, S.; Hedin, E. R.; Kim, Y. D.; Joe, Y. S. Enhancement of Charge Transport in DNA Molecules Induced by the Next Nearest–Neighbor Effects. J. Appl. Phys., 2012, 112, 094703 . (49) Klotsa, D.; Römer, R. A.; Turner, M. S. Electronic Transport in DNA. Biophys. J., 2005, 89, 2187 . (50) Lambropoulos, K.; Chatzieleftheriou, M.; Morphis, A.; Kaklamanis, K.; Lopp, R.; Theodorakou, M.; Tassi, M.; Simserides, C. Electronic Structure and Carrier Transfer in B–DNA Monomer Polymers and Dimer Polymers: Stationary and Time–Dependent Aspects of a Wire Model Versus an Extended Ladder Model. Phys. Rev. E, 2016, 94, 062403 .

18


Page 18 of 26

Page 19 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(51) Guo, A. M.; Xu, H. Sequence Dependent Charge Transport through DNA Molecules: The Role of Periodicity and Long–Range Correlations. Physica B, 2007, 391, 292–298 . (52) Páez, C. J.; Schulz, P. A.; Wilson, N. R.; Roemer, R. A. Robust Signatures in the Current-Voltage Characteristics of DNA Molecules Oriented between Two Graphene Nanoribbon Electrodes. New J. Phys., 2012, 14, 093049 . (53) Bogár, F.; Bende, A.; Ladik, J. Influence of the Sequence on the ab initio Band Structures of Single and Double Stranded DNA Models. Phys. Lett. A, 2014, 378, 2157 . (54) Abrahams, E.; Anderson, P. W.; Licciardello, D. C.; Ramakrishnan, T. V. Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions. Phys. Rev. Lett., 1979, 42, 673 . (55) Caetano, R. A.; Schulz, P. A. Sequencing–Independent Delocalization in a DNA–Like Double Chain with Base Pairing. Phys. Rev. Lett., 2005, 95, 126601 . (56) Carpena, P.; Bernaola-Galván, P.; Ivanov, P. C.; Stanley, H. E. Metal–Insulator Transition in Chains with Correlated Disorder. Nature, 2002, 418, 995 . (57) Cuniberti, G.; Craco, L.; Porath, D.; Dekker, C. Backbone–Induced Semiconducting Behavior in Short DNA Wires. Phys. Rev. B, 2002, 65, 241314 . (58) Zhang, Y.; Austin, R. H.; Kraeft, J.; Cox, E. C.; Ong, N. P. Insulating Behavior of λ–DNA on the Micron Scale. Phys. Rev. Lett., 2002, 89, 198102 . (59) Lambropoulos, K.; Simserides, C, Electronic Structure and Charge Transport Properties of Atomic Carbon Wires. Phys. Chem. Chem. Phys., 2017, 19, 26890–26897 . (60) Nogues, C.; Cohen, S. R.; Daube, S.; Apter, N.; Naaman, R. Sequence Dependence of Charge Transport Properties of DNA. J. Phys. Chem. B, 2006, 110, 8910–8913 . 19



(61) Di Ventra, M.; M. Zwolak. DNA Electronics in “Encyclopedia of Nanoscience and Nanotechnology," HS Nalwa, American Scientific Publishers, 2004 .

20


Page 20 of 26

Page 21 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Figure captions Fig. 1 A simple sketch of a DNA transistor sites. A double stranded DNA chain with two base pairs (N = 2) which every base is connected to a bath site; and, two stranded left and right leads with one site in every strand (k = 1). Fig. 2 Nearest neighbour level distribution for J◦ /ωc values (a) 1, (b) 2, (c) 3, (d) 4, (e) 20, (f) 40. Fig. 3 Inverse participation ratio with respect to the bath parameters for a 45% C − G content sequence. Fig. 4 Inverse participation ratio with respect to the bath parameters for different sequences. Fig. 5 Nearest neighbour level distribution for the sequences with (a) 45%, (b) 60%, (c) 85%, (d) 100% C − G content.

21



Figure 1: A simple sketch of a DNA transistor sites. A double stranded DNA chain with two base pairs (N = 2) which every base is connected to a bath site; and, two stranded left and right leads with one site in every strand (k = 1).

22


Page 22 of 26

Page 23 of 26

2 (a)

(b)

Numeric Wigner Poisson


1.5

1

P(s)

P(s)

1.5

0.5

1

0.5

0

0 0

1

2

3

4

5

0

1

2

s 1.5

3

4

5

s

(c)


(d)

1


0.8 P(s)

P(s)

1

0.6 0.4

0.5

0.2 0

0 0

1

2

3

4

5

0

1

2

s 1

3

4

5

s 1

(e)


0.8

(f)


0.8 0.6 P(s)

0.6 P(s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.4

0.4

0.2

0.2

0

0 0

1

2

3

4

5

0

1

s

2

3

4

5

s

Figure 2: Nearest neighbour level distribution for J◦ /ωc values (a) 1, (b) 2, (c) 3, (d) 4, (e) 20, (f) 40.

23



0.13 0.12 0.11 IPR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 26

0.1 0.09 0.08 5

10

15

20 J°/ωc

25

30

35

40

Figure 3: Inverse participation ratio with respect to the bath parameters for a 45% C − G content sequence.

24


Page 25 of 26

0.13 60% CG 85% CG 100% CG

0.12 0.11 IPR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.1 0.09 0.08 5

10

15

20 J°/ωc

25

30

35

40

Figure 4: Inverse participation ratio with respect to the bath parameters for different sequences.

25



1

1

(a)


0.8

(b)


0.8

P(s)

0.6

P(s)

0.6 0.4

0.4

0.2

0.2

0 0

1

2

3

4

0 0

5

1

2

s 1

3

4

5

s 1

(c)


0.8

(d)


0.8 0.6 P(s)

0.6 P(s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 26

0.4

0.4

0.2

0.2

0 0

1

2

3

4

0 0

5

1

s

2

3

4

5

s

Figure 5: Nearest neighbour level distribution for the sequences with (a) 45%, (b) 60%, (c) 85%, (d) 100% C − G content.

26


Engineering DNA Molecule Bridge between Metal Electrodes for High

Recommend Documents