1. Charge transport in DNA molecules: Structural and dynamical disorder 张伟 北京应用物理与计算研究所 2007 年 10 月

2. Outline: 2. Structure disorder and correlation 3. Dynamical disorder Effects of disorder and correlation of DNA base sequences Effects of twist modes, rotational polarons 4. Conclusions 1. Introduction

3. Charge transport in DNA is not only of fundamental importance, but also has important applications in biological process (such as in repair mechanism after radiation damage), and in possible novel device designs. Motivation: Introduction (a) DNA-Based devices 1-D Nanowire 2-D network Self-assembly Recognition

4. Experiments DNA molecules are found to be insulator, (semi-)conductor, etc. Theories The mechanism for transport is complex, likely via-orbital overlap repair protein (b) Applications in biological processes

5. www.accessexcellence.org DNA Different sequences / structure  properties Flexible structure ‘Twisting’ modes

6. Anderson localization, scaling theory One puzzle: Why there is conductive behavior for 1D-DNA chain with random sequences ? Structure disorder and correlations AACCG T G GGTCC AABBBB Random variable

7. D-dimensional system with volumeconductance Strong disorder Weak disorder d=3 d=2 d=1 All eigenstates in 1-D disordered systems are localized states. the zero temperature conductance vanishes. Localized state Extended state Charge transport

8. One-parameter scaling theory All eigenstates in 1-D disordered systems are localized states. Anderson localization For 1-D system with correlated disorderExistence of extended states Short-range correlationrandom dimer model,Extended states Long-range correlationexistence of mobility edge BUT

9. T AACCGG GGTCC Theoretical model one-dimensional DNA chain with base pairs AT and CG: Main point : Disorder with local correlation Diagonal disorder is correlated to off-diagonal disorder. 1. Zhang et al, Phys. Rev. B 2004 2. Zhang et al, Microelectro. J. AABBBB Random variable

10. Limiting cases 1. Anderson model, localized eigenstates 2.Low concentration limit BAAAAA Repulsive impurity model, existence of extended states

11. Correlation enhances transport Local correlation leads to Enhancement of transport Additional correlation in sequences improves transport further A: random sequences with local correlation B: random sequences without local correlation C: random dimer sequences with local correlation Calculation method: Transfer matrix method AABBBB Transmission coefficient Physics origin: competition between disorder and correlation

12. High T even for high concentration of impurities Local correlation leads to resonant scattering Golden Correlation Dependence of concentration of impurities With increasing concentration, transmission coefficient decreases the peak positions shift.

13. AACCG T G GGTCC AACCCC one-dimensional DNA chain with base pairs AT and CG: Endres et al, cond-mat/0201404 Structural disorder and charge transport in DNA Watanabe et al, APL 2001

14. DNA Lead Mobile states Mobility gap I-V curves Landauer-Büttiker formalism Fermi function : a possible non-symmetric voltage drop at each contact

15. (a) Correlation enhance transport A: random sequences with local correlation B: random sequences without local correlation C: random dimer sequences with local correlation (b) Sequence dependence Different DNA molecules E: random sequences w/local correlations F: sequence D1S80 G: PolyG-PolyC DNA L=562 base pairs T=330K 300 average over disorder configurations

16. (d) Effects of temperature I-V curve is nearly insensitive to Fermi level broadening. At low temperature, I-V curve is sharper. (c) Dependence of concentration of impurities With increasing of impurity concentration current amplitude decreases current gap increases

17. “Leads”: end group DNA bases linking molecule to current electrodes For D1S80: DNA 414 bases & “leads” 148 bases In DNA D1S80, “leads” increase current gap suppressing current amplitudes but within one order of magnitude (e) Effects of leads nearly periodic sequence “lead”

18. Solids or molecular systems with flexible structure so that twist or rotational degrees of freedom are important. Swaminathan, et al J. Am. Chem. Soc. 1991 Dynamical disorder Rotational Holstein polarons Zhang et al, PRB; Bruinsma PRL;

19. Vibrational polaron A quasiparticle formed by a conduction electron (or hole) together with its self-induced polarization in solid or molecular systems. Oscillation of atoms or molecules PolarizationElectric field Electrons or holes Interaction Phonons Interaction Polarons

20. Polarons: electronic phonon-“hairy” balls If coupling is weak: “heavier” electrons, nearly extended, fermions still, e 0 If strong coupling (alkali halides, organic crystals…): localized/trapped electrons, fermions, e 0

21. Rotational Holstein model Local EP Interaction Anharmonic oscillation Nonlinear interaction electron-phonon (EP) coupling constant e-e-

22. Weak coupling regime Polaronic energy shift Effective mass Energy of phonon clounds Unlike the usual polaron (associated with translation modes), andcome from different orders of EP interaction

23. In Non-adiabatic and strong coupling regime: polaron energy shift: Bandwidth: vs usual vibrational Holstein polaron bandwidth: In adiabatic regime: weaker power-law suppression of bandwidth for rotational Holstein polaron Effective mass

24. Non-adiabatic regime Adiabatic regime Weak coupling regimestrong coupling regime

25. Conclusions: Other issues The “interference” effects between twist- and vibrational-polarons The effects of water molecules and ions Other complex molecule systems We have shown that correlations introduced by chemical structure in DNA greatly affect charge transport in the molecule and torsional motion along the DNA chain results in electron-twiston coupling effects which reduce the electronic transport. 1.Local correlation generates new conduction channels and enhance transport. 2.Additional correlation in sequences improves transport further 3.Backbone changes the local correlation power-law 4.Local twist-coupling yields power-law vs exponential bandwidth renormalization.

27. Experimental realization of the system in superlattice For fixed U is smaller, BUT transport is poorer