A possible origin of semiconducting DNA Hiori KinoNIMS

A possible origin of semiconducting DNA Hiori Kino(NIMS) Masaru Tateno(TIT & AIST) Mauro Boero(Univ. Tsukuba &AIST) Jose Torres(Univ. Tsukuba) Takahisa Ohno(NIMS) Kiyoyuki Terakura(Univ. Hokkaido & AIST) Hidetoshi Fukuyama(Univ. Tohoku)

• Introduction • DC conductivity measurements • Theoretical study so far • This work, theoretical study • Anderson localization

History 1. Radiation damage DNA is damaged by ultraviolet rays. “How does a hole or electron created by ultraviolet rays move in DNA? ” → electron transfer theory 2. Is DNA metallic or insulating? They measured DC conductivity.

Electron/hole hopping measurements in DNA UV energy LUMO (band) DNA in a living body Gap ~ 6 -7 e. V m UV light (trigger) HOMO (band) If electrons/holes move rapidly, little radiation damage Motion of a existing hole/electron

DC transport measurement V (trigger) I m. R m. L m dry DNA ~T m. L m. R (Landauer formula) n. F(w) If V is very small ~Temperature m w Possibility of low energy excitation ~T Where does a hole/electron come from?

Two kinds of exp. Electron transfer by UV light DC transport energy LUMO (band) Gap ~ 6 -7 e. V Chemical potential m ~T UV light (trigger) HOMO (band) Energy scale < 102 Kelvin Energy scale ~ 100 e. V No density of states→No transport Q. Finite DOS at m?

Nano device? • Etching technology of ultra-fine structures will encounter the barrier in the near future • DNA : small crosssection (~2 nm) : self-assemble (utilizing complementary pairs of base molecules) Holliday junction Seeman’s cube Figures, from C. Dekker, Phys. World. 14, 29 (2001). • Low resistance useful nanowire

Another example 1. 4 kbase single-stranded DNA→octahedron Raw mages by cryo-electron microscopy Diameter~14 nm W. M. Shih, et al. , Nature, 427, 618 (2004).

DNA nano-machine DNA gear DNA biped walking device J. Am. Chem. Soc. , 126 (37), 11410 -11411, 2004. “Molecular Gears: A Pair of DNA Circles Continuously Rolls against Each Other “ Ye Tian and Chengde Mao* Nano Letters, 4 (7), 1203 -1207, 2004 “A Precisely Controlled DNA Biped Walking Device “ (bike=二本足歩行) William B. Sherman and Nadrian C. Seeman*

• Introduction • DC conductivity measurements • Theoretical study so far • This work, theoretical study • Anderson localization

DC conductivity measurement l-DNA, scanning force microscopy ~105 cm (>70 nm) (T=RT) Bundle of DNA De Pablo et al. Phys. Rev. Lett. 85, 4992 (2000)

Summary of Experiments l-DNA 105 cm (70 nm) l-DNA T=RT Pablo et al. Phys. Rev. Lett. 85, 4992 (2000). 106 cm (4 mm) l-DNA T=RT? Zhang et al. Phys. Rev. Lett. 89, 198102 -1 (2002). 10 -4 cm(600 nm-900 nm), T=RT Fink et al. , Nature 398, 407(1999) d. G-d. C 10 -2 cm (>20 nm) d. G-d. C 1 cm (50 nm) T=RT Cai, et al. , APL 77 (2000) 3105 T=4. 2 K-RT Yoo, et al. RPL 87 (2001) 198102 10. 4 nm, T=100 K-RT Porath et al. , Nature 403, 635(2000)

Metal, Insulator and doped semiconductor metal E m insulator semiconductor E m E ~e. V m schematically E Conductivity of semiconductor several order of magnitude depending on the density of impurities m Impurity E Band gap~T* host Thermally doped Intrinsically doped

• Introduction • DC conductivity measurements • Theoretical study so far • This work, theoretical study • Anderson localization

Structure of DNA base molecules backbone sugar PO 4 Figures, from C. Dekker, Phys. World. 14, 29 (2001). • G: C, A: T= hydrogen bond • PO 4= -1 charged, DNA=negatively charged system at p. H~7 • charge neutrality= cations (Na+, K+, Mg++, …)

Theoretical Study Electronic structure of base molecules Gp. C: HOMO G LUMO C Ap. T: HOMO A LUMO T PW 91/6 -31 G(d, p)

Theoretical study (2) Electronic structure of DNA (acid) Poly(d. G)-poly(d. C) (PO 4 - is terminated by H+, the system is neutral) C EF G G C e. g. HOMO band Artacho et al. Mol. Phys. 101 (2003), 1587. DFT/GGA, SIESTA Blue=HOMO, Red=LUMO completely separated, G-C: hydrogen bonding →Insulating(gap~2 e. V), (LDA underestimates band gap. )

Is semiconducting DNA possible? There can be some methods to dope carriers into insulating DNA. E. g. P is added to dope carriers into insulating Si. ppm order of P is sufficient to make Si conducting. E m E ~e. V Shift m ~e. V m insulator semiconductor carriers!

• Introduction • DC conductivity measurements • Theoretical study so far • This work, theoretical study • Anderson localization

Possible electronic structures Poly(d. G)-poly(d. C) [(d. G) 2 -X+? ] (X: impurity) (Without dopant) (With dopant) LUMO(C) m HOMO(G) DOS hole HOMO(G) DOS(dopant) DOS(host) impurity G G Intrinsic doping

Condition of DNA in experiments DNA in solution C G H 2 O Dry DNA C G Most cation metals are with solvation shells, some may be anhydrous

Possible loci of cations (study of effects of solvation shell of catons) DNA cation There are many possible loci of cations. There may be many possible loci of cations which dope carriers into DNA. In this study, examine the electronic structure of one typical locus.

Electronic structure of DNA hydrate v. s. anhydrous Mg [(d. G)2 Mg(H 2 O)n]+ PO 4 -1 Mg 2+ C G hydrated Mg cations (GGA/PBE gap~0. 7 e. V) Mg 2+ Sz=0 LUMO anhydrous Mg cation (c) (c’) HOMO (b) (c’) SOMO Sz=1 (a) (b) (a) Unoccupied state Occupied state B (a) LUMO@G (b) LUMO 7. 6 e. V (b) (c) G Mg+ (c’) G Calc. UHF/6 -31 G(d)

Schematic electronic structure of dry DNA poly(d. G)-poly(d. C) with anhydrous Mg [(d. G) 2 -Mg 2+] LUMO impurity m G HOMO hole m HOMO(G) DOS(dopant) DOS(host) • Intrinsic doping = localized spin moment at Mg # of injected holes into guanine HOMO band = # of anhydrous Mg

Q. A possible origin of the diverse experimental results A. degree of drying Maybe it is very hard to remove solvation shells. c. f. P@Si, ppm order Very small # of injected holes can make DNA conducting There will be a number of methods to dope carriers into insulating DNA chains. Experimental suggestion of another method of doping I 3 - , M. Taniguchi et al. Jpn. J. Apl. Phys. 42 (2003), L 215 Comment: doping a hole is different from moving of the hole easily

ion cat str uc tur e Other divalent cations Sz=0(para) Sz=0(AF) Sz=1(ferro) the most stable Doping mechanism A Mg B Mg -2604. 691 -2604. 700 -2604. 725 -2604. 680 -2604. 711 ferro AF/ferro Intrinsic A Zn B Zn -4182. 521 -4182. 482 -4182. 581 -4182. 555 -4182. 546 -4182. 536 AF AF Intrinsic A Ca B Ca -3081. 868 -3081. 857 -3081. 864 -3081. 838 NG -3081. 829 Unit: A. U. , Gaussian 6 -31 G(d)/UHF abbreviation: A Mg = Mg@A-DNA E EF E Band gap~T* para Thermal? PO 4 - X X PO 4 - J PO 4 - Mg+ X PO 4 - X X PO 4 Impurity Mother material PO 4 - X C G

• Introduction • DC conductivity measurements • Theoretical study so far • This work, theoretical study • Anderson localization

Anderson localization E EF band Nonzero DOS at EF • If DNA has doped one-dimensional band → Anderson localization • In one-dimension, no mobility edge → the wavefunction is always localized. • Long-ranged hopping mechanism → maybe variable range hopping (VRH) (Assumption of VRH=doped band) Polaron and so on. may be necessary at higher temperatures. We do not deny their theories. At very low temperature, Anderson localization plays important roles.

I-V curve ---electronic contribution--Log[ conductivity ] Stacked DNA into the gate Replot from Yoo, et al. RPL 87 (2001) 198102 n=dimension+1 Mott VRH n=2 Efros-Shklovskii(ES) VRH n=2 T 0~90 K (poly(d. G)-poly(d. C)) (103/T)1/2 (V) 4. 2 K a-1: localization length Non-ohmic conductivity OK! Nonohmic threshold band gap Exp. Yoo, et al. RPL 87 (2001) 198102. Theory. adopted theory by H. Fukuyama and K. Yosida, J. Phys. Soc. Jpn. 46, 102 (1979).

Summary Anhydrous cation HOMO Hydrated cation SOMO J LUMO An injected hole • Intrinsic doping: Mg->ferro, Zn->antiferro • (Thermal doping: Ca ? ) (Longer chains must be calculated ) # of doped holes= # of anhydrous Mg or Zn, or thermally doped

Comments The most stable structures of Mg@G 2 Siesta (GGA+PCC): paramagnetic, HOMO=G, LUMO=Mg (G: guanosine) Gaussian 98(HF): Ferromagnetic, SOMO=Mg, LUMO=G Guassian 98(PW 91): Ferromagnetic, SOMO=Mg, LUMO=G In STATE(ultrasoft PS, GGA) and CPMD(GGA), to achieve selfconsistency is harder. Ferromagnetic solution seems to be the most stable. Some LDA/GGA calculations of anhydrous Mg@DNA are unstable probably due to the self-interaction correction problem. Mg is spatially localized. Maybe it is connected with the result of siesta. Siesta uses localized PAOs which may raise the orbital energy of isolated Mg more than those of extended states of DNA base molecules. Careful consideration may be necessary to use PAOs in this case.

Electronic structure of DNA (GGA/PBE) EF G P G O Paramag. (Sz=0) Mg++ O- “Mg++” e (ev) G HOMO-1 HOMO LUMO siesta

Doped semiconductors Log[ conductivity ] DNA exp. Replot from Yoo, et al. RPL 87 (2001) 198102 e (103/T)1/2 ec ed textbook Log[nc] -1/2(ec-ed) -1/2 Eg Eg (ec-ed) 1/T Aschcroft and Mermin, Solid State Physics, page 580 on ‘Homogenious Semiconductors’ DOS