Carbon nanorings for spintronics applications and

Detection of biomolecules using quantum inference in a functionalized carbon nanoring with magnetic flux

Authors: Mark Jack and Mario Encinosa Dept. of Physics, Florida A&M University, 205 Jones Hall, Tallahassee, FL 32307.

Email: mark.a.jack@gmail.com, mencinosa@comcast.net

Motivation Carbon nanotubes [1,2] and single-, bi- or multilayer graphene [3] show the promise of defining the key technological advancements in nanoelectronics in the 21st century. Toroidal carbon nanotubes have been demonstrated experimentally together with cylindrical carbon nanotubes and form 3-dim mesoscopic (macromolecular) rings. Metallic (armchair) nanorings show highly sensitive quantum interference phenomena in electronic transport such as Aharonov-Bohm effect, universal conductance fluctuations, Van Hove singularities etc. Their 2-dim counterparts, i.e. flat graphene rings, have shown interesting band structure and transport features resulting from valley symmetry of quasi-relativistic Dirac electrons due to the two equivalent sublattices of graphene [4]. Carbon nanotori have the technological advantage of not having to be treated to define exact armchair or zigzag edges as for the flat 2-dim rings but should show all the spin and charge transport features of graphene rings and possibly additional effects due to the additional degree of freedom in electron motion along the smaller torus circumference.

Two unique applications of carbon nanotori devices as molecular biosensor and for spintronics are presented here utilizing their unique quantum interference and spin-transport characteristics:

•  Carbon nanotori as biosensors for detection of biopolymers with high sensitivity and selectivity through non-covalent functionalization and using quantum interference in charge transport with magnetic flux;

•  Carbon nanotori as spin-polarized current injector into a graphene lead for spin transport using microwaves (two oscillating and rotating magnetic fields B0(t), B1(t)).

Device geometry Electronic transport characteristics in a mesoscopic device configuration are calculated for variable source-drain voltage bias with a fast tight-binding algorithm using a non-equilibrium recursive Greenʼs function method (NEGF) [5,6,7]. The basic geometry with the carbon nanotorus centered as device and adjustable metallic lead attachments at the sides of (or below) the torus is shown in Fig. 1. Typical torus dimensions for initial studies are a minor radius a = 0.2 nm and a major radius R = 11.6 nm (N=3600 atoms).

Tight-binding approximation and NEGF method

Hamiltonian of device region (time-independent):

Definition of Greenʼs function (retarded/advanced):

: Self-energy corrections due to metal-torus contacts.

Carbon nanotorus as spin-injector

Following [11], illumination of torus region with proper microwave field and on-axis oscillating magnetic field (see Fig. 6) is predicted to generate spin-polarized current, with or without source-drain bias

In a photon-assisted transport model, time-averaged charge and spin currents can be expressed as sum or difference of a diagonal current term in spin space [11]:

ʻSpin injectorʼ + ʻspin valveʼ: It is is known that zigzag graphene nanoribbons should exhibit spin-polarized edge states [12] (Fig. 7). Attach a graphene nanoribbon as one of the leads to the nanotorus and a spin-polarized current could be generated via microwaves in the torus and injected into the ribbonʼs edge states. Contact resistance should be minimal due to matching hexagonal carbon lattices. Edge states are controlled via electrical gates. Long spin relaxation times in graphene could allow spin transport over micrometer distances and open possibility for quantum information processing.

Conclusions Quantum charge and spin transport in carbon nanorings allow for unique applications in biosensor and spin-based information tech- nology using static magnetic flux or polarized microwave fields with electric gate control. Theoretical simulations are conducted on high-performance parallel computer clusters of NSF TeraGrid. Accounting for corrections to transport and band structure charac- teristics beyond tight-binding due to electron valley symmetry, e-phonon coupling, Coulomb blockade and e-e-correlation effects, curvature etc. will be crucial for proper device design parameters.

Acknowledgments M.E. would like to thank M.P. Anantram and M. Meyyapan for initially suggesting this project and for helpful support at the NASA Ames Research Center. M.J. would like to thank the Materials and Manufacturing Directorate AFRL/RXPJ at Wright Patterson Air Force Base, Dayton, Ohio for helpful support through the 2008 ASEE Summer Fellowship Program.

Source drain current with transmission function T(E) (time-independent):

General: Time-dependent currents at left/right contact [8]:

Carbon nanotorus as Aharonov-Bohm oscillator:

Non-covalent functionalization with biopolymer (nanosensor)

Quantum interference in transport will be highly sensitive to attaching a biopolymer non-covalently via a small benzene-ring tether to the carbon atom lattice of the torus (see Fig. 4) [9]. Non-covalence of binding maintains conductive properties of torus and guarantees easy removal of the biopolymer and ʻreactivationʼ of the torusʼ sensor capabilities.

An effective hopping parameter tʼ for electron transport is calculated from density functional theory using Quantum Espresso [10] for a short segment of torus with attached bio- polymer. Preliminary analysis shows significant modification of electronic features (Fig. 5).

Abstract The authors have extended earlier studies for mesoscopic metallic toroidal structures to calculating the transport properties of toroidal carbon nanotubes under bias with attached metallic leads. The Green's function of the nanodevice region is calculated in tight-binding approximation using a recursive non-equilibrium Greenʼs function formalism. Initial investigations for a smaller model have been expanded to simulations of larger, more realistic systems with different geometric attachments of the leads. Expected quantum interference effects in charge transport under static magnetic flux have been shown. The existence and relevance of solenoidal surface currents in a microwave field and their effects on the total magnetic moment had been investigated for a metallic nanotorus surface. Substantial enhancements of the magnetic momentʼs solenoidal mode versus the dipole mode with additional spin-polarized currents are expected on carbon nanorings. Highly sensitive quantum interference signatures in charge transport with the possible generation of spin-polarized currents in these 3-dim nanorings create fascinating opportunities in biosensor and spintronics device technology.

Figure 1: Device setup with toroidal carbon nanotube and metallic leads.

Figure 3: Coherence in electronic transport: a) T(E) at E = 0.01eV as a function of magnetic field B0 for different angles between leads. b) Source-drain current ISD as function of magnetic field B0. for 90o angle btw. leads.

ΣL ,R

ISD =2e

dE T (E) fL E( ) − fR E( )⎡⎣ ⎤⎦∫ ,

T E( ) = Trace ΓLGrΓRGa⎡⎣ ⎤⎦,

H = Eici†ci

i∑ + tijci

†cj + h.c.( )i> j∑ .

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Ek( ) I − H

k( ) − ΣL − ΣR ± iη⎡⎣ ⎤⎦Gda,r( ) k( ) = I

�

Ii t( ) = −2e

dt1−∞

t

∫ dε2π

ImTr e−iε t1 − t( )Γ i ε,t1,t( ){∫ × G< t,t1( ) + f i ε( )Gr t, t1( )[ ]}; i = L,R.

�

ISD

Fig. 7: Spin-polarization along edge-states of zigzag graphene nanoribbons [12].

Figure 5: a) Local density of states D(E) and b) transmission function T(E). Locally modified coupling tʼ perpendicular to tube axis (t = - 3.1 eV).

Figure 4: -stacking of benzene tether with biopolymer onto torus [9].

�

π

�

B 1 t( ) = B1 cos ω1t( )ˆ z oscillating magnetic field

�

B 0 t( ) = B0 sinθ cos ω0t( ) ˆ x +sin ω0t( ) ˆ y ( )[ +cosθ ˆ z ] rotating magnetic field

Figure 6: Magnetic field arrangement B0(t), B1(t) for spin current generation [11].

�

VSD = 0( ).

�

Iγ ,σσ = −2

Im dε Jn2 Λ( )

n∑ Γγ ε − nω( )∫

× 12G σσ

< ε( ) + fγ ε − nω( )G σσr ε( )⎡

⎣ ⎢ ⎤ ⎦ ⎥ ; σσ =↑↑,↓↓ .�

Iγ ,σσ