The Quantum Interference Effect Transistor David M. Cardamone, Charles A. Stafford, and Sumit Mazumdar

Nano and Giga Challenges in Electronics and Photonics, March 16, 2007

“Controlling Quantum Transport through a Single Molecule”Nano Letters 6, 2422 (2006)

Patent application (in preparation)

Funding: NSF Grant Nos. PHY0210750 and DMR0312028

Fundamental challenges of nanoelectronics(a physicist’s perspective)

1. Switching mechanism:

Raising/lowering energy barrier necessitates dissipation of minimumenergy kBT per cycle → extreme power dissipation at ultrahigh device densities.

Tunneling & barrier fluctuations in nanoscale devices.

2. Fabrication:

For ultrasmall devices, even single-atom variations from device to device (or in device packaging) could lead to unacceptable variationsin device characteristics → environmental sensitivity.

The molecular electronics solution

Fabrication: large numbers of identical “devices” can be readily synthesized with atomic precision.

But does not (necessarilly) solve fundamental problem of switching mechanism.

Alternative switching mechanism: Quantum interference

(a) Phase difference of paths 1 and 2: kF 2d = π → destructive interference blocks flow of current from E to C.

All possible Feynman paths cancel exactly in pairs.

(b) Increasing coupling to third terminal introduces new paths that do notcancel, allowing current to flow from E to C.

Many-body Hamiltonian

π-electron molecular Hamiltonian (extended Hubbard model):

Molecule coupled to metallic leads (capacitively and via tunneling):

Ohno parametrization:

Theory:

Nonequilibrium Green function approach

Retarded and Keldysh Green functions:

Nonequilibrium current formula (Meir & Wingreen, PRL ’92):

Tunneling widths:

Multi-terminal quantum transport

Mean-field (e.g., Hartree-Fock) self-energies:

Transmission probabilities:

Multi-terminal current formula (M. Büttiker, PRL 57, 1761 (1986)):

Linear response calculation for benzene

Proposed structure for a QuIET:

1

2

3

Tunable Fano anti-resonancedue to vinyl linkage

Real (not decoherence)3

I-V Characteristic of a QuIET based on sulfonated vinylbenzene

Despite the unique quantum mechanical switching mechanism, the QuIET mimics the functionality of a macroscopic transistor on the scale of a single molecule!

Increasing gate voltage causes electronic states of vinyl linkage to couple morestrongly to benzene, introducing symmetry-breaking scattering.

General schematic of a QuIET

Source, drain, and gate nodes of QuIET can be functionalized with “alligator clips”e.g., thiol groups, for self-assembly onto pre-patterned metal/semiconducting electrodes (cf. Aviram, US Patent No. 6,989,290).

Example of a class of QuIETs based on benzene

Conducting polymers (e.g., polythiophene, polyaniline) connect to source and drain; semiconducting polymer (e.g., alkene chain) connects to gate electrode.

Lengths of polymeric sidegroups can be tailored to facilitate fabrication and fine-tune electrical properties.

Example of a class of QuIETs based on [18]-annulene

Interference due to aromatic ring;

Polymeric sidegroups for interconnects/control element(s).

Conclusions•Transport through single molecules can be controlled by exploiting quantum interference due to molecular symmetry.

•Alternative to modulating energy barriers could overcome fundamental problems of power dissipation and tunneling.

•Mechanism operates in the energy gap of molecule; does not require fine tuning!

•Open questions:

Interactions beyond mean-field (Hartree-Fock, DFT)?

Fabrication, fabrication, fabrication…

Many-body Green function calculation

Exact many-body Green function of isolated molecule:

Retarded self-energy including lead-molecule coupling to 2nd order:

Broad-band limit:

Justin Bergfield & CAS (unpublished)

Full many-body calculation for C6H4S2(Au) including exact intramolecular correlations

Includes:

Transmission nodeat the Fermi energyin meta configuration

Coulomb blockade

Emergence ofMott-Hubbard gap

Acknowledgements

Coauthors: David Cardamone (Ph.D. 2005) & Sumit Mazumdar

Current students:Justin Bergfield, Nate Riordan

Postdoc: Jérôme Bürki

Funding:NSF Grant Nos. PHY0210750 and DMR0312028

Image:Helen Giesel