## The Calculation of the Switching of Molecular Quantum Dot Cellular Automata for Mixed Valence Molecules

Principal Supervisor (Director of Studies): Dr G. Edwards, Department of Electronic & Electrical Engineering

Second Supervisor: Dr G. Spink, Department of Chemical Engineering

Suitable Background for Prospective Student:

Upper Second Class in Undergraduate Degree (BSc Physics, BEng Electrical & Electronic Engineering, BSc Applied Mathematics)

### Project Description:

The Quantum Dot Cellular Automata (QDCA) paradigm for nano-computing, put forward by the Notre Dame group, manages to achieve the minimal heat dissipation and the ultimate in coding one bit, in the charge configuration state of a mixed valence molecule. The elementary device for a QDCA system is a molecular six dot cell [Enrique P. Blair et al. 2010, 2016]. There are four ‘active’ dots forming a square in the ‘upper’ plane and two ‘null’ dots located in the ‘lower’ plane (see fig. 1 & 3). Two mobile electrons occupy these dots and due to the Coulombic electrostatics repulsion they will tend to sit in the antipodal sites (see fig. 1 & 2). These two states of the cell with electrons occupying the sites at diagonal opposite corners encode a binary ‘0’ and ‘1’. For a single cell in the absence of neighbouring molecules, these two states are degenerate. As fig. 1 shows these two states of the cell with electrons occupying the sites at diagonal opposite corners encode ‘0’ and ‘1’ binary states [Enrique P. Blair et al. 2010, 2016]. The electrons can transfer between dots located in a molecule via quantum mechanical tunnelling. The basic interaction for QDCA circuits is the cell – cell coupling via the Coulombic force. Fig 2 shows that for cells placed next to each other, the Coulombic interaction will cause the cells to align.

## Fig1.jpg

Figure 1 The three states of a six dot cell ('0', '1', 'Null' ). The ('0', '1') states are for dots occupied in the upper molecular plane while the 'null' state is for dots occupied in the lower molecular plane.

## Fig2.jpg

Figure 2 The cells align as '1' - '1' or '0' - '0' according to the state of the left cell, due to the Coulombic repulsion between electrons.

As molecules are too small to be contacted directly, the QDCA nano-computing is controlled by using clocking wires buried inside the substrate with the molecules placed at the surface (see fig. 3) [Enrique P. Blair et al. 2010, 2016]. In the null state the clock potential beneath the molecule pulls the electrons into the lower plane. In the active state, the clock potential beneath the molecule pushes the electrons out of the lower plane. The computational state is then determined by the geometry of the cellular array. A multiphase clock signal applied to the wires can then sweep bit packets through the system.

## Fig3.jpg

Figure 3 The Clocking for molecular QDCA. Buried wires produce the clocking signal at the surface of the substrate where the molecules are attached. The biases to the wires are phase shifted so that bit packets are 'pushed' along the line of molecules.

The present project is to calculate the switching response for a pair of cells composed of a mixed valence Diferrocenylacetylene (DFA) molecules. The physical system consists of the external driver molecular and the test molecule (electronic system) being driven [Enrique P. Blair et al. 2016]. However the test molecule can vibrate (vibronic modes) so this aspect must be included. The vibration system can exchange energy with the thermal environment (see fig. 4). The density matrix for this system, whose time evolution is given by a Lindblad equation, employing the Markovian approximation, will be solved, giving a treatment of the molecular switching including dissipation [Enrique P. Blair et al. 2016]. The MATLAB Quantum Optics Toolbox will be used to solve for the density matrix as it has advanced features (representation of tensor operators and superoperators) designed for this purpose [Sze M Tan 1999].

The extensions to the density matrix formalism for the non-Markovian case will also be tackled for the molecular switching problem [H. P. Breuer and F. Petruccione (2010)].

## Fig4.png

Figure 4 An overview of the entire physical system. The subsystems consist of the external driver, electronic system, vibrational system and the environment (heat bath). The electronic system (test molecule) is coupled to a time dependent driver system (driver molecule). The electronic system is coupled to the environment indirectly through the vibrational system.

### References

Enrique P. Blair, Steven A. Corcelli, and Craig S. Lent, ‘Electric field driven electron transfer in mixed valence molecules’, J. of Chemical Physics 145, (2016), 014307

Enrique P. Blair, Eric Yost , and Craig S. Lent, ‘Power dissipation in clocking wires for clocked molecular quantum-dot cellular automata’, J. Computational Electronics 9, (2010), 49

Sze M Tan, ‘A computational toolbox for quantum and atomic optics’, J. Opt. B: Quantum Semiclass. Opt. 1, (1999), 424

H. P. Breuer and F. Petruccione, ‘The Theory of Open Quantum Systems’, Oxford Uuniversity Press, 2010

Contact

For self-funding PhD candidates interesting in the above project and the research area of nano-electronics in general, contact Dr Gerard Edwards, Tel. (01244) 512314   Email: gerard.edwards@chester.ac.uk