Cascaded spintronic logic with low-dimensional carbon

Abstract

Remarkable breakthroughs have established the functionality of graphene and carbon nanotube transistors as replacements to silicon in conventional computing structures, and numerous spintronic logic gates have been presented. However, an efficient cascaded logic structure that exploits electron spin has not yet been demonstrated. In this work, we introduce and analyse a cascaded spintronic computing system composed solely of low-dimensional carbon materials. We propose a spintronic switch based on the recent discovery of negative magnetoresistance in graphene nanoribbons, and demonstrate its feasibility through tight-binding calculations of the band structure. Covalently connected carbon nanotubes create magnetic fields through graphene nanoribbons, cascading logic gates through incoherent spintronic switching. The exceptional material properties of carbon materials permit Terahertz operation and two orders of magnitude decrease in power-delay product compared to cutting-edge microprocessors. We hope to inspire the fabrication of these cascaded logic circuits to stimulate a transformative generation of energy-efficient computing.

Figure 1. All-carbon spin logic gate.

Magnetoresistive GNR unzipped from carbon nanotube and controlled by two parallel CNTs on an insulating material above a metallic gate. As all voltages are held constant, all currents are unidirectional. The magnitudes and relative directions of the input CNT control currents I_CTRL determine the magnetic fields B and GNR edge magnetization, and thus the magnitude of the output current I_GNR.

Figure 2. Graphene nanoribbon edge magnetization.

(a) On-site magnetization profile of a zigzag graphene edge. The magnetic field created by an adjacent CNT current causes strong on-site magnetization at the GNR edge. The colour of each circle represents the spin species, while the radius corresponds to the magnitude of the magnetization. (b) The on-site magnetization of each site in a unit cell as a function of distance from the edge. (c) Graphene nanoribbon edge magnetization in the absence and presence of an externally applied magnetic field. In the absence of a magnetic field, the GNR exhibits global AFM ordering with edges of opposite polarities. The application of a magnetic field aligns the edge polarities, achieving global FM ordering.

Figure 3. Magnetoresistive behaviour of GNR controlled by adjacent CNTs.

(a,b) Band diagrams for the AFM and FM global ordering of a 12-atom-wide zigzag GNR with zero current in the CNTs and Hubbard parameter U=2.7 eV, as in equation (1) of Methods. In the global AFM state (a), there is a large gap between the valence and conduction bands, within which lies the Fermi energy, E_F. Therefore, there are no available conduction modes, and the conductance is zero. In the FM state (b), there is no bandgap and there is at least one conduction mode at all energies. (c,d) The magnetic instability energy in μeV for zigzag GNRs with widths of (c) 20 nm and (d) 35 nm. The blue region designates a positive instability energy (the insulating AFM state), while the red region indicates negative instability energies (the conductive FM state). In the narrower GNR transistor, the axes of the CNTs are 10 nm from the GNR edge, while the wider GNR has CNTs placed 1 nm away. The critical switching current, which depends on U, is denoted with a dashed line. (e) The transmission function of the AFM state defines the number of available conduction modes as well as the probability for an electron to travel across the device. Thus, for E_F values within the bandgap, the GNR conductance switches when the global ordering switches between the FM and AFM states. (f) A typical switching event, where the GNR conductance increases by G₀ when the CNT current overcomes the critical switching current I_C.

Figure 4. All-carbon spin logic one-bit full adder.

(a) The physical structure of a spintronic one-bit full adder with magnetoresistive GNR FETs (yellow) partially unzipped from CNTs (green), some of which are insulated (brown) to prevent electrical connection. The all-carbon circuit is placed on an insulator above a metallic gate with constant voltage V_G. Binary CNT input currents A and B control the state of the unzipped GNR labelled XOR1, which outputs a current with binary magnitude ⊕B. The output of XOR1 flows through a CNT that functions as an input to XOR2 and XOR3 before reaching the wired-OR gate OR2, which merges currents to compute C_INV(A⊕B). This current controls XOR4 and terminates at V₋. The other currents operate similarly, computing the one-bit addition function with output current signals S and C_OUT. (b) In the symbolic circuit diagram shown here with conventional symbols, the output of XOR1 is used as an input to OR2 and XOR3 along with C_IN. The full adder S output is computed as S=C_INV⊕(A⊕B). OR2 outputs C_INV(A⊕B), which is used along with S as an input to XOR4 to compute (C_INV(A⊕B))⊕(C_IN⊕(A⊕B)). This output of XOR4 is equivalent to (A∧C_IN)V(B∧C_IN). OR3 takes this signal as an input along with the output of XOR2, which is equal to A∧B, to compute C_OUT=(A∧B)V(A∧C_IN)V(B∧C_IN). As the wired-OR gates simply sum the currents and have no significant delay, the total propagation time is that of three XOR gates, determined by the XOR1–XOR3–XOR4 worst-case path.

Figure 5. Analysis of switching and propagation delay.

Following a switch in the current through CNT₀ at a time t=0, the magnetic field at the edge of GNR₁ switches at t=t_mag, the resistance of GNR₁ switches at t=t_mag+t_gnr and the current through CNT₁ switches at t=t_mag+t_gnr+t_prop. This marks the end of one complete switching and propagation cycle, and is immediately followed by the switching of GNR₂.

Figure 6. Proposed proof-of-concept experiment.

By measuring the change in I_OUT in response to a change in I_IN, the central component of all-carbon spin logic can be demonstrated. The carbon nanotube CNT_OUT can be partially unzipped such that a portion forms a GNR. A second CNT, CNT_IN, is then placed nearly parallel to CNT_OUT. A constant voltage should be applied across CNT_OUT. It is not necessary to achieve the dimensions described in this work; rather, to make the experiment more facile, CNT_IN must merely be close enough to the GNR to cause a measurable response in I_OUT when I_IN is varied. Furthermore, as shown in the figure, CNT_IN need not be as long as CNT_OUT, thereby preventing the CNTs from making contact even if the CNTs are not perfectly parallel.