Quantum phenomena in nanoscale structures        -      P. Hadley

One fascinating and potentially useful aspect of nanotechnology is that nanostructures can be made that behave quantum mechanically. Quantum mechanics are the laws of physics that are normally associated with the motion of subatomic particles such as electrons, protons, and neutrons. This description tells us that the electrons swarm around the nucleus of the atom in an electron cloud that has a diameter of a few tenths of a nanometer. It is hard to measure the quantum mechanical behavoir of single atoms directly because the measurement tools we presently have are typically much larger than an atom. One way around this problem is too find a way to increase the size of the atom. Artificial atoms can be constructed with sizes much bigger than ordinary atoms. For instance, embedding the atom in a semiconductor crystal can increase the diameter of the electron cloud of an atom. Figure 1 shows and image of the electron cloud of a silicon atom that has been embedded in a semiconducting crystal of GaAs. The stripes in the figure are rows of the atoms of the semiconductor and the large bump is the electron cloud of the silicon atom. The diameter of the electron cloud of the silicon atom has been increased to a few nanometers. At this length scale it is possible to put an electrical contact close to the silicon atom and by applying a voltage to that electrode it is possible to deform the electron cloud of the individual silicon atom. This sort of interaction between the macroscopic world of electrical contacts and microscopic world of atoms is an important aspect of science at a nanometer scale.
Figure 1. The large structure is the electron cloud of a single silicon atom and the fine structure is the atomic lattice of the GaAs crystal. (M.C.M van der Wielen, A.J.A van Roij, and H. van Kempen, University of Nijmegen) One of the possible applications of such artificial atoms is a quantum computer. Quantum computing makes use of coherent states to process information. Rather than the sequential discrete logic of conventional information processing, use is made of quantum superposition of so called qubits. Quantum computers, if they would exist, could perform complicated tasks faster than conventional computers. For the realization of quantum computers the emphasis has so far been on quantum optics, using trapped atoms or ions. Nanotechnology could make solid state quantum devices for quantum computing possible.

One of the difficulties in coupling the macroscopic world to the microscopic world is bringing probes close enough to a nanostructure to be able to measure it. Figures 2 and 3 show how a small metallic cluster and a carbon nanotube have been coupled to electrical leads so that they can be measured. The nanotube is only a few atoms thick. A close-up image of a carbon nanotube is shown in Fig. 4. It is possible to manipulate the nanotubes on the substrate by pushing them with an atomic force microscope (AFM) tip and it is possible to cut the nanotubes into segments by applying a voltage pulse to an STM tip.
 

Figure 2. A 20 nm Pd particle (yellow) that has been electrostatically trapped between two electrodes (red). (A. Bezryadin, Delft University of Technology) 
Figure 4. Atomic resolution image of a carbon nanotube. The diameter of the tube and the twist of the atomic arrangement along the tube determines the electrical conductivity of the tube. (Jeroen Wildoër, Delft University of Technology).
 Using nanofabrication it is possible to create a large variety of structures that exhibit quantum effects. Figure 4 shows a copper surface has been modified by the addition of some iron atoms. The images show how the electron clouds of the copper surface electrons have been modified by the addition of the iron atoms. The interference patterns visible are a manifestation of the wave nature of electrons.
Figure 4. Iron atoms placed on copper surface. Courtesy of Don Eigler, IBM. Figure 5 shows a vertical quantum dot that was fabricated at NTT in Japan. The electrons in this structure are trapped in a thin disc between two tunnel barriers. Measurements show that the electrons behave as if they were part of a two dimensional atom.
 
Figure 3. Schematic drawing of a vertical quantum dot. A two dimensional disc-like atom is formed in a semiconducting structure at the position labeled "Dot" in the figure. (S. Tarucha, NTT, Japan) Figure 6 shows the data that is used to determine the amount of energy that is necessary to add an additional electron to the vertical quantum dot of Fig. 5. This energy is the ionization energy of a disc-like atom. Two-dimensional atoms have a different shell structure than three-dimensional atoms. Whole new periodic tables need to be drawn up to describe these atoms. These artificial atoms have properties that can be very different than the properties of real atoms. For instance, it is possible to couple a thousand times more magnetic flux to an artificial atoms than to real atoms simply because the artificial atoms are bigger. This enables the study of magnetically induced atomic states are inaccessible in the realm of real atoms. We are just beginning to be able to couple these artificial atoms together to make artificial molecules and artificial materials. These artificial atoms can be manipulated by electric and magnetic fields in ways not possible with real atoms. Having new atoms with properties that can be tuned could have many applications.
Figure 6. The current through a vertical quantum dot as a function of the gate voltage and the bias voltage. The size of the blue diamonds determines the ionization energy of this artificial atom. (L.P. Kouwenhoven, Delft University of Technology) Another example of a quantum effect in a nanostructure is the single-electron charging effect. This arises due to the finite energy needed to charge very small structures with a single electron. This effect can be used to monitor and manipulate individual electrons. Charging effects can be used to construct a three terminal device called a single-electron tunneling (SET) transistor. Logic and memory circuits can be made using SET transistors. Unlike conventional semiconductor transistors, single-electron tunneling transistors can be scaled down to atomic dimensions. The current that flows through a superconducting single-electron tunneling transistor is shown in Fig. 7. The pattern repeats itself horizontally each time another electron tunnels onto the central island of a single-electron tunneling transistor.
Figure 7. Current through a superconducting single-electron tunneling transistor as a function of the gate voltage and the bias voltage. The current is periodic in the gate voltage with a periodicity of e/Cg, where e is the charge of an electron and Cg is the gate capacitance. Blue corresponds to nearly no current and red corresponds to a current of about 1 nA.
 Many of the experiments carried out on artificial atoms have been performed at low temperatures. This is because the characteristic energies of artificial atoms depend on the size of the structure. These energies have to be larger than the energies of thermal fluctuations in order for the atomic structure to be observable. In real atoms the energy spacing between quantum levels is typically a few electron volts (eV) while thermal the energy of a thermal fluctuation at room temperature is 0.025 eV. Thus quantized energy levels of real atoms are easily distinguished at room temperature. So far most of the artificial atoms that have been made are relatively large and the temperature where the atomic structure becomes apparent is rather low. As advances in nanotechnology continue, the size of the structures will decrease and the temperatures at which the atomic structures will be observable will increase. This will open the way to room temperature applications.

One of the most exciting areas of research is the possibility of coupling artificial atoms together to form artificial molecules or they can be placed in a regular pattern to form wires or crystals. A number of predictions have been made for the electrical conductivity in such systems. Normally, electrical conduction is governed by the motion of electrons that flow like a liquid through a conducting material. As the electron liquid is cooled, it can condense into a number of different quantum states. These states include superconductivity, Luttinger liquids, magnetism, charge density waves, spin density waves, and Wigner crystals. The type of condensed state that is observed in a given material depends on the electron - electron interactions in that material. The effects of electron - electron interactions are intensified in quasi-one dimensional conductors such as molecular wires and single rows of atoms on a substrate. The interactions are more important in one-dimensional conductors because the diameter of the wire is smaller than the effective radius of the conduction electrons. In that case, the electrons cannot pass by each other and the motion of the electrons is determined by the interactions. Using nanofabrication it is possible to fabricate one-dimensional wires by a number of different means. Atoms can be deposited in a row, or atoms can be pushed into a row with an STM, or individual long conducting molecules can be attached to the electrodes. The enhanced electron-electron interactions in these structures and the condensed states they produce can then be explored by cooling the atomic wires down. Work is continuing towards fabricating such quantum wires. Figure 8 illustrates the sort of control that has presently been achieved. The lines in the figure are only a few atoms wide.
  

Figure 8. The closely spaced vertical lines are rows of atoms on a silicon surface. The modification of the surface was done with an STM. (Sven Rogge, Delft University of Technology).