Condensed-Matter and Materials Physics The Science of the World Around Us (2007) / Chapter Skim
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2 How Do Complex Phenomena Emerge from Simple Ingredients?
2 How Do Complex Phenomena Emerge from Simple Ingredients?
Pages 30-52
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From page 30... ...
In the fractional quantum Hall state, a bizarre liquid state of electrons, an added electron will break up into new particles, each of which carries a precise fraction of the charge of the original electron. In a superconductor, an electrical current can flow indefinitely without decaying.
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From page 31... ...
While Dutch physicist Kamerlingh Onnes did envision producing magnetic fields using solenoids wound from superconducting wire, he could never have foreseen superconducting magnets big enough to surround a human, nor that such a magnet would be the heart of a technological marvel (magnetic resonance imaging; see Figure 1.1 in Chapter 1) that would revolutionize medicine.
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From page 32... ...
That example is followed by more general discussions of current trends in research on Fermi and non-Fermi liquids, on quantum Hall effect systems, and on critical phenomena and universality in clas sical and quantum-phase transitions. Emergence in ultracold atomic gases and in granular matter round out the list of case studies.
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From page 33... ...
The existence of a persistent current is a concrete demonstration of quantum mechanics at a macroscopic scale. Since currents produce magnetic fields, it is perhaps not surprising that the magnetic properties of superconductors are likewise unprecedented.
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From page 34... ...
theory. Not surprisingly, since superconductivity involves only a subtle, low-temperature change in the properties of the electrons in the metal, the BCS theory is based on the equally successful Fermi liquid theory of the properties of normal metals.
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From page 35... ...
occur in this class of materials -- understanding the relation between the various types of ordered phases of these materials and understanding how they relate to the properties of the non-Fermi liquid normal
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From page 36... ...
If the positions of two identical particles are interchanged, quantum mechanics naturally insists that there be no observable consequence. Except in certain rare cases to be described below, there are only two ways in which the quantum wave function of the material can satisfy this requirement: either (1)
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From page 37... ...
A system in which the properties of a dense electron fluid can be related to those of a gas of weakly interacting quasi-particles is called a Fermi liquid. The very successful theory of normal metals, as well as the equally successful theory of simple semiconductors, is based on Fermi liquid theory.
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From page 38... ...
However, this is just the tip of the iceberg. The broad occurrence of non-Fermi liquid phenomena suggests that it is related to new quantum phases, or at least to extremely new regimes of matter.
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From page 39... ...
In a crystal, there is a lattice on which the atoms or molecules are localized in a pattern that repeats periodically through space, so that different points within the unit cell are different from each other, and different directions, relative to the axes of symmetry defined by the crystalline order, are distinct from each other. Liquid crystalline states exhibit patterns of symmetry breaking intermediate between those of a simple liquid and a crystal.
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From page 40... ...
An electron nematic phase is also difficult to detect for various technical reasons, including the fact that crystalline imperfections can mask its occurrence on macroscopic scales and that it can be hard to distinguish from a more conven tional strain-driven change in the crystal structure of the host material. However, as discussed below, strong evidence for an electronic nematic phase has recently been found in extremely high mobility quantum Hall devices.
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From page 41... ...
It is in this regime that Tsui, Stormer, and Gossard discovered the famous fractional quantum Hall effect (FQHE) in 1982. They observed that when the lowest Landau level is one-third filled, a wholly unexpected quantized plateau in the Hall resistance appears, signaling the opening of an energy gap.
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From page 42... ...
The dark regions, where the resistivity becomes vanishingly small as the temperature tends toward absolute zero, are various quantum Hall effect states, where the integers label the value of the quan tized Hall conductance in units of the quantum of conductance. The bright regions mark the points at which quantum phase transitions occur between the different phases.
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From page 43... ...
At modest magnetic fields, where several Landau levels are occupied, collective states emerge that are reminiscent of both classical liquid crystals and pinned charge density waves. For example, near one-half filling of highly excited Landau levels, electrical conduction in the two-dimensional system spontaneously becomes extremely anisotropic at very low temperature (below about 150 mK)
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From page 44... ...
The graph and the insets describe the development of quantum liquid crystalline behavior in a collection of electrons moving on a plane surface of a nematic liquid crystal in the presence of a perpendicular magnetic field. The red and blue traces show how the electri cal resistance of the system, measured in two mutually perpendicular directions, becomes extremely anisotropic at temperatures close to absolute zero.
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From page 45... ...
Phase transitions can occur as a function of temperature, or pressure, or magnetic field, or composition, and so forth. When water freezes, the water at temperatures just below the freezing point is a solid (ice)
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From page 46... ...
As with any revolutionary change, the full implications of the renormalization group approach continue to reverberate. When continuous phase transitions occur at zero temperature, quantum mechanics on a macroscopic scale becomes impor tant.
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From page 47... ...
Another vast area in which many related open problems exist is systems with quenched disorder -- in which there are degrees of freedom, such as the locations of impurity atoms, which are not in thermal equilibrium. Phase transitions -- even classical phase transitions -- in the presence of quenched disorder are not fully understood, and where quenched disorder and quantum phase transitions intersect, there is a growing understanding that entirely new conceptual tools are needed.
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From page 48... ...
Most importantly, ultracold atoms offer the prospect of discovery of wholly new and highly exotic states of condensed matter that have no roots in traditional material systems. Emergence in Classical Condensed-Matter SYSTEMS A number of examples of emergence in classical condensed-matter systems illustrate the scope and unity of the concepts underlying the study of emergence, where neither quantum mechanics nor even conventional thermal physics plays any direct role in determining the emergent behavior (see Figure 2.6)
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From page 49... ...
Put another way, the ratio of the entropic and interaction contributions to the free energy at any fixed temperature decreases rapidly with the size of the grains. Thus, granular matter effectively presents scientists with a problem in which temperature can also be ignored, so the collective phenomena typically involve nonequilibrium physics, as discussed in Chapter 5.
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From page 50... ...
50 C o n d e n s e d - M at t e r and M at e r i a l s P h ys i c s FIGURE 2.7 A collapsing grain silo provides a dramatic example of the unexpected behavior of granu lar materials. If the grains are flowing in some regions and jammed in others within the silo, there can be large variations of the stress on the silo walls, leading to disaster.
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From page 51... ...
Superconductivity and the fractional quantum Hall effect were discovered by investigating the properties of matter under extreme conditions. Kamerlingh Onnes, having recently succeeded in liquefying helium, was studying the resistivity of metals cooled to near absolute zero.
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From page 52... ...
Emergent phenomena beautifully illustrate the inseparability of the fundamen tal and applied research in CMMP. In some cases, the application of an emergent phenomenon is nearly immediate; in other cases it takes decades to occur; and in still others it may never occur.
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