Condensed-Matter and Materials Physics Basic Research for Tomorrow's Technology (1999) / Chapter Skim
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3 Novel Quantum Phenomena
3 Novel Quantum Phenomena
Pages 137-167
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From page 137... ...
Quantum mechanics is a strange business, and the quantum mechanics of large collections of atoms and molecules can be stranger still. It inevitably happens that when assembling a collection of atoms to form a material, the whole is greater than the sum of the parts in the sense that "emergent phenomena," such as spontaneously broken symmetries and quantum or classical phase transitions, often appear in large collections of atoms.
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From page 138... ...
In the past decade there has been tremendous progress in the discovery and study of a variety of novel quantum phenomena. This chapter presents brief descriptions of a few examples drawn from superfluidity, superconductivity, Bose-Einstein condensation, quantum magnetism, and the quantum Hall effect.
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From page 139... ...
To understand the concept of the hole, consider the fact (illustrated schematically in Figure 3.1.1) that when atoms are assembled into a solid, the discrete quantum energy levels of the individual atoms smear out into bands of quantum levels.
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From page 140... ...
This isotope of helium is a fermion, and it is Cooper pairs of helium-3 atoms that just barely condense at exceedingly low temperatures. Unlike the electrons in an ordinary superconductor, which form pairs in a state of zero relative angular momentum, helium-3 atoms pair in a p-wave if= 1)
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From page 141... ...
The bright spot in the central ring is an image based on a scanning-probe measurement, using superconducting quantum interference devices, of the local magnetic field. [Reprinted with permission from Barbara Levi, Physics Today 49, 19-22 (1996~.
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From page 142... ...
The small size of Cooper pairs in high-temperature superconductors has the benefit that, at least naively, it increases their tolerance for very strong magnetic fields. However, it may also be one of the many factors that limit the critical currents in these materials.
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From page 143... ...
Because of the "floppiness" of vortex lines in high-TC materials (because of the short coherence length and the extremely weak coupling between copper oxide planes along the c axis) , random point defects are not very effective at
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From page 144... ...
This "Bose glass" generalization of the vortex glass idea can be pursued further to include analogs of the Mott-Hubbard Bose insulator, Mott variable range hopping, and boson tunneling between localized states. Furthermore, our knowledge of the dynamical structure factor for quantum bosons makes predictions for the static structure factor for the vortex fluctuations that have been confirmed by small-angle neutron scattering experiments.
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From page 145... ...
This quantum boson analogy clearly demonstrates the existence of a phase transition in which the vortices can become localized by columnar pins leading to a state with truly zero resistivity in linear response. The relatively small size of the Cooper pairs in high-temperature superconductors puts the superconducting transition in a new regime, closer to the BoseEinstein condensation limit.
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From page 146... ...
opening up the possibility of studying macroscopic quantum coherence effects in a totally new time domain. The other aspect that is new is the unprecedented ability to dynamically change the trap parameters and optically probe the detailed response of the condensate.
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From page 147... ...
The condensed-matter theory community is supplying expertise in two areas: many-body calculation techniques and experience with the study of collective effects. It turns out that in this low-density regime, straightforward and standard mean-field theory calculation methods appear to be quite accurate for low temperatures, so there appear to be few theoretical challenges in this regard (except for questions of metastability for systems with negative scattering lengths that have not yet been fully settled)
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From page 148... ...
However, this reduction in the potential energy comes at the expense of increased kinetic energy associated with the extra nodes in the spatial wave function. Roughly speaking, if the potential energy term dominates, the system will have a ferromagnetic ground state.
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From page 149... ...
The antiferromagnet (whose order parameter is the staggered magnetization) is somewhat different: quantum fluctuations reduce the order parameter below the classical value even at zero temperature; hence, the exact ground state is not known.
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From page 150... ...
It is possible to show that each of these domain-wall defects acts like a quantum particle carrying half of the S = l angular momentum of the original spin flip. An immediate experimental consequence of the spin-wave fractionalization is that there is much more phase space available for spin excitations.
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From page 151... ...
FIGURE 3.5 Spinon production observed by spin-flip inelastic neutron scattering. There is much more phase space available for spinons than for ordinary spin waves.
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From page 152... ...
This novel order is completely invisible to the ordinary, experimentally measured, spin correlation function and can only be detected theoretically using a nonlocal "string order" correlation function that includes a factor of -1 for each of the nonzero spins within the string of spins connecting two sites. The most obvious experimental manifestation of this hidden topological order is that it costs a finite amount of energy to break it; hence, the system has a spin excitation gap.
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From page 153... ...
This is illustrated in Figure 3.9, which shows a segment of an S = 1 chain cut off from the rest of the chain by a nonmagnetic impurity at each end. The disruption of the valence bond solid ground state liberates a nearly free spin-l/2 at each end of the segment.
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From page 154... ...
In the limit J2 = 0, the exact ground state is a "valence bond solid" (VBS) of singlets on the Jo bonds.
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From page 155... ...
probes that continue to advance our knowledge as well as raise intriguing new questions. The quantum Hall effect takes place in a two-dimensional electron gas subjected to a high magnetic field.
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From page 156... ...
This permits uniform charge flow of the incompressible electron liquid and, hence, a quantized Hall conductivity. The microscopic correlations leading to the excitation gap are captured in a revolutionary wave function, developed by R.B.
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From page 157... ...
Flatland cosmologists have theorized that the charged particles seen drifting around are topological defects left over from the Big Chill at the beginning of the universe. Flatland particle theorists decide that the apparently featureless vacuum in which everyone lives each day is actually a roiling sea, filled with strange but invisible objects that have precisely three times the charge of one of these quasiparticles.
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From page 158... ...
magnetic field, as illustrated schematically in Figure 3.11. The condensate wave function of these bosons defines a hidden off-diagonal long-range order not visible in the ordinary correla ( FIGURE 3.11 Illustration of the condensation of composite bosons in the v = 1/3 fractional quantum Hall effect.
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From page 159... ...
Second, the special case of v = 1/2 is naturally described as composite fermions in zero mean magnetic field. The characteristic Fermi surface wave vector 2kF of these composite fermions has been observed in surface acoustic wave attenuation experiments.
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From page 160... ...
A Laughlin quasiparticle is represented by a composite fermion in the next Landau level. Edge States At low energies, the bulk of an FQHE system appears as a featureless vacuum with an excitation gap; however, very unusual gapless modes exist at the edges.
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From page 161... ...
According to current theory, one of the most important features of the chiral Luttinger liquids realized at the edge of FQHE systems is that g is universal, dependent only on the quantized value of the Hall conductivity in the bulk and independent of all details of the electron interactions. In particular, this makes the temperature and voltage dependence of the tunneling current have a power-law form that is universal and independent of all microscopic details.
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From page 162... ...
For reasons peculiar to the band structure of the gallium arsenide host semiconductor, the external magnetic field couples exceptionally strongly to the orbital motion, giving a large Landau level splitting, and exceptionally weakly to the spin degrees of freedom, giving a very small Zeeman gap. The resulting low-energy spin degrees of freedom of this ferromagnet have some rather novel properties, which have recently begun to be probed by NMR, specific heat, and other measurements.
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From page 163... ...
This long-range transverse order has been observed experimentally through the strong response of the system to a weak magnetic field, applied in the plane of the electron gases, in the presence of weak tunneling between the layers. Very recent work indicates that a two-layer quantum Hall system at filling factor v = 2 may even allow for an antiferromagnetic or a canted spin phase, further demonstrating the complexity and richness of the magnetic phase diagrams of quantum Hall systems.
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From page 164... ...
is absorbed only in the quantum wells. The angular momentum of the photons is transferred to the orbital motion of excited electrons and then, via the spin-orbit interaction, to the electron spins.
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From page 165... ...
In addition, despite valiant efforts, there does not yet exist a simple quantum field theory for this transition from which we can analytically compute the critical exponent. Finally, there remains an interesting set of puzzles about what happens at weak magnetic fields as Landau level mixing becomes strong and direct transitions apparently occur from quantum Hall effect states to insulating states.
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From page 166... ...
. Numerous new discoveries in quantum Hall physics including direct observation of the fractional charge of quantum Hall effect quasiparticles, composite particles, edge-state modes, Raman observation of the fractional quantum Hall effect neutral excitation gap, discovery of drag and spontaneous coherence in double-layer systems, and NMR and nuclear specific heat anomalies due to skyrmions.
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From page 167... ...
· Finally, if the past is any guide, we will be faced with completely unexpected and surprising quantum phenomena as new materials are synthesized. What new techniques will have to be developed to deal with these surprises?
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