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The stability of the Laughlin ν=1/2 state of boson can be seen by flux attachment argument. Since there are two flux quanta per boson, attaching one flux quanta to each boson maps the Laughlin ν=1/2 state of boson to an integer quantum Hall state of fermion, which is gapped and incompressible. In contrast, a ν=1 quantum Hall state for boson is mapped to a free fermion gas upon attaching one flux quanta to each boson, and hence is unstable.
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The stability of the Laughlin ν=1/2 state of boson can be seen by flux attachment argument. Since there are two flux quanta per boson, attaching one flux quanta to each boson maps the Laughlin ν=1/2 state of boson to an integer quantum Hall state of fermion, which is gapped and incompressible. In contrast, a ν=1 quantum Hall state for boson is mapped to a free fermion gas upon attaching one flux quanta to each boson, and hence is unstable.
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67650053509
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The k quantum numbers should be regarded as center-of-mass crystal momentum of the Hall condensate.
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The k quantum numbers should be regarded as center-of-mass crystal momentum of the Hall condensate.
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The gapless mode described here can be considered as the Goldstone mode associated with a spontaneous symmetry broken ground state (cf. Ref.). With this association, the superconductivity can be seen as arising from the usual Anderson-Higgs mechanism in which this Goldstone mode is "eaten up" by the electromagnetic field.
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The gapless mode described here can be considered as the Goldstone mode associated with a spontaneous symmetry broken ground state (cf. Ref.). With this association, the superconductivity can be seen as arising from the usual Anderson-Higgs mechanism in which this Goldstone mode is "eaten up" by the electromagnetic field.
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67650013152
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The existence of the zero mode (and hence superconductivity) is in fact a rather general consequence of zero total Hall number (i.e., all species ν=0). See Ref..
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The existence of the zero mode (and hence superconductivity) is in fact a rather general consequence of zero total Hall number (i.e., all species ν=0). See Ref..
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67650008464
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For this intuitive picture to be accurate, the sign of the component must also be taken into account.
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For this intuitive picture to be accurate, the sign of the component must also be taken into account.
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67650062128
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In the ordinary case, (c1, c2) are simply eigenvalues of Tx and Tr2, respectively, and are related to the crystal momentum k in the original Brillouin zone via exp (ik x) = c1 and exp (ik r2) = c2.
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In the ordinary case, (c1, c2) are simply eigenvalues of Tx and Tr2, respectively, and are related to the crystal momentum k in the original Brillouin zone via exp (ik x) = c1 and exp (ik r2) = c2.
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67650036364
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More generally, given in the transformed basis, the corresponding is determined up to multiples of 9.
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More generally, given in the transformed basis, the corresponding is determined up to multiples of 9.
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67650018567
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It can even be checked that K contains irrational eigenvalues that are not eigenvalues of K
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It can even be checked that K contains irrational eigenvalues that are not eigenvalues of K.
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25
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10.1103/PhysRevLett.100.157205
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