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Can somebody explain what is a "gapless excitation"? If it is an excitation, why does it require no energy (gapless) to excite the system?

Thanks,

Mavi

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- Thread starter mavipranav
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- #1

- 25

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Can somebody explain what is a "gapless excitation"? If it is an excitation, why does it require no energy (gapless) to excite the system?

Thanks,

Mavi

- #2

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Gapless modes are fluctuation modes that have a spectrum that vanishes at zero momentum. Therefore, it does not require too much energy to excite modes of lower values of momenta (k). On the other hand, a gapless mode means a long-range correlation of fluctuations. An excitation at one point can cause another point far from it to have a chance to fluctuate as well.

By Goldstone theorem, gapless modes arise when the ground state of the system spontaneously breaks a symmetry that the system possesses. Examples of this are phonons in solids, magnons in ferromagnets, photons in EM vacuum, helimagnons in helimagnets etc.

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In cond mat. gapless modes need not be related to Goldstone bosons. For example within a critical region the system has the full conformal symmetry yet critical excitations are gapless.

The 'gap' of a spectrum can be thought of as the mass of the excitations. Spin gaps usually refer to spin excitations that requires a finite energy. Excitations in an Ising ferromagnet is gapped because the simplest excitation above the ordered state would require one of the spins to flip costing [tex]2J[/tex] amount of energy, where [tex]J[/tex] is the spin-spin coupling strength.

The 'gap' in superconductor (sc) is the energy required to break Cooper pairs, which is finite. Hence any excitation above the sc state needs a finite amnt of energy. This can in turn be thought of as being the mass of the excitation (similar to the energy that a photon needs to possess in order to produce an electron positron pair).

The s-wave sc is always gapped, while the d-wave ones have certain channels in which one can have gapless excitations.

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The s-wave sc is always gapped, while the d-wave ones have certain channels in which one can have gapless excitations.

So if there is a continuous band of energies connecting the ground and excited state of the d-wave superconductor (because it is gapless), why should the superconductivity be stable, since arbitrarily small thermal fluctuations can excite it? This should be true even if we consider large correlation lengths.

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