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There is certainly a way to preserve the time-reversal symmetry with open boundary conditions: just put the two edge spins into a singlet state. You may say that this is cheating, since essentially we will have periodic boundary conditions by pairing the edge spins up. This depends on perspective, but indeed there are no other ways to have a completely ...

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Mercury is slightly soluble in water. At room temperature the solubility is about 56$\mu$g/litre. So while the mercury would not evaporate if you added enough water, or kept replacing the water, the bead of mercury would eventually dissolve away. In principle the mercury solution could evaporate the mercury into the air, but in practice the rate of ...

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There is an one to one correspondence between momentum space and real space through Fourier Transform. Thus a crystal in real space has the same dimensionality in momentum space also. However one must remember that when we say 2D crystals we do not necessarily mean exactly 2D. There are several things as multilayered 2d crystals such as MoS2 etc..

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The BCS wave function is a superposition of components with definite particle number $N=0,2,4,\ldots$. In the infinite volume limit, the particle number is sharply peaked around $N=nV$, where $V$ is the volume and $n$ is the partcle density. It is intuitively clear that projecting the BCS state on a definite particle number should not make a difference. This ...

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The nearly free electron model is a good thing to read about, but it's slightly different then what you want. The nearly-free electron model starts with non-interacting electrons that are not bound by any periodic potential, and treats the potential as a perturbation. You want to START with non-interacting electrons in a periodic potential, and treat the ...

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A generic procedure to obtain the particle-hole conjugate of a quantum Hall wavefunction is described in http://journals.aps.org/prb/abstract/10.1103/PhysRevB.29.6012. It is not clear whether this is the most "general" form. But even for the Pfaffian state, we do not know the most general form either.

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