The valley physics in the two-dimensional graphenelike system has been put forward recently, and one of the key issues is to produce valley currents. We propose in this work to realize the topological valley resonance effect in graphene by using the time-dependent lattice vibration of optical phonon modes, which can pump out a noiseless and quantized valley current flowing into graphene leads. This optimal topological valley pump is protected by a nonzero valley Chern number and is robust against perturbations that could even break the time-reversal symmetry and valley conservation. The electrical measurement of the pumped valley currents is also discussed.Recently, the valley physics [1-4] has drawn much attention of researchers in the two-dimensional graphenelike system such as silicene [5], germanene [6], and MoS 2 [7]. Due to the honeycomb lattice structure, the low-energy Dirac electrons acquire an extra valley degree of freedom besides the usual spin one, which originates from the two inequivalent conical (Dirac) points in the Brillouin zone, K and K . The two valleys are degenerate in energy and related by the time-reversal symmetry. This valley degree of freedom was also proposed to carry and store information and believed to have advantages over the traditional charge carriers such as lower electric power consumption and faster data proceeding speed [1,2]. Moreover, the valley degree of freedom is related to the honeycomb lattice structure and is theoretically immune to the disturbance from the electric and magnetic fields. Similar to spintronics, the principal issue in the valley physics field is how to efficiently generate valley currents. Many proposals were studied to produce valley currents in the graphene system based on lattice strain [8,9], line defects [10,11], electric pump effect [12,13], optical excitation [14,15], etc.Corresponding to the spin Hall current [16] generated in semiconductor or metal materials due to the relativistic spinorbit interaction, the valley Hall current was also proposed in a gapped graphene [3], in which the low-energy spectrum of electrons exhibits an energy gap due to the introduced staggered potential between the two sublattices, and moreover the valley Hall conductivity is quantized when the Fermi energy resides in the energy gap. As is well known, the ordinary and effective method to produce spin currents is the ferromagnetic resonance effect excited by microwaves. Naturally, one may ask whether there is a similar valley resonance effect for valley currents in the two-dimensional graphenelike system and whether the pumped valley current is quantized or not.In this work, we study the possible valley resonance effect in graphene by introducing a time-dependent lattice distortion (TLD). In order to couple two inequivalent valleys, the TLD should have an atomic-scale periodic oscillation in space. Thus the excitation of optical phonon modes in graphene [17][18][19] meets such a TLD requirement as a typical example. We showed that the intervalley coupling enables the ...

Through the Higgs mechanism, the long-range Coulomb interaction eliminates the low-energy Goldstone phase mode in superconductors and transfers spectral weight all the way up to the plasma frequency. Here we show that the Higgs mechanism breaks down for length scales shorter than the superconducting coherence length while it stays intact, even at high energies, in the long-wavelength limit. This effect is a consequence of the composite nature of the Higgs field of superconductivity and the broken Lorentz invariance in a solid. Most importantly, the breakdown of the Higgs mechanism inside the superconducting coherence volume is crucial to ensure the stability of the BCS mean-field theory in the weak-coupling limit. We also show that changes in the gap equation due to plasmoninduced fluctuations can lead to significant corrections to the mean-field theory and reveal that changes in the density-fluctuation spectrum of a superconductor are not limited to the vicinity of the gap. arXiv:1711.11382v2 [cond-mat.supr-con]

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Energy transport can reveal information about interacting many-body systems beyond other transport probes.In particular, in one dimension it has been shown that the energy current is directly proportional to the central charge, thus revealing information about the degrees of freedom of critical systems. In this paper, we explicitly verify this result in two cases for translationally invariant systems based on explicit microscopic calculations. More importantly, we generalize the result to nontranslation invariant setups and use this to study a composite system of two subsystems possessing different central charges. We find a bottleneck effect, meaning the smaller central charge limits the energy transport.