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Register a new userWeyl semimetal to metal phase transitions driven by quasiperiodic potentials
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We explore the stability of three-dimensional Weyl and Dirac semimetals subject to quasiperiodic potentials. We present numerical evidence that the semimetal is stable for weak quasiperiodic potentials, despite being unstable for weak random potentials. As the quasiperiodic potential strength increases, the semimetal transitions to a metal, then to an inverted semimetal, and then finally to a metal again. The semimetal and metal are distinguished by the density of states at the Weyl point, as well as by level statistics, transport, and the momentum-space structure of eigenstates near the Weyl point. The critical properties of the transitions in quasiperiodic systems differ from those in random systems: we do not find a clear critical scaling regime in energy; instead, at the quasiperiodic transitions, the density of states appears to jump abruptly (and discontinuously to within our resolution).
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We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three dimensional systems where absent disorder the non-interacting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a non-Fermi liquid phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled $epsilon$-expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. We find that the non-Fermi liquid fixed point is unstable to disorder, and demonstrate that the problem inevitably flows to strong coupling, outside the regime of applicability of the perturbative RG. An examination of the flow to strong coupling suggests that disorder is asymptotically more important than interactions, so that the low energy behavior of the system can be described by a non-interacting sigma model in the appropriate symmetry class (which depends on whether exact particle-hole symmetry is imposed on the problem). We close with a discussion of general principles unveiled by our analysis that dictate the interplay of disorder and Coulomb interactions in gapless semiconductors, and of connections to many-body localized systems with long-range interactions.
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