Ground-state atlas of a three-dimensional semimetal in the quantum limit

Abstract

An interplay between electron correlation and reduced dimensionality due to the Landau quantization gives rise to exotic electronic phases in three-dimensional semimetals under high magnetic field. Using an unbiased theoretical method, we clarify for the first time comprehensive ground-state phase diagrams of a three-dimensional semimetal with a pair of electron and hole pockets in the quantum limit. For the electron interaction, we consider either screened Coulomb repulsive interaction or an attractive electron-electron interaction mediated by a screened electron-phonon coupling, where a screening length is generally given by a dimensionless constant times magnetic length l. By solving the parquet RG equation numerically and employing a mean-field argument, we construct comprehensive ground-state phase diagrams of the semimetal in the quantum limit for these two cases, as a function of the Fermi wave length and the screening length (both normalized by l). In the repulsive interaction case, the ground state is either excitonic insulator (EI) in strong screening regime or Ising-type spin density wave in weak screening regime. In the attractive interaction case, the ground state is either EI that breaks the translational symmetries (strong screening regime), topological EI, charge Wigner crystal (intermediate screening regime), plain charge density wave or marginal Fermi liquid (weak screening regime). We show that the topological EI supports a single copy of massless Dirac fermion at its side surface, and thereby exhibit a √ H ⊥ -type surface Shubnikov-de Haas (SdH) oscillation in in-plane surface transports as a function of a canted magnetic field H ⊥ . Armed with these theoretical knowledge, we discuss implications of recent transport experiments on graphite under the high field.

Unconventional Hall response in the quantum limit of HfTe5

“…Nevertheless, it has been predicted that a generalized version of the QHE can emerge in 3D electron systems that exhibit a periodically modulated superstructure [6][7][8] . Analogous to as in two dimensions, in the vicinity of the quantum limit, 3D electron systems are also prone to form a variety of correlated electron states, including Luttinger liquids; charge, spin and valley density waves; excitonic insulators; Hall and Wigner crystals; or staging transitions in the case of highly anisotropic layered systems 3,4,6,[9][10][11][12][13] . It has been theoretically pointed out that some of these states are related to quantum Hall physics in three dimensions and likewise could manifest themselves in a Hall response that should be observable in the quantum limit of 3D semimetals 10,13,14 .…”

Theory of phonon instabilities in Weyl semimetals at high magnetic fields

“…The nonadiabatic regime has also been addressed in Ref. [35], albeit for a different model of semimetal with spin-polarized electron and hole bands in the quantum limit. In that paper, an attractive electron-electron interaction mediated by a screened electron-phonon coupling have been considered, and phases such as an excitonic insulator, charge Wigner crystal and charge-density wave have been predicted using a parquet renormalization group analysis.…”

“…From a purely theoretical point of view, much of the existing effort has been directed specifically towards examining the effect of electronic interactions in threedimensional semimetals at high fields 21,[34][35][36][37][38][39] . In this context, the appearance of a chiral symmetry-breaking, fully gapped charge-density wave (CDW) order, even for sufficiently weak repulsive electron-electron interactions, for topological Dirac and Weyl semimetals has been discussed in the literature 34,[36][37][38][39] .…”

Field-induced multiple metal-insulator crossovers of correlated Dirac electrons of perovskite CaIrO$_3$

“…Electrons in the lowest Landau level with the index n=0 are confined in a scale of magnetic length l B = /eB within a plane perpendicular to the magnetic field, whereas the momentum along the magnetic field is preserved. Previous the-oretical studies proposed that various nontrivial phases such as the axion charge density wave (CDW) and excitonic insulator are induced, if the QL of the Dirac/Weyl electron can be realized in materials with the strong electron correlation [9][10][11]. However, the experimental realization of quantum limit in the strongly correlated electron material is a challenge, and hence the emergence of collective ordering and/or liquid of high-mobility relativistic electron has rarely been demonstrated so far.…”