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 possible non-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 $\sqrt{H_{\perp }}$-type surface Shubnikov-de Haas (SdH) oscillation in in-plane surface transports as a function of a canted magnetic field $H_{\perp }$. Armed with these theoretical knowledge, we discuss implications of recent transport experiments on graphite under the high field.

arXiv comment25 pages, 11 figures; a discussion section (Sec. VIII) has been revised in the 2nd version

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Cited by in corpus (8)

• Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect
• Unconventional Hall response in the quantum limit of HfTe5
• Signatures of a magnetic-field-induced Lifshitz transition in the ultra-quantum limit of the topological semimetal ZrTe${}_5$
• Gap-opening transition in Dirac semimetal ZrTe${}_5$
• Field-induced multiple metal-insulator crossovers of correlated Dirac electrons of perovskite CaIrO${}_3$
• Wide critical fluctuations of the field-induced phase transition in graphite
• Magnetic-field-induced nonlinear transport in HfTe5
• Theory of phonon instabilities in Weyl semimetals at high magnetic fields