2015/09/30 by Lukas Janssen, Igor F. Herbut · 1 citation
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Cold Atom Physics and Bose-Einstein Condensates #Combinatorics #Condensed matter physics #Gapless playback #Ground state #Mathematical physics #Mathematics #Order (exchange) #Parameterized complexity #Physics #Quantum mechanics #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el #hep-th
paper · pdf · doi:10.1103/physrevb.93.165109
published as Phys. Rev. B 93, 165109 (2016) · 6 pages, 1 figure, v2: section on experimental implications expanded, references added, published version
arxiv created 2016/04/06 · openalex publication_date 2016/04/06 · arxiv updated 2016/04/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Three-dimensional gapless semiconductors with quadratic band touching, such as HgTe, \ensuremathα-Sn, or Pr2Ir2O7, are believed to display a non-Fermi-liquid ground state due to long-range electron-electron interaction. We argue that this state is inherently unstable towards spontaneous formation of a (topological) excitonic insulator. The instability can be parameterized by a critical fermion number Nc. For N<Nc the rotational symmetry is spontaneously broken, the system develops a gap in the spectrum, and features a finite nematic order parameter. To leading order in the 1/N expansion and in the static approximation, the analogy with the problem of dynamical mass generation in (2+1)-dimensional quantum electrodynamics yields Nc=16/[3\ensuremathπ(\ensuremathπ\ensuremath-2)]. Taking the important dynamical screening effects into account, we find that Nc\ensuremath≥2.6(2) and therefore safely above the physical value of N=1. Some experimental consequences of the nematic ground state are discussed.