Plasmon signature in Dirac-Weyl liquids

Abstract

We consider theoretically as a function of temperature the plasmon mode arising in threedimensional Dirac liquids, i.e., systems with linear chiral relativistic single-particle dispersion, within the random phase approximation. We find that whereas no plasmon mode exists in the intrinsic (undoped) system at zero temperature, there is a well-defined finite-temperature plasmon with superlinear temperature dependence, rendering the plasmon dispersion widely tunable with temperature. The plasmon dispersion contains a logarithmic correction due to the ultraviolet-logarithmic renormalization of the electron charge, manifesting a fundamental many-body interaction effect as in quantum electrodynamics. The plasmon dispersion of the extrinsic (doped) system displays a minimum at finite temperature before it crosses over to the superlinear intrinsic behavior at higher temperature, implying that the high-temperature plasmon is a universal feature of Dirac liquids irrespective of doping. This striking characteristic temperature dependence of intrinsic Dirac plasmons along with the logarithmic renormalization is a unique manifestation of the three-dimensional relativistic Dirac nature of quasiparticle excitations and serves as an experimentally observable signature of three-dimensional Dirac materials. In Dirac semimetals the valence and conduction bands touch only in isolated points of the Brillouin zone with a Fermi energy that is tuned close to these band touching points, giving rise to particle excitations with an effective linear relativistic band dispersion ε ± (k) = ± v F k. Much of the interest in these novel materials stems from the topological properties of Weyl semimetals which are manifest in anomalous transport properties [1,2] and Fermi arc surface states [3]. Recent hallmark experiments have realized these materials in Cd 3 As 2 , Na 3 Bi, and TaAs and have demonstrated the Dirac cone structure in ARPES measurements [4][5][6][7][8][9] and detected topological surface states in Na 3 Bi and TaAs [9,10]. These initial experiments, which serve to verify the expected band structure, motivate the search for definitive experimental signatures of Dirac materials which establish unique observable effects distinct from standard electron gases and normal metals. In this Rapid Communication, we show that the collective charge oscillation of a Dirac liquid, the plasmon, is widely tunable as a superlinear function of temperature (with ∼ −T / ln T ), which allows us to extract high-precision information on the Dirac material. Moreover, the dispersion reveals a subtle logarithmic electron charge renormalization effect which is an additional specific signature of a three-dimensional Dirac system. Note that previous work exclusively studies the plasmon mode at zero temperature [11][12][13][14][15]. In this Rapid Communication, we establish a different mechanism for finite-temperature plasmons which arises due to the thermal excitation of electrons from the valence to the conduction band. It turns out that this interband mechanis...

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