Temperature-dependent many-body effects in Dirac-Weyl materials: Interacting compressibility and quasiparticle velocity

Abstract

We calculate, within the single-loop or equivalently the Hartree-Fock approximation (HFA), the finite-temperature interacting compressibility for three-dimensional (3D) Dirac materials and renormalized quasiparticle velocities for 3D and two-dimensional (2D) Dirac materials. We find that in the extrinsic (i.e., doped) system, the inverse compressibility (incompressibility) and renormalized quasiparticle velocity at k = 0 show nonmonotonic dependences on temperature. At low temperatures the incompressibility initially decreases to a shallow minimum with a T 2 ln T dependence. As the temperature increases further, the incompressibility rises to a maximum and beyond that it decreases with increasing temperature. On the other hand, the renormalized quasiparticle velocity at k = 0 for both 2D and 3D Dirac materials first increases with T 2 , rises to a maximum, and after reaching the maximum it decreases with increasing temperature. We also find that within the HFA, the leading-order temperature correction to the low-temperature renormalized extrinsic Fermi velocity for both 2D and 3D doped Dirac materials is ln(1/T ).

Thermal plasmon resonantly enhances electron scattering in Dirac/Weyl semimetals

“…Although non-interacting WSMs are already intriguing due to their nontrivial topological properties, the interaction effects in these materials are of great interest. In particular, inelastic electron-electron scattering is expected to be crucial for determining the conductivity [10,11] and spectral properties [18][19][20] of clean samples at low temperatures, which can be directly probed in transport and angle-resolved photoemission spectroscopy (ARPES)/scanning tunneling microscopy (STM) measurements, respectively.…”

The two-dimensional electron self-energy: Long-range Coulomb interaction

“…For ε T , the higher order self-energy corrections to the real part of the 2D self-energy go as O(ε 2 ) + O(ε 3 ln ε) + O(ε 3 )the appearance of the log here is again special to 2D systems. We also note that the full RPA low-energy and lowtemperature self-energy expression derived by us in this work does not suffer from the leading-order logarithmic corrections found in the Hartree-Fock theories [10,28]. The full analytical expressions (when ε ∼ T ) for the imaginary and real parts of the 2D self-energy, given in Eqs.…”

“…In other words, the imaginary part of the retarded self-energy Im Σ (R) (k, ε) should be much smaller compared with ε + Re Σ (R) (k, ε) at low energy ε in order to have well-defined quasiparticles, satisfying the Landau Fermi liquid paradigm. The electron self-energy is a crucial quantity, which determines not only the lifetime of the quasiparticles [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], but also their effective mass [17][18][19][20][21][22][23][24][25], the renormalization factor, and many other single particle properties [26][27][28][29]. It is well-established that for low T ( T F ) and |ε| ( E F ), Im Σ (R) (ε) goes as T 2 and ε 2 (up to logarithmic corrections) in threedimensional (3D) and two-dimensional (2D) Fermi systems, leading to the existence of well-defined 2D and 3D Landau Fermi liquids.…”

Breakdown of Fermi liquid theory in topological multi-Weyl semimetals

“…If one varies the temperature T , there is an analogous crossover between the FL and non-FL regimes: the system exhibits FL behavior at kT < µ and non-FL behavior kT > µ. We notice that the crossover from a usual FL state to a singular FL state, in which Z f approaches to a finite value in the lowest energy limit but the fermion velocity receives singular renormalization, has been studied in DSMs at finite chemical potential [80,81]. In the double-and triple-WSMs considered in this paper, the unconventional non-FL state always has observable effects as long as the chemical potential is not large enough, as explained in Sec.…”