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arXiv:1004.1806

Unconventional Fermi surface in two-dimensional systems of Dirac fermions

Jing-Rong Wang, Guo-Zhu Liu

Published Apr 11, 2010• 0 citations
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Abstract

At the low energy regime, the decay rate of two-dimensional massless Dirac fermions due to interactions can be written as $\mathrm{Im}Σ(ω) \propto |ω|^{x}$ at zero temperature. We find that the fermion system has: I) no sharp Fermi surface and no well-defined quasiparticle peak for $01$. In the presence of long-range gauge/Coulomb interaction or certain massless boson mode, the system exhibits unusual behavior belonging to class II.

DOI
10.48550/arxiv.1004.1806

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At the low energy regime, the decay rate of two-dimensional massless Dirac fermions due to interactions can be written as ImΣ(ω)∝∣ω∣x\mathrm{Im}Σ(ω) \propto |ω|^{x}ImΣ(ω)∝∣ω∣x at zero temperature. We find that the fermion system has: I) no sharp Fermi surface and no well-defined quasiparticle peak for 010101. In the presence of long-range gauge/Coulomb interaction or certain massless boson mode, the system exhibits unusual behavior belonging to class II.
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s -wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature vs. doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.
We show how strongly interacting two-dimensional Dirac fermions can be realized with ultracold atoms in a two-dimensional optical square lattice with an experimentally realistic, inherent gauge field, which breaks time-reversal and inversion symmetries. We find remarkable phenomena in a temperature range around a tenth of the Fermi-temperature, accessible with present experimental techniques: at zero chemical potential, besides a conventional s-wave superconducting phase, unconventional superconductivity with non-local bond pairing arises. In a temperature versus doping phase diagram, the unconventional superconducting phase exhibits a dome structure, reminiscent of the phase diagram for high-temperature superconductors and heavy fermions.
We analyze the form of the fermionic propagator for two-dimensional fermions interacting with massless overdamped bosons. Examples include a nematic and Ising ferromagnetic quantum-critical points and fermions at a half-filled Landau level. Fermi-liquid behavior in these systems is broken at criticality by a singular self-energy, but the Fermi surface remains well defined. These are strong-coupling problems with no expansion parameter other than the number of fermionic species, NNN. The two known limits, N⪢1N⪢1N⪢1 and N=0N=0N=0, show qualitatively different behavior of the fermionic propagator $G({ϵ}_{k},\ensuremath{\omega})$. In the first limit, $G({ϵ}_{k},\ensuremath{\omega})$ has a pole at some ϵk{ϵ}_{k}ϵk​; in the other it is analytic. We analyze the crossover between the two limits. We show that the pole survives for all NNN, but at small NNN it only exists in a range O(N2)O({N}^{2})O(N2) near the mass shell. At larger distances from the mass shell, the system evolves and $G({ϵ}_{k},\ensuremath{\omega})$ becomes regular. At N=0N=0N=0, the range where the pole exists collapses and $G({ϵ}_{k},\ensuremath{\omega})$ becomes regular everywhere.
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It is shown that certain analytical properties of the propagators of many-fermion systems lead rigorously to the existence of sharp discontinuities of the momentum distribution at absolute zero. This discontinuity in the momentum distribution is used to define a Fermi surface for a system of interacting fermions. It is shown that the volume of this surface in momentum space is unaffected by the interaction. The same analytic properties are shown to lead, by direct statistical mechanical arguments, to simple expressions for the low-temperature heat capacity, the spin paramagnetism, and the compressibility of the system. These expressions are very analogous to the corresponding expressions for noninteracting particles. Finally, it is shown how the whole formalism may be generalized when an external periodic potential is present (band case).