Interactions-controlled magnetotransport in two-dimensional massless-massive fermion mixtures

TL;DR

This work demonstrates that interparticle Coulomb interactions in a 2D HgTe-based semimetal, which hosts coexisting Dirac (massless) and massive holes, generate temperature- and magnetic-field-dependent corrections to magnetotransport by breaking Galilean invariance. A Boltzmann-transport treatment reveals that massless Dirac holes alone yield finite corrections to magnetoconductivity but not to magnetoresistivity or the Hall effect at leading order, whereas the presence of both Dirac and massive holes produces finite corrections across magnetoconductivity, magnetoresistivity, and Hall response. The temperature dependence of these corrections depends on the interaction range: for massless holes, $\sigma_0^D(T) o T^4\ln(\mu/T)$ for short-range and $\sim T^2$ for unscreened Coulomb; in the massless-massive mixture, corrections scale as $\sim T^2$ (short-range) or $\sim T^2\ln(1/T)$ (Coulomb). A strong magnetic field suppresses these interaction-induced corrections, and the results highlight how intercomponent scattering in a two-band 2D system can strongly modify transport, offering a route to detect interaction effects in HgTe QWs and related layered materials.

Abstract

The presence of two types of holes, namely the Dirac holes and the massive holes, in a two-dimensional sample exposed to an external permanent magnetic field leads to the emergence of the temperature and magnetic field-dependent contribution to the resistivity due to their interactions. Taking a HgTe-based two-dimensional semimetal as a testbed, we develop a theoretical model describing the role of interactions between the degenerate massive and massless Dirac particles for the magnetoconductivity and resistivity in the presence of a classical magnetic field. If only the Dirac holes are present in the system, the magnetoconductivity acquires a finite interaction-induced contribution, which would vanish for the parabolic spectrum. It demonstrates $T^4\ln(1/T)$ behavior at low temperatures for short-range interhole interaction potential, and $T^2$-like behavior in the case of long-range interhole interaction potential. However, the magnetoresistivity and the Hall effect are not affected by the Dirac holes interparticle correlations in the lowest order of interparticle interaction. In contrast to this, the presence of two types of holes provides a finite contribution to the magnetoconductivity, magnetoresistivity, and the classical Hall effect resistivity. The temperature behavior of the magnetoconductivity here is $\sim T^2$ in the case of the short-range constant interparticle interaction potential and $T^2\ln(1/T)$ for the bare unscreened Coulomb interaction. A classically strong magnetic field suppresses the interaction-induced corrections to magnetoresistivity of massless-massive hole gas mixture.

Figures (6)

• Figure 1: Band structure of a 2D gas containing Dirac particles and massive particles. Red domain of the dispersion corresponds to the electron-like excitations, whereas the blue domain indicates the hole-like excitations of the system. Green (dashed) horizontal lines indicate three different regimes under study. The chemical potentials $\mu_1$ and $\mu_2$ correspond to the exciting of only degenerate massless electron or hole Fermi gas, respectively. The position of $\mu_3$ represents a degenerate massive-massless Fermi gas mixture (given $\mu_3-\Delta\gg T$). The right-hand side panel shows a schematic of relative positions of two hole and electron valleys: the blue circles correspond to the holes with a quadratic dispersion, and the red one is either for the Dirac electrons or Dirac holes with a linear dispersion.
• Figure 2: Temperature dependence of the correction to the massless Dirac hole conductivity. Left panel: short-range interaction potential between holes, $\sigma_0^D$ exhibits a $T^4 \ln(\mu/T)$ behavior; right panel: long-range Coulomb potential, $\sigma_0^D\sim T^2$. The following parameters for a typical HgTe structures were used: Fermi velocity $v = 7 \times 10^5$ m/s, effective mass $m = 0.15m_e$ (with $m_e$ the free electron mass), dielectric constant $\epsilon = 10$, momentum relaxation time $\tau = 100$ fs, and chemical potential $\mu = 10$ meV.
• Figure 3: The massless Dirac hole longitudinal magnetoconductivity $\delta\sigma_{xx}$ and transverse magnetoconductivity $\delta\sigma_{xy}$ as functions of the magnetic field for the case of short-range interaction potential. The following parameters were used in the calculations: $T=40$ K, Dirac hole density $N_d = 1.9 \times 10^{14}$ cm$^{-2}$, massive hole density $N_h = 3.2 \times 10^{15}$ cm$^{-2}$. Other parameters are the same as in Fig. \ref{['Fig2']}
• Figure 4: The magnetoelectric conductivity correction for massless holes $\delta\sigma_{xx,yx}^{D}$ due to scattering massless holes off massive ones (top panels) and massive holes $\delta\sigma_{xx,yx}^{h}$ due to the scattering massive holes off massless ones (bottom panels) as functions of the magnetic field at different temperatures: 10 K (blue), 20 K (red), and 30 K (green). Here, $\beta=\tau_p m v/(\tau_k p_0)$ characterizes the ratio of the relaxation times and velocities for the holes, and $\tilde{g}=g_{s}^{D} g_{v}^{D} g_{s}^{h} g_{v}^{h}=8$, with $g_{s}^{h}=2$ and $g_{v}^{h}=2$. Parameters: the Dirac hole density and the massive hole density are the same as in Fig. \ref{['Fig3']}; Dirac hole mobility $\mu_d=24$ m$^2$/V$\cdot$s; massive hole mobility $\mu_h=1.3$ m$^2$/V$\cdot$s; the short-range (contact) interaction potential $U_0 = 2\pi e^2/(\epsilon q_s)$ with the screening wave-vector $q_s$. Other parameters are the same as in previous plots.
• Figure 5: Comparison of interaction-induced corrections to magnetoconductivity for the (i) pure Dirac hole gas (upper panels, Eq. \ref{['nregime8']}), and (ii) massive-massless hole gas mixture (lower panels, sum of Eqs. \ref{['masslessholes']} and Eqs. \ref{['massiveholes']}) for the temperatures 10 K (blue), 20 K (red), and 30 K (green) calculated for short-range interhole interacting potential.