Microscopic theory of radiation-induced zero-conductance states in the nondegenerate two-dimensional electron system on liquid helium

In the nondegenerate two-dimensional electron system (2DES) formed by surface-state electrons on liquid helium, resonant intersubband microwave excitation in a perpendicular magnetic field produces giant magnetoconductivity oscillations which, below approximately 0.3 K at high radiation power, collapse into states with vanishing longitudinal conductivity. These zero-conductance states are accompanied by magnetic-field-sweep hysteresis, a strong resonant photovoltaic redistribution of the electron density, self-generated audio-frequency oscillations, and incompressible states in which the density is pinned to a fixed value independent of the confining potential. The mechanism of the oscillations themselves is now understood (a nonequilibrium population of the excited surface subband combined with quasielastic intersubband scattering into Landau levels, producing sign-changing conductivity terms and absolute negative conductivity), but the stabilization mechanism and internal spatial structure of the zero-conductance state in this strongly correlated, impurity-free Coulomb liquid, the mechanism selecting the pinned incompressible density, and the quantitative role of electron heating remain unresolved.

Background

Electrons trapped above the free surface of liquid helium form a model two-dimensional electron system that is the classical, nondegenerate counterpart of semiconductor 2D electron gases. An electron is bound above the liquid by its image potential and a repulsive barrier at the surface; a pressing electric field $E_{\perp}$ tunes the binding. The motion perpendicular to the surface is quantized into discrete 'surface subbands' with energies $\epsilon_n$, and the intersubband transition frequency $\omega_{21}=(\epsilon_2-\epsilon_1)/\hbar$ lies in the millimeter-wave range and can be tuned through the linear Stark shift by $E_{\perp}$. In a perpendicular magnetic field $B$ the in-plane motion is Landau-quantized into levels $\hbar\omega_c(l+1/2)$, where $\omega_c=eB/m_{\mathrm{e}}$ with the free electron mass $m_{\mathrm{e}}$; these levels are broadened only by collisions with helium vapor atoms (dominant above roughly 0.3 K on liquid $^3$He) or with ripplons — the quantized capillary waves of the surface, dominant below about 0.3 K — because the system contains no disorder or impurities at all. Since the low achievable densities ($n_s\sim10^6$–$10^7$ cm$^{-2}$) together with the free-electron mass make the Fermi temperature tiny, the electron gas is nondegenerate and strongly Coulomb-correlated: the mean Coulomb energy exceeds the kinetic energy, and at low enough temperature the gas forms a Wigner solid. In this system the longitudinal conductivity $\sigma_{xx}$ is measured by capacitive coupling to a Corbino disk (the Sommer–Tanner technique), so $\sigma_{xx}$, rather than resistivity, is the primary observable.

In high-mobility GaAs/AlGaAs heterostructures, microwave radiation produces microwave-induced resistance oscillations (MIRO), periodic in $B^{-1}$ and governed by the ratio $\omega/\omega_c$ of microwave to cyclotron frequency, whose minima deepen at high power into zero-resistance states (ZRS). The prevailing theoretical picture is that photon-assisted scattering of electrons off disorder generates absolute negative conductivity (ANC, a negative dc dissipative conductivity), which is unstable and stabilizes through the formation of current domains; the microscopic nature of semiconductor ZRS nevertheless remains debated (reviewed by Dmitriev, Mirlin, Polyakov and Zudov, Rev. Mod. Phys. 84, 1709 (2012)).

Konstantinov and Kono (Phys. Rev. Lett. 103, 266808 (2009)) discovered the helium counterpart of this phenomenon: magnetoconductivity oscillations of surface-state electrons on liquid $^3$He induced by resonant intersubband excitation, originating from quasielastic scattering of the microwave-excited electrons into the collision-broadened Landau levels of the first subband, with the oscillation structure affected both by the Landau-level broadening and by the many-electron fluctuating in-plane electric field produced by the Coulomb interaction. The companion experiment (Phys. Rev. Lett. 105, 226801 (2010)) showed that below approximately 0.3 K and at high microwave power the oscillation minima collapse into states with vanishing $\sigma_{xx}$, exhibiting hysteresis in magnetic-field sweeps; the authors noted that the effect 'may be related' to the zero-resistance states of degenerate semiconductor 2D electron systems and that the role of electron heating 'requires further investigation'. Subsequent experiments established that the zero-conductance regime is accompanied by a resonant photovoltaic effect with a strong in-plane redistribution of the electron density (J. Phys. Soc. Jpn. 81, 093601 (2012)), by self-generated audio-frequency oscillations (J. Phys. Soc. Jpn. 82, 075002 (2013)), and by incompressible states in which the electron density is pinned to a fixed value independent of both the confining potential and the initial density (Chepelianskii et al., Nat. Commun. 6, 7210 (2015)).

On the theory side, Monarkha's series of papers (Low Temp. Phys. 37, 90 and 655 (2011); 38, 451 (2012)) established the oscillation mechanism: resonant excitation creates a nonequilibrium population of the first excited subband, and quasielastic intersubband scattering — which, unlike semiconductor MIRO, does not involve photon absorption in the scattering event — produces sign-changing corrections to $\sigma_{xx}$ that can turn negative. This intersubband theory accounts quantitatively for the observed oscillations, including their Coulomb-interaction dependence verified experimentally (Phys. Rev. Lett. 111, 266802 (2013)) and their circular-polarization dependence (Phys. Rev. Lett. 120, 046802 (2018)). What is not settled is how the state with negative conductivity is stabilized in this strongly correlated liquid: the current-domain stabilization argued for semiconductor ZRS is considered unlikely here because the system is close to Wigner crystallization, and Monarkha instead proposed stabilization by density domains bounded by two critical densities $n_L$ and $n_H$ (Low Temp. Phys. 42, 441 (2016)). The 2019 review by Monarkha and Konstantinov (J. Low Temp. Phys. 197, 208) endorses this picture as plausible while stating explicitly that 'the internal structure of the ZRS of SE on liquid helium requires an additional investigation', that the mechanism selecting the particular pinned density value 'was not explained', and that the observed hysteresis 'can be caused by decay heating of SE, which requires an additional theoretical investigation in the ripplon dominated scattering regime'.

Problem Statement

Establish the microscopic theory of the radiation-induced zero-conductance states of the nondegenerate, strongly correlated two-dimensional electron system on liquid helium under resonant intersubband microwave excitation — the problem left open by the 2009–2010 experiments of Konstantinov and Kono and their successors. Specifically, determine: (a) the stabilization mechanism and internal spatial structure of the state with vanishing longitudinal conductivity $\sigma_{xx}\to0$ that forms below approximately 0.3 K at high microwave power — whether it is a density-domain pattern (and if so its structure, domain-wall properties, critical densities and dynamics), a nonlinear-conductivity-stabilized configuration, an edge/current-state phenomenon, or another state — recognizing that the current-domain stabilization argued for semiconductor zero-resistance states is expected to fail in this Coulomb liquid close to Wigner crystallization (the freezing of the electron liquid into a lattice stabilized by Coulomb repulsion); (b) the origin of the incompressible states (states whose density is pinned and no longer responds to the confining potential) observed in compressibility measurements, in particular the mechanism that selects and pins the observed density values (such as $n_c\approx3.4\times10^6$ cm$^{-2}$), how these values depend on the conductivity-minimum index $m$ — the integer labeling the conductivity minima, which occur near $\omega_{21}/\omega_c\simeq m+1/4$, where $\omega_{21}$ is the intersubband transition frequency and $\omega_c$ the cyclotron frequency (the level-matching points, where the Landau-level ladders of the two surface subbands align, lie a quarter step below the conductivity minima in $\omega_{21}/\omega_c$, at integer values of that ratio) —, and why the primary plateau value is independent of the total electron number $N_e$; and (c) the steady-state electron temperature $T_e$ under resonant drive as a function of electron density, magnetic field, and microwave power in both scattering regimes — collisions with helium vapor atoms above roughly 0.3 K and with ripplons (the quantized capillary waves of the helium surface) below it — so that heating-induced Landau-level smearing and its role in the observed magnetic-field-sweep hysteresis can be quantitatively separated from collision-broadening and many-electron effects. These three targets are each independently required components of one objective — a complete microscopic account of the nonequilibrium state of the photo-excited Coulomb liquid on helium — and they are jointly sufficient when the derived $\sigma_{xx}(B,n_s,T,P)$, the zero-conductance field intervals, the stabilized density profile, and the hysteresis are all quantitatively consistent, within the experimental resolution reported in those works, with the corresponding published experimental datasets: the magnetoconductance measurements of Refs. 1, 2, 19 and 20, the photovoltaic and self-generated-oscillation measurements of Refs. 6 and 7, and the compressibility measurements of Ref. 9. Resolving only a proper subset of (a)–(c) leaves the remaining components open and does not resolve the task.

References

1. D. Konstantinov and K. Kono, 'Novel Radiation-Induced Magnetoresistance Oscillations in a Nondegenerate Two-Dimensional Electron System on Liquid Helium', Phys. Rev. Lett. 103, 266808 (2009). DOI: 10.1103/PhysRevLett.103.266808, https://doi.org/10.1103/PhysRevLett.103.266808 (preprint arXiv:0910.3040, https://arxiv.org/abs/0910.3040)
2. D. Konstantinov and K. Kono, 'Photon-induced vanishing of magnetoconductance in 2D electrons on liquid helium', Phys. Rev. Lett. 105, 226801 (2010). DOI: 10.1103/PhysRevLett.105.226801, https://doi.org/10.1103/PhysRevLett.105.226801 (preprint arXiv:1006.0349, https://arxiv.org/abs/1006.0349)
3. Yu. P. Monarkha, 'Microwave-induced magnetooscillations and absolute negative conductivity in the multisubband two-dimensional electron system on liquid helium', Low Temp. Phys. 37, 90 (2011). DOI: 10.1063/1.3552915, https://doi.org/10.1063/1.3552915
4. Yu. P. Monarkha, 'Microwave-resonance-induced magnetooscillations and vanishing resistance states in multisubband two-dimensional electron systems', Low Temp. Phys. 37, 655 (2011). DOI: 10.1063/1.3652923, https://doi.org/10.1063/1.3652923
5. Yu. P. Monarkha, 'Coulombic effects on magnetoconductivity oscillations induced by microwave excitation in multisubband two-dimensional electron systems', Low Temp. Phys. 38, 451 (2012). DOI: 10.1063/1.4723658, https://doi.org/10.1063/1.4723658
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7. D. Konstantinov, M. Watanabe, and K. Kono, 'Self-Generated Audio-Frequency Oscillations in 2D Electrons with Nonequilibrium Carrier Distribution on Liquid Helium', J. Phys. Soc. Jpn. 82, 075002 (2013). DOI: 10.7566/JPSJ.82.075002, https://doi.org/10.7566/JPSJ.82.075002
8. D. Konstantinov, Yu. Monarkha, and K. Kono, 'Effect of Coulomb Interaction on Microwave-Induced Magnetoconductivity Oscillations of Surface Electrons on Liquid Helium', Phys. Rev. Lett. 111, 266802 (2013). DOI: 10.1103/PhysRevLett.111.266802, https://doi.org/10.1103/PhysRevLett.111.266802
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17. Yu. P. Monarkha, 'Quantum oscillations induced by heating electrons on Rydberg states at the surface of superfluid 4He', Low Temp. Phys. 52, 269 (2026). DOI: 10.1063/10.0042664, https://doi.org/10.1063/10.0042664
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