Quantum-lifetime control of the microwave-induced zero-resistance state in unidirectional lateral superlattices

The 2016 experiment of Bykov and co-workers produced the first microwave-induced zero-resistance state (ZRS) in a two-dimensional electron gas carrying a unidirectional periodic modulation (lateral superlattice), pinned to minima of the commensurability oscillations, and showed that the ZRS is destroyed as the modulation amplitude $V_0$ grows — a suppression the authors attribute to a reduction of the quantum lifetime $\tau_q$ through the Dingle factor. The problem remains open: $\tau_q(V_0)$ has still neither been measured nor calculated for any lateral superlattice (overlapping commensurability and Shubnikov–de Haas oscillations defeat the standard extraction methods, and the commensurability-envelope model fails for these samples); the microscopic mechanism by which the modulation alters $\tau_q$ is undetermined; and the microscopic origin of the ZRS itself remains contested across the displacement and inelastic frameworks and further alternative theories, even though the current-domain phenomenology of the ZRS has now been imaged directly. The objective is to give a quantitative, experimentally anchored microscopic account of how a unidirectional periodic potential controls $\tau_q$ and, through it, the microwave-induced zero-resistance state in high-mobility two-dimensional electron systems.

Background

A two-dimensional electron gas (2DEG) — electrons confined to the interface of a semiconductor heterostructure such as GaAs/AlAs — under a perpendicular static magnetic field $B$ and microwave irradiation at frequency $\omega$ develops oscillations of its longitudinal resistance that are periodic in $\omega/\omega_c$ (the ratio of the microwave frequency to the cyclotron frequency), called microwave-induced resistance oscillations (MIRO). At sufficiently high microwave power the oscillation minima deepen until the measured dc resistance vanishes: the zero-resistance state (ZRS), discovered experimentally in 2002–2003 in ultraclean GaAs 2DEGs. The ZRS is not superconductivity: the broadly accepted phenomenological picture is that microwave driving makes the diagonal conductivity negative in certain field windows, and the system then spontaneously breaks into domains of opposing internal Hall field (a current-domain state), so that the measured dc resistance is zero. The microscopic origin of the negative conductivity, however, remains unsettled more than two decades after discovery. The two workhorse microscopic frameworks are the displacement mechanism — impurity-assisted photon absorption shifts the guiding centers (the fixed centers about which cyclotron orbits oscillate) of electron orbits — and the inelastic mechanism, in which microwave heating modifies the electron distribution function; their relative contributions are still debated, and further alternatives keep being proposed: ponderomotive forces (radiation-pressure forces exerted by the microwave field on the electrons) near the current contacts, synchronization of the cyclotron phase with the microwave phase, Franck–Condon blockade (suppression of impurity scattering when radiation-driven wavefunctions of the Landau levels — the quantized cyclotron-orbit energy levels of electrons in a magnetic field — stop overlapping in space), and coherent-state effects.

Two lifetimes characterize disorder scattering in a 2DEG. The transport lifetime $\tau_{tr}$ weights the large-angle scattering events that relax current, while the quantum lifetime $\tau_q$ counts all elastic-scattering events and sets the Landau-level broadening; through the Dingle factor $\delta=\exp(-\pi/\omega_c\tau_q)$, it is $\tau_q$ that controls the amplitude of both Shubnikov–de Haas (SdH) oscillations (the quantum resistance oscillations periodic in $1/B$) and the microwave-induced corrections, whose amplitude scales roughly as $\delta^2$. The two lifetimes can differ by an order of magnitude when small-angle scattering dominates.

Imposing a one-dimensional periodic potential (period $a$, amplitude $V_0$, in mV) on the 2DEG — a unidirectional lateral superlattice (LSL), patterned by electron-beam lithography into metallic strip gates on top of the heterostructure — produces classical commensurability oscillations (CO, also called Weiss oscillations) of the magnetoresistance whenever the cyclotron diameter fits the modulation period, with minima at $2R_c/a=i-1/4$, where $R_c$ is the cyclotron radius and $i$ is an integer. The established method for extracting $\tau_q$ in an LSL is the CO-envelope analysis of Endo, Katsumoto, and Iye, which fits the magnetic-field damping of the CO.

In the experiment at the origin of this problem (Bykov et al., Applied Physics Letters 108, 012103 (2016)), LSLs with $a=200$ and $500\,\mathrm{nm}$ were defined on a GaAs/AlAs 2DEG of mobility $\approx210\,\mathrm{m^2/Vs}$ and density $n_e\approx7.9\times10^{15}\,\mathrm{m^{-2}}$, with $V_0$ tunable by the gate voltage. Under 110–150 GHz irradiation at $T=1.6\,\mathrm{K}$ the samples showed MIRO and — for the first time in any periodically modulated 2DEG — a ZRS, appearing at a minimum of the CO satisfying $2R_c/a=i-1/4$, in the qualitative direction predicted by the Iñarrea–Platero theory of microwave-driven Weiss oscillations. Raising $V_0$ from 0.17 to 0.21 mV suppressed and then destroyed the ZRS, while the transport lifetime decreased only from 78.7 to 73.7 ps — far too little to explain the suppression, which the authors therefore attribute to a reduction of $\tau_q$ through the Dingle factor. They could not quantify this: $\tau_q(V_0)$ can neither be calculated for these LSLs nor extracted from SdH data, because the CO and SdH oscillations overlap in the same field range and the observed CO amplitudes do not follow the available envelope model. The same collaboration had earlier shown that $\tau_q$ depends strongly on electron density in similar but unmodulated quantum wells, and the gate sweep also changes the density — a further ambiguity the authors themselves note.

Problem Statement

Give a quantitative, experimentally anchored microscopic account of how a unidirectional periodic potential controls the quantum lifetime and, through it, the microwave-induced zero-resistance state in high-mobility two-dimensional electron systems. The problem, motivated by the findings of Bykov et al. (2016) and left open by subsequent literature, has three deliverables in service of this single objective:

1. A determination of $\tau_q(V_0)$ for unidirectional lateral superlattices on high-mobility GaAs/AlAs 2DEGs — including its dependence on the period $a$ and the carrier density — by a theory that can be compared with experiment, and/or by an experimental protocol that extracts $\tau_q$ in the presence of overlapping commensurability and Shubnikov–de Haas oscillations, for which the standard CO-envelope analysis fails in these samples.
2. Identification and quantification of the microscopic mechanism by which the periodic modulation alters $\tau_q$, if at all, including its dependence on $a$, $V_0$, and carrier density, and of why any such reduction of $\tau_q$ proceeds much faster than the observed change in $\tau_{tr}$.
3. The incorporation of (1) and (2) into the description of MIRO and ZRS in modulated systems sufficiently to explain quantitatively the observed facts: the appearance of the ZRS at commensurability minima satisfying $2R_c/a=i-1/4$, and its suppression and disappearance as $V_0$ grows from 0.17 to 0.21 mV (145 GHz, 1.6 K, $a=200\,\mathrm{nm}$) while $\tau_{tr}$ changes by less than 10%.

The three deliverables are interrelated parts of one objective: (1) supplies the controlling parameter, (2) the mechanism, and (3) the confrontation with the ZRS phenomenology. A secondary, sample-specific sub-question flagged by the same authors — the origin of the weak negative magnetoresistance of these lateral-superlattice samples for $B>0.1\,\mathrm{T}$ — stands somewhat apart from the ZRS objective and does not have to be resolved together with it.

The field-level question of which microscopic mechanism generates the negative conductivity underlying the ZRS even in unmodulated 2DEGs is a famous still-open problem surrounding the findings of Bykov et al. (2016); the problem posed here is the modulated-system version of that question, in which the gate-tunable modulation amplitude supplies an additional experimental control that any candidate mechanism must survive.

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