Scaling behavior of electron decoherence in a graphene Mach-Zehnder interferometer

The field of electron quantum optics explores the analogy between electron behavior in quantum conductors and photons in quantum optics. Two-dimensional conductors in the quantum Hall effect regime, achieved under strong perpendicular magnetic fields, are key systems. These systems feature one-dimensional, chiral, dissipationless edge channels, analogous to optical fibers for electrons. Much research has used GaAs/AlGaAs heterostructures, but decoherence from various sources (edge reconstruction, intra-channel Coulomb interactions, inter-channel Coulomb interactions) limits advanced quantum manipulations. This work investigates graphene as an alternative, aiming to explore regimes where decoherence is significantly reduced. Graphene's different intrinsic parameters (electron velocity, capacitive coupling, screening, geometry) compared to GaAs offer a unique opportunity to gain a comprehensive understanding of decoherence mechanisms. The study focuses on probing decoherence in a graphene PN junction Mach-Zehnder interferometer in the quantum Hall regime, where decoherence energy scales are significantly higher than in GaAs/AlGaAs systems. The researchers hypothesized that graphene would allow the observation of a universal behavior in the temperature dependence of interference, with a potential focus on intra-channel Coulomb interactions as the primary decoherence source.

Previous studies on electron quantum optics using GaAs/AlGaAs heterostructures have identified several sources of decoherence, including edge reconstruction due to disorder, intra-channel Coulomb interactions within a single edge channel, and inter-channel Coulomb interactions between adjacent channels. The latter has been highlighted as a major obstacle in creating complex quantum circuits. While efforts have been made to mitigate inter-channel interactions through engineering of the edge channels, identifying and understanding decoherence sources remains a challenge. Existing experimental observations and interpretations remain debated. The use of different 2D materials, such as graphene, offers a promising avenue for investigating these phenomena by providing a system with similar characteristics but with distinct intrinsic parameters. Prior work on graphene Mach-Zehnder interferometers has demonstrated the feasibility of such devices, laying the foundation for the current investigation.

The researchers fabricated a graphene Mach-Zehnder interferometer using a PN junction. A monolayer of graphene, encapsulated by hexagonal boron nitride layers, had its electron density controlled independently in left and right halves via top and bottom gates. Under a perpendicular magnetic field, a P region (filling factor ν = -1) and an N region (νN = 2) were formed. Three co-propagating channels existed at the junction interface. The interferometer was formed by applying gate voltages to create beam splitters. The transmission probability (TMZ = IT/(I0/2)) was measured as a function of magnetic field and temperature, for three different interferometer configurations: a "large" interferometer (ν1 = ν2 = -1, L ≈ 1.5 μm), an "intermediate" interferometer (ν1 = -1, ν2 = 0 or vice versa, L ≈ 1.05 μm), and a "small" interferometer (ν1 = 0, ν2 = 0, L ≈ 0.62 μm). Interference visibility (Vis = (TMZ,max - TMZ,min)/(TMZ,max + TMZ,min)) was analyzed as a function of temperature and bias voltage. The electron temperature was determined using Johnson-Nyquist noise measurements to rule out heating effects. An intra-channel interaction model based on a simple capacitive Hamiltonian was used to compare with experimental findings. This model accounts for charge density fluctuations within the interferometer arms, providing a mechanism for decoherence. The researchers also investigated the influence of inter-channel interactions by varying the filling factors and analyzing the visibility decay. Finally, the bias voltage dependence of the visibility (lobe pattern) was studied by varying the current injection point (from the N or P region) and comparing the results.

The study revealed a remarkable scaling behavior in the thermal decoherence of the graphene Mach-Zehnder interferometer. The interference visibility exhibited a universal crossover from exponential decay at higher temperatures to algebraic decay at lower temperatures, with the crossover temperature inversely proportional to the interferometer length. This scaling behavior was consistent across all three interferometer configurations. This indicates that the decoherence is not solely determined by length and temperature independently but rather their product. The algebraic decay at low temperatures signifies a suppression of thermal decoherence, a phenomenon not previously observed in GaAs interferometers. Johnson-Nyquist noise measurements confirmed that the observed behavior was not due to electron heating. Analysis of the visibility's dependence on filling factor indicated that inter-channel interactions played a negligible role in the decoherence, unlike in GaAs systems. The weak dependence of the lobe pattern (visibility's dependence on bias voltage) on the current injection point further supported the dominance of intra-channel interactions as the primary decoherence mechanism. The intra-channel interaction model accurately captured the observed scaling behavior and the crossover from algebraic to exponential decay, validating the researchers' interpretation. The coherence length extracted from the exponential decay regime was 1.24 μm at 1 K, considerably larger than in GaAs systems.

The findings demonstrate that graphene offers a unique platform to study electron interferometry in regimes where decoherence is significantly suppressed. The observed scaling behavior of thermal decoherence, with its universal crossover from exponential to algebraic decay, provides strong evidence for the dominance of intra-channel Coulomb interactions as the primary decoherence mechanism in this system. This contrasts sharply with GaAs interferometers, where inter-channel interactions often dominate. The suppression of decoherence at low temperatures, evidenced by the algebraic decay, opens exciting possibilities for building more complex quantum circuits and devices. The close proximity of the top and bottom gates to the graphene layer likely contributes to the screening of inter-channel interactions, further contributing to the observed low decoherence.

This study provides compelling evidence for the superior coherence properties of graphene-based Mach-Zehnder interferometers compared to their GaAs counterparts. The observed scaling behavior and suppression of decoherence at low temperatures highlight the potential of graphene for realizing advanced quantum information processing technologies. Future research could explore the application of these findings to the development of flying qubits, orbital entanglement generation, and valleytronics. Further investigation into the specific microscopic mechanisms underlying intra-channel interactions in graphene could enhance the design and control of future devices.

While the study effectively demonstrates the scaling behavior of decoherence and the dominance of intra-channel interactions, the exact physical origin of the algebraic decay at low temperatures warrants further investigation. Also, the reasons for the observed maximum visibility of only 60% remain unclear. More detailed theoretical models accounting for more subtle effects or experimental variations could provide a more complete description. Finally, the study was limited to a specific type of graphene (NGS graphenium flakes) and further studies using other graphene samples are needed to generalize the findings.