A Symmetric Superconducting Dome Hosts Non-Fermi Liquid Behavior at Optimal Doping in MoS2

By employing a refined gating protocol to map a complete, symmetric superconducting dome in ionic liquid-gated MoS₂, this study reveals an anticorrelation between superconductivity and non-Fermi liquid behavior in the normal state, where scattering rates reach the Planckian limit, thereby offering new insights into the emergence of superconductivity in transition metal dichalcogenides.

The Gist

Imagine a thin, two-dimensional sheet of material called MoS2 (Molybdenum Disulfide). Think of this sheet as a tiny, flat dance floor for electrons. Normally, these electrons just shuffle around in a predictable, orderly way, like people walking in a straight line at a quiet library. This orderly behavior is what physicists call a "Fermi liquid."

However, scientists have discovered that if you can "tune" this dance floor just right, the electrons start behaving like a chaotic, energetic crowd at a mosh pit. This chaotic state is called a "non-Fermi liquid" or "strange metal." Even more surprisingly, when the electrons are in this chaotic state, they sometimes pair up and dance in perfect unison, creating superconductivity (electricity that flows with zero resistance).

Here is what this paper discovered, explained simply:

1. The "Dome" of Superconductivity

In the past, scientists could only see the beginning of the superconducting party. They could turn up the "volume" (add more electrons) to get the dance floor started, but they couldn't see what happened when they turned the volume up too high. The "party" seemed to fizzle out or disappear on the high-volume side.

In this study, the researchers used a special "remote control" called ionic liquid gating. Imagine this as a magical faucet that pours charged water (ions) onto the MoS2 sheet, pushing more and more electrons onto the dance floor. By refining how they used this faucet, they managed to turn the volume all the way up and all the way down.

The Discovery: They found a perfect, symmetrical "dome" shape.

• The Left Side (Underdoped): Not enough electrons; the superconductivity is weak.
• The Peak (Optimal Doping): Just the right amount of electrons; superconductivity is at its strongest (the "sweet spot").
• The Right Side (Overdoped): Too many electrons; the superconductivity gets weaker again.

Crucially, the left side and the right side look almost identical, like a perfect mirror image. This symmetry was a surprise and hadn't been clearly seen before in this material.

2. The "Chaotic" Connection

The most exciting part of the paper is what happens in the "normal" state (when the superconductivity isn't active).

Usually, when you add more electrons to a metal, it behaves more predictably. But here, the researchers found something strange:

• At the Peak: Right where the superconductivity is strongest, the electrons stop behaving like orderly library-goers. Instead, they behave like a strange metal. In this state, the resistance (friction) of the electrons increases in a straight line as the temperature goes up.
• The Scattering Rate: The electrons are bouncing around so fast and chaotically that they hit a fundamental speed limit known as the Planckian limit. Think of this as the "speed of chaos." The electrons are moving as fast as the laws of physics allow them to move before they lose their identity.

The Big Reveal: The paper shows that this "chaotic" behavior is anti-correlated with the superconductivity.

• When the electrons are most chaotic (at the peak), the superconductivity is strongest.
• When the electrons calm down and become orderly (on the sides of the dome), the superconductivity fades away.

3. Why Does This Happen? (The "Zig-Zag" Theory)

The paper offers a fascinating explanation for why this happens.

When the researchers poured the ionic liquid onto the MoS2, the positive ions didn't spread out evenly. Instead, at high voltages, they arranged themselves in a zig-zag pattern on top of the sheet.

• Imagine these ions as a row of fence posts.
• At the "sweet spot" (optimal doping), these fence posts create a pattern that traps some electrons in place while letting others move freely.
• This creates a mix of localized (stuck) and delocalized (free) electrons.
• The paper suggests that the "chaos" (non-Fermi liquid behavior) comes from the intense competition between these stuck electrons and the free ones. This competition creates the perfect conditions for the electrons to pair up and become superconductors.

Summary

This paper is like finding a missing piece of a puzzle. It shows that in MoS2, superconductivity isn't just a simple "on/off" switch. It is a delicate balance that exists right in the middle of a chaotic, high-energy state where electrons are moving at the absolute limit of speed. The fact that this behavior looks so much like the mysterious high-temperature superconductors found in other materials suggests that nature might be using the same "recipe" for superconductivity in very different materials.

Technical Summary

Technical Summary: A Symmetric Superconducting Dome Hosts Non-Fermi Liquid Behavior at Optimal Doping in MoS₂

Problem Statement
Transition metal dichalcogenides (TMDCs), particularly ionic liquid-gated MoS₂, exhibit phase diagrams strikingly similar to high-temperature superconductors (cuprates and iron-based superconductors), featuring a superconducting dome and non-monotonic dependence of the order parameter on carrier density. However, previous investigations into ionic liquid-gated TMDCs have been limited by two major gaps: (1) an incomplete mapping of the superconducting phase diagram, which typically captures only the underdoped regime and the vicinity of optimal doping while failing to reach the deep overdoped regime; and (2) a lack of detailed insights into the normal state properties, specifically regarding the presence of non-Fermi liquid (non-FL) behavior. These limitations have hindered a comprehensive comparison between TMDCs and high-Tc superconductors, preventing a full elucidation of the mechanisms driving superconductivity in these 2D systems.

Methodology
The authors employed a refined ionic liquid gating protocol using the electrolyte DEME-TFSI on etched MoS₂ flakes (~10 nm thick) patterned into standard Hall bar geometries. A critical aspect of their methodology was the systematic investigation of the relationship between gate voltage ($V_{ig}$) and carrier concentration ($n_{2D}$).

• Gating Optimization: The team identified that carrier concentration does not increase monotonically with gate voltage. Instead, it peaks at moderate voltages and decreases at higher voltages due to the formation of zig-zag distributed ions at the interface, which induce carrier localization. By keeping $V_{ig}$ below 4.5 V, they avoided the dominant localization regime while accessing high carrier densities.
• Transport Measurements: Electrical transport measurements were conducted in a cryostat (down to low temperatures) to map the superconducting transition temperature ($T_c$) across a wide range of $n_{2D}$ (from deep underdoped to deep overdoped).
• Normal State Analysis: The temperature dependence of resistance ($R-T$) was analyzed using power-law fitting ($R = R_0 + A \times T^\alpha$). To characterize the nature of the scattering, the authors analyzed the anisotropy between longitudinal resistivity ($\rho_{xx}$) and Hall angle ($\Theta_H$), and performed scaling analyses based on the extended Kohler's rule to test for multi-band contributions.
• Planckian Limit Estimation: The scattering rate was calculated using the Drude relation and compared against the Planckian dissipation limit ($\Gamma_P = k_B T / \hbar$) to determine if the system exhibited strange metal behavior.

Key Contributions and Results

1. Complete and Symmetric Superconducting Dome: The study successfully mapped a complete superconducting dome extending from the deep underdoped to the deep overdoped regime. The critical temperature ($T_c$) reached a maximum of ~10.21 K at an optimal carrier concentration of $n_{2D} \approx 12.1 \times 10^{13} \text{ cm}^{-2}$.

   • The dome is highly symmetric. The $T_c$ dependence on carrier concentration follows a square-root law, $T_c \propto |n_{2D} - n_c|^{0.52 \pm 0.05}$, on both the underdoped and overdoped sides. This contrasts with previous reports of highly asymmetric domes with long tails in the overdoped region.
   • The ratio $T_c/T_F$ (superconducting transition temperature to Fermi temperature) at optimal doping is approximately 0.006, a value consistent with unconventional superconductors like cuprates and iron-based systems.

2. Anticorrelated Non-Fermi Liquid Behavior: The normal state exhibits a distinct evolution of transport properties that is anticorrelated with the superconducting dome.

   • Exponent $\alpha$: The exponent $\alpha$ in the $R \propto T^\alpha$ relation displays a saddle-shaped profile. At the edges of the dome (underdoped and overdoped), $\alpha \approx 2$, indicating Fermi liquid (FL) behavior. At optimal doping, $\alpha \approx 1$, indicating linear-in-temperature resistance characteristic of non-FL or "strange metal" behavior.
   • Scattering Rate Anisotropy: Analysis of $\rho_{xx}$ and $\Theta_H$ revealed that while $\rho_{xx}$ is linear in $T$, $\cot \Theta_H$ is quadratic in $T$. Furthermore, scaling analysis using the extended Kohler's rule failed to collapse the Hall resistance data using parameters derived from magnetoresistance. This discrepancy confirms an anisotropy between longitudinal and transverse scattering rates, a hallmark of non-FL behavior, independent of multi-band effects.

3. Planckian Dissipation: The transport scattering rate in the optimally doped region was found to reach the Planckian limit. The dimensionless ratio $C = \Gamma / \Gamma_P$ was calculated to be approximately 1.2 in two different devices. This suggests that the dissipation in the normal state is limited by fundamental quantum mechanical constraints rather than conventional electron-phonon or impurity scattering mechanisms.

Significance and Claims
The paper argues that the emergence of a symmetric superconducting dome coupled with Planckian-limited, non-Fermi liquid transport in the normal state suggests that the physics of ionic liquid-gated MoS₂ extends beyond simple electron-phonon interaction scenarios.

• Connection to High-Tc Superconductors: The observed phenomenology—specifically the symmetric dome, the square-root dependence of $T_c$, and the coexistence of strange metal behavior with superconductivity—strongly parallels that of high-Tc cuprates and iron-based superconductors.
• Role of Localization: The authors propose that the ionic liquid gating induces a localized-delocalized transition. At high gate voltages, zig-zag ion distributions create a periodic potential that localizes electrons. The optimal doping point corresponds to a regime where electrons are on the verge of strong localization, creating a mixture of localized and delocalized states. This competition may drive the system toward a quantum critical point, fostering the observed non-FL behavior and superconductivity.
• Implications: These findings advance the understanding of the resemblance between TMDCs and high-Tc superconductors, suggesting that ionic liquid gating can be used to engineer exotic quantum states by modulating the strength of electron localization. The results provide a more complete phase diagram that facilitates a detailed cross-check between 2D TMDCs and other unconventional superconducting families.