[Paper Review] Electronic anisotropy in magic-angle twisted trilayer graphene

Naiyuan J. Zhang, Yibang Wang+4 more|arXiv (Cornell University)|Nov 2, 2022

Graphene research and applications4 citations

TL;DR

This study establishes the first experimental link between electronic anisotropy and the Coulomb-driven cascade of isospin transitions in magic-angle twisted trilayer graphene using angle-resolved transport measurements (ARTM) in a 'sunflower' device geometry. It reveals that electron anisotropy is strongly tied to both the cascade phenomenon near integer fillings and a novel $PT$-symmetry-breaking state at low temperatures, with anisotropy suppressed when $PT$ breaking is absent.

ABSTRACT

Due to its potential connection with nematicity, electronic anisotropy has been the subject of intense research effort on a wide variety of material platforms. The emergence of spatial anisotropy not only offers a characterization of material properties of metallic phases, which cannot be accessed via conventional transport techniques, but it also provides a unique window into the interplay between Coulomb interaction and broken symmetry underlying the electronic order. In this work, we utilize a new scheme of angle-resolved transport measurement (ARTM) to characterize electron anisotropy in magic-angle twisted trilayer graphene. By analyzing the dependence of spatial anisotropy on moiré band filling, temperature and twist angle, we establish the first experimental link between electron anisotropy and the cascade phenomenon, where Coulomb interaction drives a number of isospin transitions near commensurate band fillings. Furthermore, we report the coexistence between electron anisotropy and a novel electronic order that breaks both parity and time reversal symmetry. Combined, the link between electron anisotropy, cascade phenomenon and PT-symmetry breaking sheds new light onto the nature of electronic order in magic-angle graphene moiré systems.

Motivation & Objective

• To establish a direct experimental connection between electronic anisotropy and the cascade of isospin transitions driven by strong Coulomb interactions in magic-angle twisted trilayer graphene.
• To disentangle the role of Coulomb interaction from strain and twist inhomogeneity in inducing electronic anisotropy.
• To probe the nature of low-temperature electronic order by correlating anisotropy with nonreciprocal transport responses.
• To characterize spatially uniform electronic anisotropy using a novel 'sunflower' geometry device for enhanced resolution.

Proposed method

• Employed angle-resolved transport measurements (ARTM) on a 'sunflower'-shaped device with eight contacts to map the angular dependence of longitudinal resistance $R_{\parallel}(\phi)$.
• Used two current bias configurations (I and II) to extract the full conductivity tensor and distinguish between intrinsic anisotropy and extrinsic effects like strain.
• Applied a circular sample geometry (~2 μm diameter) to minimize spatial inhomogeneity from twist angle variations.
• Analyzed the angular dependence of $R_{\parallel}(\phi)$ to identify nematic order and detect director axis rotation with doping and temperature.
• Correlated anisotropy with nonreciprocal transport responses to identify $PT$-symmetry-breaking order at $T < 5$ K.
• Systematically varied moiré band filling, temperature, and twist angle to isolate the influence of Coulomb interaction on anisotropy.

Experimental results

Research questions

• RQ1 Does electronic anisotropy in magic-angle twisted trilayer graphene correlate with the cascade of isospin transitions driven by Coulomb interactions near integer band fillings?
• RQ2 How does the orientation and magnitude of electron anisotropy depend on moiré band filling and temperature?
• RQ3 Is the observed electron anisotropy primarily driven by Coulomb interaction or by extrinsic factors such as strain and twist inhomogeneity?
• RQ4 What is the role of $PT$-symmetry-breaking order in shaping the temperature dependence of electronic anisotropy at low temperatures?
• RQ5 Can the angular symmetry of nonreciprocal transport responses be used to identify the nature of the low-temperature electronic order?

Key findings

• Electron anisotropy is strongly correlated with the cascade of isospin transitions near integer fillings, with a sharp onset at $\nu = +2$ in the magic-angle regime.
• At $\theta = 1.33^\circ$, the suppression of isospin transitions upon detuning from the magic angle leads to a collapse of electron anisotropy, especially in the hole-doped regime.
• In the $T < 5$ K regime, electron anisotropy is suppressed when the nonreciprocal response exhibits three-fold symmetry, indicating a transition to an isotropic state.
• A one-fold symmetric nonreciprocal response at low temperature coincides with a sharp enhancement in the anisotropy ratio, linking it to the emergence of $PT$-symmetry-breaking order.
• The coexistence of electron anisotropy and $PT$-breaking order, with no coupling to lattice distortion, provides strong evidence for a Coulomb origin of the anisotropy.
• The broadened onset of anisotropy at low temperatures is attributed to uniaxial strain, but the overall doping and twist-angle dependence confirms a dominant role for Coulomb interaction.