Correlated Insulating States and Transport Signature of Superconductivity in Twisted Trilayer Graphene Superlattices

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Correlated Insulating States and Transport Signature of Superconductivity in Twisted Trilayer Graphene Superlattices

Xi Zhang, Kan-Ting Tsai, Ziyan Zhu, Wei Ren, Yujie Luo, Stephen Carr, Mitchell Luskin, Efthimios Kaxiras, and Ke Wang

Phys. Rev. Lett. 127, 166802 – Published 11 October 2021

Abstract

Layers of two-dimensional materials stacked with a small twist angle give rise to beating periodic patterns on a scale much larger than the original lattice, referred to as a “moiré superlattice.” Here, we demonstrate a higher-order “moiré of moiré” superlattice in twisted trilayer graphene with two consecutive small twist angles. We report correlated insulating states near the half filling of the moiré of moiré superlattice at an extremely low carrier density ( $\sim 10^{10} {cm}^{- 2}$ ), near which we also report a zero-resistance transport behavior typically expected in a 2D superconductor. The full-occupancy ( $ν = - 4$ and $ν = 4$ ) states are semimetallic and gapless, distinct from the twisted bilayer systems.

Received 2 November 2020
Accepted 3 September 2021

DOI:https://doi.org/10.1103/PhysRevLett.127.166802

Physics Subject Headings (PhySH)

Electrical conductivity Superconductivity

Two-dimensional electron system

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Xi Zhang ^1,*, Kan-Ting Tsai^1,*, Ziyan Zhu², Wei Ren¹, Yujie Luo³, Stephen Carr², Mitchell Luskin⁴, Efthimios Kaxiras^2,5, and Ke Wang ^1,†

¹School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455, USA
²Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
³Department of Mechanical Engineering, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁴School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
⁵John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

^*These authors contributed equally to this work.
^†kewang@umn.edu

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Vol. 127, Iss. 16 — 15 October 2021

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Images

Figure 1
MoM superlattices in tTLG. (a) Schematic of the hBN-encapsulated tTLG device, consisting of three-monolayer graphene consecutively twisted with respect to the previous layer. Bottom left: optical microscope image of a typical device under study. Bottom right: AFM topology of tTLG on hBN, made at consecutive twist angles of 1.64° for demonstration of tTLG MoM. Irregular and triangularlike patterns with a length scale on the order of 300 nm are barely visible, suggesting a plethora of coexisting MoM length scales accompanying the dominating MoM lattice. Inset: dominating Fourier components in the FFT spectrum, corresponding to length scales of 120–260 nm, which qualitatively agrees with experimental design. (b) Atomic positions in tTLG at a set of commensurate angles $θ_{12} = θ_{23} = 9.43 °$ demonstrating the MoM superlattice. White parallelogram: MoM supercell. Inset: enlargement of the area inside the black box showing the bilayer moiré pattern. The left (right) shows only layers 2 and 1 (3), and the red (blue) parallelograms show the corresponding bilayer moiré supercells. Both scale bars are 10 Å. (c) Possible twist-angle combinations for MoM area $A_{1} = 6438 {nm}^{2}$ (MOM 1). Color scale represents the density of state maximum. (d) 1D cuts along twist-angle configurations near $θ_{12} = θ_{23}$ , $θ_{12} = 2 θ_{23}$ , and $θ_{12} = 3 θ_{23}$ , respectively. (e) Monolayer Brillouin zone of the three individual layers (top) and the bilayer moiré Brillouin zone formed between adjacent bilayer pairs (bottom). (f) Band structure at $θ_{12} = 2.9 °$ and $θ_{23} = 1.4 °$ along the high symmetry line indicated by the dashed line in (e). Colors indicate the projected weight onto the state at the center momentum in each layer. Red, layer 1; blue, layer 2; green, layer 3. (g) Normalized density of states corresponding to band structure shown in (f), with a zero-energy peak value comparable to that of tBLG.
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Figure 2
Insulating and semimetallic behavior at $ν = even$ integer fillings of two MoM superlattices. (a) Measured four-probe resistance of MoM 1 (unit cell $size = 6438 {nm}^{2}$ ) and (b) MoM 2 (unit cell size $A_{2} = 4778 {nm}^{2}$ ) as a function of the temperature and carrier density $n$ . Resistance peaks are observed at all $ν = n / (n_{s} / 4) = even$ integer fillings, where $n_{s}$ is the carrier density corresponding to four charge carriers per MoM unit cell. (c) Line traces of four-probe conductance as a function of the carrier density taken at different temperatures of MoM 1 and (d) MoM 2. (e) Conductance as a function of the temperature at each even filling for MoM 1 and (f) MoM 2. Data are offset to separate each curve.
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Figure 3
Temperature and bias characteristics of superconductinglike states. (a) Measured four-probe resistance of MoM 1 as a function of the carrier density and temperature. At half filling of the MoM superlattice ( $n \sim - 3.22 \times 10^{10} {cm}^{- 2}$ ), correlated insulating behavior is observed with two adjacent zero-resistance domes. (b) Differential resistance as a function of the temperature near the center of the right zero-resistance dome. (c) Differential resistance as a function of the carrier density and dc bias offset at 3 K. Zero-resistance states symmetric with respect to zero bias exist up to $J_{c} \sim 200 nA$ . (d) $I − V$ characteristics at different temperatures, near the center of the right zero-resistance dome. The $I − V$ curve power law exponent goes from 1 to 3 as the temperature decreases, consistent with the BKT model for a typical 2D superconductor. Inset: the temperature dependence of the power law exponent $α$ , from which a critical temperature $T_{BKT} \sim 3.4 K$ is extracted.
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Figure 4
Magnetotransport at larger carrier density span. (a) Resistance of MoM 1 as a function of the magnetic field and a large range of carrier density. Zero-resistance states are observed only in a very small density range near zero carrier density. (b) Magnetotransport data in a smaller range of carrier density, displaying a very complicated Hofstadter butterfly pattern, in which zero-resistance states exist up to $\sim 500 mT$ .
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