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Register a new userRe-entrant Superconductivity Through a Quantum Lifshitz Transition in Twisted Trilayer Graphene
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A series of recent experiments have demonstrated robust superconductivity in magic-angle twisted trilayer graphene (TTG). In particular, a recent work by Cao et al. (arxiv:2103.12083) studies the behavior of the superconductor in an in-plane magnetic field and out-of-plane displacement field, finding that the superconductor is unlikely to be spin-singlet. This work also finds that at high magnetic fields and a smaller range of dopings and displacement fields, it undergoes a transition to a distinct field-induced superconducting state. Inspired by these results, we develop an understanding of superconductivity in TTG using a combination of phenomenological reasoning and microscopic theory. We describe role that that an in-plane field plays in TTG, and use this understanding to argue that the re-entrant transition may be associated with a quantum Lifshitz phase transition, with the high-field phase possessing finite-momentum pairing. We argue that the superconductor is likely to involve a superposition of singlet singlet and triplet pairing, and describe the structure of the normal state. We also draw lessons for twisted bilayer graphene (TBG), and explain the differences in the phenomenology with TTG despite their close microscopic relationship. We propose that a singlet-triplet superposition is realized in the TBG superconductor as well, and that the $ u = -2$ correlated insulator may be a time reversal protected $mathbb{Z}_2$ topological insulator obtained through spontaneous spin symmetry breaking.
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Magic-angle twisted trilayer graphene (MATTG) recently emerged as a highly tunable platform for studying correlated phases of matter, such as correlated insulators and superconductivity. Superconductivity occurs in a range of doping levels that is bounded by van Hove singularities which stimulates the debate of the origin and nature of superconductivity in this material. In this work, we discuss the role of spin-fluctuations arising from atomic-scale correlations in MATTG for the superconducting state. We show that in a phase diagram as function of doping ($ u$) and temperature, nematic superconducting regions are surrounded by ferromagnetic states and that a superconducting dome with $T_c approx 2,mathrm{K}$ appears between the integer fillings $ u =-2$ and $ u = -3$. Applying a perpendicular electric field enhances superconductivity on the electron-doped side which we relate to changes in the spin-fluctuation spectrum. We show that the nematic unconventional superconductivity leads to pronounced signatures in the local density of states detectable by scanning tunneling spectroscopy measurements.
We study the symmetries of twisted trilayer graphenes band structure under various extrinsic perturbations, and analyze the role of long-range electron-electron interactions near the first magic angle. The electronic structure is modified by these interactions in a similar way to twisted bilayer graphene. We analyze electron pairing due to long-wavelength charge fluctuations, which are coupled among themselves via the Coulomb interaction and additionally mediated by longitudinal acoustic phonons. We find superconducting phases with either spin singlet/valley triplet or spin triplet/valley singlet symmetry, with critical temperatures of up to a few Kelvin for realistic choices of parameters.
We report the observation of superconductivity in rhombohedral trilayer graphene electrostatically doped with holes. Superconductivity occurs in two distinct regions within the space of gate-tuned charge carrier density and applied electric displacement field, which we denote SC1 and SC2. The high sample quality allows for detailed mapping of the normal state Fermi surfaces by quantum oscillations, which reveal that in both cases superconductivity arises from a normal state described by an annular Fermi sea that is proximal to an isospin symmetry breaking transition where the Fermi surface degeneracy changes. The upper out-of-plane critical field $B_{Cperp}approx 10 mathrm{mT}$ for SC1 and $1mathrm{mT}$ for SC2, implying coherence lengths $xi$ of 200nm and 600nm, respectively. The simultaneous observation of transverse magnetic electron focusing implies a mean free path $ellgtrsim3.5mathrm{mu m}$. Superconductivity is thus deep in the clean limit, with the disorder parameter $d=xi/ell<0.1$. SC1 emerge from a paramagnetic normal state and is suppressed with in-plane magnetic fields in agreement with the Pauli paramagnetic limit. In contrast, SC2 emerges from a spin-polarized, valley-unpolarized half-metal. Measurements of the in-plane critical field show that this superconductor exceeds the Pauli limit by at least one order of magnitude. We discuss our results in light of several mechanisms including conventional phonon-mediated pairing, pairing due to fluctuations of the proximal isospin order, and intrinsic instabilities of the annular Fermi liquid. Our observation of superconductivity in a clean and structurally simple two-dimensional metal hosting a variety of gate tuned magnetic states may enable a new class of field-effect controlled mesoscopic electronic devices combining correlated electron phenomena.
Topological superconductivity is an exotic phase of matter in which the fully gapped superconducting bulk hosts gapless Majorana surface states protected by topology. Intercalation of copper, strontium or niobium between the quintuple layers of the topological insulator Bi$_2$Se$_3$ increases the carrier density and leads to superconductivity that is suggested to be topological. Here we study the electronic structure of strontium-intercalated Bi$_2$Se$_3$ using angle resolved photoemission spectroscopy (ARPES) and Shubnikov-de Haas (SdH) oscillations. Despite the apparent low Hall number of $sim2 times 10 ^{19}$cm$^{-3}$, we show that the Fermi surface is shaped as an open cylinder with a larger carrier density of $sim 10 ^{20}$cm$^{-3}$. We suggest that superconductivity in intercalated Bi$_2$Se$_3$ emerges with the appearance of a quasi-2D open Fermi surface.
Superconductivity was recently discovered in rhombohedral trilayer graphene (RTG) in the absence of a moire potential. Intringuigly, superconductivity is observed proximate to a metallic state with reduced isospin symmetry, but it remains unknown whether this is a coincidence or a key ingredient for superconductivity. Using a Hartree-Fock analysis and constraints from experiments, we argue that the symmetry breaking is inter-valley coherent (IVC) in nature. We evaluate IVC fluctuations as a possible pairing glue, and find that they lead to unconventional superconductivity which is $p$-wave when fluctuations are strong. We further elucidate how the inter-valley Hunds coupling determines the spin-structure of the IVC ground state and breaks the degeneracy between spin-singlet and triplet superconductivity. Intriguingly, if the normal state is spin-unpolarized, we find that a ferromagnetic Hunds coupling favors spin-singlet superconductivity, in agreement with experiments. Instead, if the normal state is spin-polarized, then IVC fluctuations lead to spin-triplet pairing.
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