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Register a new userInter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene
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Added by
Shubhayu Chatterjee
Publication date
2021
fields
Physics
and research's language is
English
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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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Motivated by the observation of two distinct superconducting phases in the moireless ABC-stacked rhombohedral trilayer graphene, we investigate the electron-acoustic-phonon coupling as a possible pairing mechanism. We predict the existence of superconductivity with the highest $T_csim 3$K near the Van Hove singularity. Away from the Van Hove singularity, $T_c$ remains finite in a wide range of doping. In our model, the $s$-wave spin-singlet and $f$-wave spin-triplet pairings yield the same $T_c$, while other pairing states have negligible $T_c$. Our theory provides a simple explanation for the two distinct superconducting phases in the experiment and suggests that superconductivity and other interaction-driven phases (e.g., ferromagnetism) can have different origins.
Motivated by recent experiments on ABC-stacked rhombohedral trilayer graphene (RTG) which observed spin-valley symmetry-breaking and superconductivity, we study instabilities of the RTG metallic state to symmetry breaking orders. We find that interactions select the inter-valley coherent order (IVC) as the preferred ordering channel over a wide range, whose theoretically determined phase boundaries agree well with experiments on both the hole and electron doped sides. The Fermi surfaces near van Hove singularities admit partial nesting between valleys, which promotes both inter-valley superconductivity and IVC fluctuations. We investigate the interplay between these fluctuations and the Hunds (intervalley spin) interaction using a renormalization group approach. For antiferromagnetic Hunds coupling, intervalley pairing appears in the spin-singlet channel with enhanced $T_c$, that scales with the dimensionless coupling $g$ as $T_csimexp(-1/sqrt{g})$ , compared to the standard $exp(-1/g)$ scaling. In its simplest form, this scenario assumes a sign change in the Hunds coupling on increasing hole doping. On the other hand, the calculation incorporates breaking of the independent spin rotations between valleys from the start, and strongly selects spin singlet over spin triplet pairing, and naturally occurs in proximity to the IVC, consistent with observations.
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.
We show that in a two-dimensional electron gas with an annular Fermi surface, long-range Coulomb interactions can lead to unconventional superconductivity by the Kohn-Luttinger mechanism. Superconductivity is strongly enhanced when the inner and outer Fermi surfaces are close to each other. The most prevalent state has chiral p-wave symmetry, but d-wave and extended s-wave pairing are also possible. We discuss these results in the context of rhombohedral trilayer graphene, where superconductivity was recently discovered in parameter regimes where the normal state has an annular Fermi surface. Using realistic parameters, our mechanism can account for the order of magnitude of $T_c$ in that system, as well as its trends as a function of electron density and perpendicular displacement field. Moreover, it naturally explains some of the outstanding puzzles in this material, that include the weak temperature dependence of the resistivity above $T_c$, and the proximity of spin singlet superconductivity to the ferromagnetic region in the phase diagram.
Superconductivity originates from pairing of electrons. Pairing channel on Fermi surface and pairing glue are thus two pivotal issues for understanding a superconductor. Recently, high-temperature superconductivity over 40 K was found in electron-doped FeSe superconductors including K$_x$Fe$_{2-y}$Se$_2$, Li$_{0.8}$Fe$_{0.2}$OHFeSe, and 1 monolayer FeSe thin film. However, their pairing mechanism remains controversial. Here, we studied the systematic evolution of electronic structure in potassium-coated FeSe single crystal. The doping level is controlled precisely by in situ evaporating potassium onto the sample surface. We found that the superconductivity emerges when the inter-pocket scattering between two electron pockets is turned on by a Lifshitz transition of Fermi surface. The nematic order suppresses remarkably at the same doping and strong nematic fluctuation remains in a wide doping range of the phase diagram. Our results suggest an underlying correlation among superconductivity, inter-pocket scattering, and nematic fluctuation in electron-doped FeSe superconductors.
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