Mixed singlet-triplet superconducting state within the moiré <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>t</mml:mi><mml:mtext>−</mml:mtext><mml:mi>J</mml:mi><mml:mtext>−</mml:mtext><mml:mi>U</mml:mi></mml:mrow></mml:math> model applied to twisted bilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">WSe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>
M. Zegrodnik, Andrzej Biborski
Abstract
We analyze an analog of the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model as applied to the description of a single moir\'e flat band of twisted ${\mathrm{WSe}}_{2}$ bilayer. To take into account the correlation effects induced by a significant strength of the Coulomb repulsion, we use the Gutzwiller approach and compare it with the results obtained by the Hartree-Fock method. We discuss in detail the graduate appearance of a two-dome structure of the superconducting state in the phase diagram by systematically increasing the Coulomb repulsion integral $U$. The two superconducting domes residing on both sides of a Mott insulating state can be reproduced for a realistic parameter range, in agreement with the available experimental data. According to our analysis, the paired state has a highly unconventional character with a mixed $d+id$ (singlet) and $p\ensuremath{-}ip$ (triplet) symmetry. Both components of the mixed paired state are of comparable amplitudes. However, as shown here, a transition between pure singlet and pure triplet pairing should be possible in the considered system by tuning the top and bottom gate voltage, which controls the magnitude of valley-dependent spin splitting in the system.