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Motivated by measurements of compressibility and STM spectra in twisted bilayer graphene, we analyze the pattern of symmetry breaking for itinerant fermions near a van Hove singularity. Making use of an approximate SU(4) symmetry of the Landau functional, we show that the structure of the spin/isospin order parameter changes with increasing filling via a cascade of transitions. We compute the feedback from different spin/isospin orders on fermions and argue that each order splits the initially 4-fold degenerate van Hove peak in a particular fashion, consistent with the STM data and compressibility measurements, providing a unified interpretation of the cascade of transitions in twisted bilayer graphene. Our results follow from a generic analysis of an SU(4)-symmetric Landau functional and are valid beyond a specific underlying fermionic model. We argue that an analogous van Hove scenario explains the cascade of phase transitions in non-twisted Bernal bilayer and rhombohedral trilayer graphene.

 

The origin of the pseudogap behavior, found in many high-T_csuperconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a “gap-filling rather than “gap-closing behavior, similar to the one observed in cuprate superconductors. Our results present direct evidence of the pseudogap state, driven by superconducting fluctuations.

 

We propose a platform for braiding Majorana non-Abelian anyons basedon a heterostructure between a d d -wavehigh- T_c T c superconductor and a quantum spin-Hall insulator. It has been recentlyshown that such a setup for a quantum spin-Hall insulator leads to apair of Majorana zero modes at each corner of the sample, and thus canbe regarded as a higher-order topological superconductor. We show thatupon applying a Zeeman field in the region, these Majorana modes splitin space and can be manipulated for braiding processes by tuning thefield and pairing phase. We show that such a setup can achieve fullbraiding, exchanging, and arbitrary phase gates (including the \pi/8 π / 8 magic gates) of the Majorana zero modes, all of which are robust andprotected by symmetries. As many of the ingredients of our proposedplatform have been realized in recent experiments, our results provide anew route toward universal topological quantum computation.