Cascade of isospin phase transitions in Bernal bilayer graphene at zero magnetic field

Abstract

Emergent phenomena arising from the collective behavior of electrons is generally expected when Coulomb interactions dominate over the kinetic energy, as in delocalized quasiparticles in highly degenerate flat bands. Bernal-stacked bilayer graphene intrinsically supports a pair of flat bands predicted to host a variety of spontaneous broken-symmetry states arising from van Hove singularities and a four-fold spin-valley (isospin) degeneracy [1][2][3][4][5][6]. Here, we show that ultra-clean samples of bilayer graphene display a cascade of symmetry-broken states with spontaneous and spin and valley ordering at zero magnetic field. Using capacitive sensing in a dual-gated geometry, we tune the carrier density and electric displacement field independently to explore the phase space of transitions and probe the character of the isospin order. Itinerant ferromagnetic states emerge near the conduction and valence band edges with complete spin and valley polarization and a high degree of displacement field tunability. At larger hole densities, two-fold degenerate quantum oscillations manifest in an additional broken symmetry state that is enhanced by the application of an in-plane magnetic field. Both types of symmetry-broken states display enhanced layer polarization at low temperatures, suggesting a coupling to the layer pseudospin degree of freedom in the electronic wavefunctions [1,6]. Notably, the zero-field spontaneous symmetry breaking reported here emerges in the absence of a moiré superlattice and is intrinsic to natural graphene bilayers. Thus, we demonstrate that the tunable bands of bilayer graphene represent a related, but distinct approach to produce flat band collective behavior, complementary to engineered moiré structures.

Competing orders and cascade of degeneracy lifting in doped Bernal bilayer graphene

“…Furthermore, a relative twist between two layers of graphene substantially reduces the Fermi velocity of Dirac fermions near the socalled magic angle [8][9][10][11], where a cascade of insulating and superconducting phases has been observed by tuning the carrier density [12][13][14][15]. Similar phenomenon has also been reported in RTLG [16,17], and very recently in BBLG [1,2]. Although the hierarchy of interaction driven competing orders in RTLG has been investigated theoretically [18][19][20][21][22][23][24], a similar expedition exploring the landscape of doped BBLG, subject to an external electric displacement (D) field, is yet to be initiated.…”

“…[1] (phase PIP 2 ), possibly also in Ref. [2] (phase A). Thus, such a phase features two-fold degenerate Fermi surfaces, however with majority and minority carriers.…”

“…

Motivated by recent experiments [1,2], here we propose a general mechanism for valley and/or spin degeneracy lifting of the electronic bands in doped Bernal bilayer graphene, subject to electric displacement (D) fields. A D-field induced layer polarization (LP), when accompanied by Hubbard repulsion driven layer antiferromagnet (LAF) and next-nearest-neighbor repulsion driven quantum anomalous Hall (QAH) orders, lifts the four-fold degeneracy of electronic bands, yielding a quarter metal for small doping, as also observed in ABC trilayer graphene.

…”

“…In BBLG subject to D-field, quantum oscillations show a single peak at frequency (in units of nφ 0 ) ν = 1 at low carrier density n. Here φ 0 is the flux quanta. The corresponding broken symmetry phase (IF 1 [1] or B (C) on the hole (electron) dope side [2]), thus lacks spin and valley degeneracy.…”

“…At even larger doping and weak D-field, one oscillation peak appears at ν = 1/4. This phase (Sym 4 [1] or D [2]), preserving the four-fold degeneracy, can result from a pure LAF order due to the dominant Hubbard repulsion, possibly persisting over the entire band [Fig. 2(d)].…”