Gapped broken symmetry states in ABC-stacked trilayer graphene

Abstract

We use a self-consistent Hartree-Fock approximation with realistic Coulomb interactions for π-band electrons to explore the possibility of broken symmetry states in weakly disordered ABC stacked trilayer graphene. The competition between gapped and gapless broken symmetry states, and normal states is studied by comparing total energies. We find that gapped states are favored and that, unlike the bilayer case, gapless nematic broken symmetry states are not metastable. Among the gapped states the layer antiferromagnetic state is favored over anomalous and spin Hall states.

Competition between spontaneous symmetry breaking and single-particle gaps in trilayer graphene

“…This gap can be suppressed by increasing charge density n, a critical temperature T c B34 K, by an interlayer potential U > of either polarity and by an in-plane magnetic field. Among the spatially uniform correlated phases in r-TLG discussed in the literature [8][9][10][11][12][13] , only LAF, in which the top and bottom layers have equal number of electrons with opposite spin polarization, is consistent with our experimental observations. For instance, the presence of an energy gap eliminates the mirrorbreaking, inversion breaking, interlayer current density wave or layer polarization density wave states 12 , and the zero conductance eliminates the superconductor, quantum spin Hall and quantum anomalous Hall states that host finite (or even infinite) conductance.…”

“…Using low temperature transport measurements, we show that, in the absence of external fields, r-TLG at the CNP is an intrinsic insulator, with an energy gap of 42 meV; the critical temperature for transition into this insulating regime is T c B36 K. This energy gap is partially suppressed by U > or a parallel magnetic field. Among the spatially uniform correlated phases that have been proposed theoretically [8][9][10][11][12][13] , our experimental results are most consistent with the presence of a layer antiferromagnet in chargeneutral r-TLG, which is expected to transition into a layer polarized state and a canted ferromagnetic state on the application of external electric and magnetic fields, respectively.…”

“…An energy gap can be generated via two different mechanisms, in the single-particle picture, on applying a potential difference U > between the outmost layers, the band structure adopts a gap that scales with U > (refs [1][2][3][4][5][6][7]. Alternatively, close to the charge neutrality point (CNP), the diverging density of states leads to strong electronic interactions, and the gapless semiconductor is expected to give way to phases with spontaneous broken symmetries; in particular, gapped phases such as layer antiferromagnetic (LAF) and quantum anomalous Hall states with broken time reversal symmetry are expected to be favoured [8][9][10][11][12][13] . Such symmetrybroken states are in direct competition with the U > -induced single-particle gap, giving rise to a rich phase diagram.…”

Accurate tight-binding models for theπbands of bilayer graphene

“…The correct sign choice (t 1 > 0,t 3 > 0) implies bands that are similar to those obtained with the incorrect choice t 1 < 0,t 3 < 0, 22,23 whereas the incorrect mixed sign choice t 1 > 0,t 3 < 0 introduces a 60 • rotation. 20,21 Taking the relative signs of t 0 and t 1 to be positive 5,6 or negative [20][21][22][23] does not affect the trigonal warping orientation, but alters the way in which the t 4 term influences particle-hole symmetry breaking in the bands. These parameter sign issues also influence small terms in the 2 × 2 low energy Hamiltonian 20,21 often used to describe the low-energy bands.…”

“…At very low carrier density this physics can in principle lead to broken symmetry states both in bilayers 22,31 and in ABC trilayers. 23,32 The most important interlayer coupling effects are controlled by the effective BA coupling of ∼ 360 meV whose structure factor does not vanish near the Dirac point, unlike the interlayer coupling mediated through terms linking AA /BB with an effective strength of ∼ 140 meV each, that accounts for most of the particle-hole symmetry breaking near the Dirac points represented in Fig. 7, and terms coupling AB sites in the order of ∼ 280 meV responsible for trigonal warping.…”