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Register a new userPossible Broken Inversion and Time-Reversal Symmetry State of Electrons in Bilayer Graphene
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With the two-band continuum model, we study the broken inversion and time-reversal symmetry state of electrons with finite-range repulsive interactions in bilayer graphene. With the analytical solution to the mean-field Hamiltonian, we obtain the electronic spectra. The ground state is gapped. In the presence of the magnetic field $B$, the energy gap grows with increasing $B$, in excellently agreement with the experimental observation. Such an energy gap behavior originates from the disappearance of a Landau level of $n$ = 0 and 1 states. The present result resolves explicitly the puzzle of the gap dependence of $B$.
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On a lattice model, we study the possibility of existence of gapped broken inversion symmetry phase (GBISP) of electrons with long-range Coulomb interaction in bilayer graphene using both self-consistent Hartree-Fock approximation (SCHFA) and the renormalized-ring-diagram approximation (RRDA). RRDA takes into account the charge-density fluctuations beyond the mean field. While GBISP at low temperature and low carrier concentration is predicted by SCHFA, we show here the state can be destroyed by the charge-density fluctuations. We also present a numerical algorithm for calculating the self-energy of electrons with the singular long-range Coulomb interaction on the lattice model.
Based on the four-band continuum model, we study the ordered-current state (OCS) for electrons in bilayer graphene at the charge neutrality point. The present work resolves the puzzles that (a) the energy gap increases significantly with increasing the magnetic field $B$, (b) the energy gap can be closed by the external electric field of either polarization, and (c) the particle-hole spectrum is asymmetric in the presence of $B$, all these as observed by the experiment. We also present the prediction of the hysteresis energy gap behavior with varying $B$, which explains the existing experimental observation on the electric conductance at weak $B$. The large energy gap of the OCS is shown to originate from the disappearance of Landau levels of $n$ = 0 and 1 states in conduction/valence band. By comparing with the existing models and the experiments, we conclude that the OCS is a possible ground state of electrons in bilayer graphene.
We show that strained or deformed honeycomb lattices are promising platforms to realize fractional topological quantum states in the absence of any magnetic field. The strained induced pseudo magnetic fields are oppositely oriented in the two valleys [1-3] and can be as large as 60-300 Tesla as reported in recent experiments [4,5]. For strained graphene at neutrality, a spin or a valley polarized state is predicted depending on the value of the onsite Coulomb interaction. At fractional filling, the unscreened Coulomb interaction leads to a valley polarized Fractional Quantum Hall liquid which spontaneously breaks time reversal symmetry. Motivated by artificial graphene systems [5-8], we consider tuning the short range part of interactions, and demonstrate that exotic valley symmetric states, including a valley Fractional Topological Insulator and a spin triplet superconductor, can be stabilized by such interaction engineering.
Using a four-band Hamiltonian, we study the phase boundary of spin-polarized-current state (SPCS) of interacting electrons in bilayer graphene. The model of spin-polarized-current state has previously been shown to resolve a number of experimental puzzles in bilayer graphene. The phase boundaries of the SPCS with and without the external voltage between the two layers are obtained in this work. An unusual phase boundary where there are two transition temperatures for a given carrier concentration is found at finite external voltage. The physics of this phenomenon is explained.
We provide numerical evidence that the Onsager symmetry remains valid for systems subject to a spatially dependent magnetic field, in spite of the broken time-reversal symmetry. In addition, for the simplest case in which the field strength varies only in one direction, we analytically derive the result. For the generic case, a qualitative explanation is provided.
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