Author: Jorge Sofo

Jorge Sofo is a Professor of Physics at Penn State.

Landau Level Phases in Bilayer Graphene under Pressure at Charge Neutrality

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Bilayer graphene exhibits ground states that can be polarized in spin, valley, or orbital. These ground states can be controlled with applied magnetic and electric fields or by reducing the distance between layers with uniaxial pressure.

We study the ground state phase diagram treating the Coulomb interaction between electrons at the Hartree-Fock level. We show that pressure and magnetic field are direct experimental methods for tuning the balance between the Landau level separation (noninteracting energy scale) and the exchange energy (interacting energy scale). We predict that using pressure to tune this balance, five ordered states can be observed, two of which are only accessible with applied pressure. These states are both orbitally polarized. One is maximally orbitally polarized but unpolarized in valley and spin, while the other is partially polarized in orbital and spin but unpolarized in valley.

We posted this paper posted in the arxiv, and has been published in Physical Review B.

See also the video presentation of Brett Green at the March Meeting 2020.

Key results:

Below are the phase diagrams depicting the five possible ground states in our model and magnetic field, electric field, and pressure which may be used to construct them. The legend at the bottom indicates which Landau levels are filled and hence in which degrees of freedom the state is ordered.

Phase diagram of Bilayer Graphene

dot diagrams
Phase diagrams for (a) zero, (b) intermediate, and (c) high pressures are given; (d) magnifies (c). Five Landau-level Slater determinant and no Landau-level coherent states appear. Notice that applied pressure literally compresses the phase diagram so that all transitions occur at progressively lower fields, as explained in the text, but that the overall topology remains unchanged. The dashed lines on P = 29.8 GPa correspond to the traces in Fig. 4. (e) A schematic of the dot-diagram depiction of states devised by Lambert and Cote [11, 12], and the dot-diagram representation of the different states appearing in our phase diagrams.

Abstract:

Bilayer graphene in a magnetic field hosts a variety of ordered phases built from eight Landau levels close in energy to the neutrality point. These levels are characterized by orbital n=0,1, valley ξ=+,- and spin σ=↑,↓; their relative energies depend strongly on the Coulomb interaction, magnetic field, and interlayer bias. We treat interactions at the Hartree-Fock level, including the effects of metallic gates, layer separation, spatial extent of the pz; orbitals, all Slonczewski-Weiss-McClure tight-binding parameters, and pressure. We obtain the ground state as function of the applied magnetic field, bias, and pressure. The gates, layer separation and extent of the pz orbitals weaken the Coulomb interaction at different length scales; these effects distort the phase diagram but do not change its topology. However, previously-predicted continuous transitions become discontinuous when all tight-binding parameters are included nonperturbatively. We find that pressure increases the importance of the noninteracting scale with respect to the Coulomb energy, which drives phase transitions to occur at lower fields. This brings two orbitally polarized states not yet predicted or observed into the experimentally accessible region of the phase diagram, in addition to previously-identified valley-, spin-, and partially orbitally polarized states.

The Art of Listening – Eric Fromm – (via Brianpickings)

Jorge SofoLeave a comment

Maria Popova wrote a post about this six rules for listening motivated by “The Art of Listening” written by Eric Fromm. I think this will be useful for me and other Ombudspeople and why not all of us!

I transcribe them here.

  1. The basic rule for practicing this art is the complete concentration of the listener.
  2. Nothing of importance must be on his mind, he must be optimally free from anxiety as well as from greed.
  3. He must possess a freely-working imagination which is sufficiently concrete to be expressed in words.
  4. He must be endowed with a capacity for empathy with another person and strong enough to feel the experience of the other as if it were his own.
  5. The condition for such empathy is a crucial facet of the capacity for love. To understand another means to love him — not in the erotic sense but in the sense of reaching out to him and of overcoming the fear of losing oneself.
  6. Understanding and loving are inseparable. If they are separate, it is a cerebral process and the door to essential understanding remains closed.

What is a model?

Jorge SofoLeave a comment

In an interview by Sam Harris, Jared Diamond was describing his work as a pathologist on the gallbladder as a model for the function of the intestine. He described a model as a system that functions in the same way as other but it is easy to study. I found this a very precise and succinct definition of a model.