Superfluidity of Hydrogenlike Gas in a Strong Magnetic Field?

Abstract

The recent claim that in a strong magnetic field hydrogenlike gas (e.g., excitons in certain semiconductors, neutron star surface layers) becomes superfluid is refuted. Molecules form by strong covalent bond along the magnetic field axis, which prohibits Bose-Einstein condensation.To appear in Phys. Rev. Lett. (1995) as a commentIn a recent letter and several papers Korolev and Liberman [1,2] claimed that in a strong magnetic field a hydrogenlike gas (e.g., excitons in certain semiconductors) can form Bose-Einstein condensate and become a superfluid. This is an interesting result as it potentially provides another system besides liquid He that displays Bose-Einstein condensation. However, the authors [1,2] failed to identify the strong covalent bonding mechanism for forming hydrogen molecule in strong magnetic field [3,4], which makes the Bose-Einstein condensation rather unlikely.For definiteness, I consider the electron-proton system. For excitons in semiconductors, the results (to the leading order) can be rescaled by introducing the effective electron mass and the dielectric constant of the medium.The atomic unit (a.u.) for the magnetic field strength is B o = m 2 e e 3 c/h 3 = 2.35 × 10 9 G, above which the Landau excitation energy of the electronhω e =heB/(m e c) is larger than the atomic unit for the energy m e e 4 /h 2 = 2 Ry. In the strong field regime b ≡ B/B o >> 1, the electron settles into the ground Landau state, and the energy levels of the atom are specified by two quantum numbers (m, ν): m measures the mean transverse separation between the electron guiding center and the proton, ρ m = (2m + 1) 1/2ρ (m = 0, 1, 2, · · ·), wherê ρ = (hc/eB) 1/2 = b −1/2 (a.u.), and ν is the number of nodes in the z-wavefunction of the electron. The ν = 0 states have binding energies less than a Rydberg. For the (m, ν) = (m, 0) state, the atom is elongated along magnetic field axis, and the energy is approximately given by (see [3] and references therein) Since the electron spins in the atoms are all aligned antiparallel to the magnetic field, two atoms in their ground states (m = ν = 0) cannot easily bind together to form a molecule according to the exclusion principle. Approximate calculations [2] indicate that the interaction between two ground-state hydrogen atoms is very weak (However, this calculation underestimates the binding energy because it neglects the overlapping of the electron wavefunctions. Recent calculations [5] indicate that the binding energy is much larger than the result of [2]). This formed the basis of the claim in [1] that hydrogenlike gas can become superfluid: because of the weak interatomic interaction, the system remains in the gaseous phase even at low temperature and high density, hence Bose-Einstein condensation may eventually sets in as temperature decreases or density increases.However, these is another mechanism by which tightlybound hydrogen molecule can form in strong magnetic field [3,4]: One of the atom is first excited to a m > 0 state; then the two atoms, one in t...

Hydrogen molecule in magnetic fields: The ground states of the Σ manifold of the parallel configuration

“…In superstrong magnetic fields with B > ∼ 10 3 a.u. it is well known that the 3 Π u state represents the ground state of the hydrogen molecule [30,37]. The ground state for magnetic-field strengths in the intermediate regime has not been investigated up to now, to our knowledge.…”

“…Hereby the ground state of the hydrogen molecule is of particular interest. Recently a controversial discussion arose concerning the electronic structure of a hydrogen molecule in a superstrong magnetic field [30,[32][33][34][35][36][37]. It was conjectured that in superstrong magnetic fields the 3 Σ u state would be the ground state of H 2 [32].…”

Hydrogen molecules in a superstrong magnetic field: Excitation levels

“…Also, their variational calculation of the weakly-bound state significantly underestimates the binding energy because it neglects the overlapping of the electron wavefunctions. As a result, their claim that hydrogenlike gas in strong magnetic field can form Bose-Einstein condensate is incorrect (see also [26,27]).…”

“…As an example, let us consider the ground electronic state of H + 2 . In general, the transverse wavefunction of the electron is a superposition of different Landau ground state wavefunctions, i.e.,Φ ⊥ (r ⊥ ) = m A m W m (r ⊥ ),(3 26). and Φ(r) = Φ ⊥ (r ⊥ )f (z) is the total wavefunction (see also Appendix B).…”

Exploring the Quantum World of Complex States

“…Our interest in the H 2 molecule arose from the contentious suggestion that a gas of such molecules has a weakly interacting gs in the superstrong magnetic field regime, and could possibly form a superfluid phase 20,21 . The crucial argument supporting the existence of a superfluid phase is that the system behaves as a weakly interacting Bose gas and as a consequence of macroscopic exchanges it becomes superfluid.…”