Abstract
We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin–orbit (SO) interaction in a magnetic field, using a combination of matrix product state and bosonization techniques. Quantum wires with strong Rashba SO interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with SO interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at k = 0 and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton–antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.
Highlights
Electron–electron (e–e) interactions have drastic effects on the physics of 1D electron conductors
We have presented a detailed analysis of the static and dynamic properties of strongly correlated quantum wires with Rashba SO interaction and Zeeman field
We investigated a microscopic model, with SO interaction, Zeeman field and tunable interactions of extended Hubbard type, and calculated the static and dynamic properties by density matrix renormalization group (DMRG) and time dependent block decimation (TEBD)
Summary
Electron–electron (e–e) interactions have drastic effects on the physics of 1D electron conductors. Interacting quantum wires in a microscopic model, at all energies. It is known that the combination of SO and Zeeman field in a 1D quantum wire, with superconductivity induced by the proximity effect, supports Majorana zero modes —elusive quasiparticles which are their own antiparticles—at the boundaries of the system [10, 11]. Due to their non-Abelian exchange statistics Majorana zero modes are promising candidates for the implementation of topologically protected quantum information processing [12, 13]. Considerable experimental effort is currently under way to investigate the physics of Majorana zero modes in 1D semiconductor nanowires with strong SO and Zeeman fields [14,15,16,17]
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