Phase diagram and phonon-induced backscattering in topological insulator nanowires

Abstract

We present an effective low-energy theory of electron-phonon coupling effects for clean cylindrical topological insulator nanowires. Acoustic phonons are modelled by isotropic elastic continuum theory with stress-free boundary conditions. We take into account the deformation potential coupling between phonons and helical surface Dirac fermions, and also include electron-electron interactions within the bosonization approach. For half-integer values of the magnetic flux ΦB along the wire, the low-energy theory admits an exact solution since a topological protection mechanism then rules out phonon-induced 2kF -backscattering processes. We determine the zero-temperature phase diagram and identify a regime dominated by superconducting pairing of surface states. As example, we consider the phase diagram of HgTe nanowires. We also determine the phonon-induced electrical resistivity, where we find a quadratic dependence on the flux deviation δΦB from the nearest half-integer value. arXiv:1911.03300v2 [cond-mat.mes-hall] 5 Jan 2020

Floquet metal-to-insulator phase transitions in semiconductor nanowires

“…Here, is a vector of operators annihilating spinless fermions in two orbitals, ∣𝒜> and ∣ >, with crystal momentum k along the wire. We write the single-particle Bloch Hamiltonian H k ( t ) in the form ( 53 – 57 ) where σ x , σ y , and σ z are Pauli matrices in the orbital basis, with σ z ∣ A〉 = ∣A〉 and σ z ∣ℬ〉 = −∣ℬ〉, and A , B , and M are constants. The periodic drive induces a local coupling between the orbitals, with strength V .…”

“…Respecting the particle-hole symmetry of the system, for small q , we take the coupling between electrons and acoustic phonons polarized along the wire to be ( 57 , 58 ) Here, g s is a coupling parameter, and U s is proportional to the unity matrix in the 𝒜, orbital space. For the electron-photon coupling, we take the simple ( q independent) form U 𝓁 = g 𝓁 σ x , where g 𝓁 is a coupling parameter and σ x is an orbital-space Pauli matrix (see text below Eq.…”

“…T is a vector of operators annihilating spinless fermions in two orbitals, | > and | ℬ >, with crystal momentum k along the wire. We write the single-particle Bloch Hamiltonian H k (t) in the form (53)(54)(55)(56)(57)…”

Tunneling into a Luttinger-liquid coupled to acoustic phonons out of equilibrium

“…In passing, the structure of the electron-electron interaction (8) in chirality indices implies that g 4 = g 2 = g in g-ology vocabulary of one dimensional studies. The above renormalization factor of the Fermi velocity has a well known form d 2 = (1 + g 4 ) 2 − g 2 2 , and for g 4 = 0 one obtains d 2 = 1 − g 2 in full agreement with [22].…”

“…Recently, the effect of electron-phonon interactions on the electrical conductance and transport properties of one-dimensional strongly correlated electronic systems was discussed in the context of helical edge states of twodimensional topological insulators [5,6], quantum Hall edge states at filling factor ν = 1 [7] and topological insulator nanowires [8]. It was emphasised that preserving time-reversal symmetry inelastic scattering processes due to phonons can drastically influence the topologically protected transport properties.…”