Fig. 3: Phonon-induced transport behavior.
From: Steady-state Peierls transition in nanotube quantum simulator
a Lowest energies of the system in different electron number sectors. Upon increasing the electron-phonon coupling g0, the electron number of ground state changes from two electrons to four electrons for the chosen local chemical potential ε/2πℏ = − 30 GHz. b–e Electron number Ne, current I, CDW structure factor C, and order parameter O in the steady state for various Vbias obtained from the Pauli master equation (dashed lines) and shift method without updating the shift parameter (solid lines); see “Methods”. In d and e, we also plot the CDW structure factor C and order parameter O of equilibrium two-electron states (black lines) for the convenience of comparison. The black dashed vertical lines in a–e label the approximate transition points in the two-electron sector identified from the equilibrium CDW structure factor and order parameter. f Phonon number Np obtained from the Pauli master equation. The insert shows the variance of phonon operator, Var(b). Here we truncate the phononic Hilbert space to a finite-dimensional Hilbert space with maximal 1000 phonons for the Pauli master equation. The shift method for eVbias/2πℏ = 80, 100, and 120 GHz is performed within a Hilbert space with maximal 40, 45, and 50 tilded phonons, respectively. Other parameters are t0/2πℏ = 5 GHz, U1/2πℏ = 200 GHz, U2/2πℏ = 20 GHz, U3/2πℏ = 2 GHz, ω0/2π = 3 GHz, Γ/2πℏ = 1 GHz, and kBT/2πℏ = 2 GHz.
