Topological phase transitions from Harper to Fibonacci crystals

Abstract

Topological properties of Harper and generalized Fibonacci chains are studied in crystalline cases, i.e., for rational values of the modulation frequency. The Harper and Fibonacci crystals at fixed frequency are connected by an interpolating one-parameter Hamiltonian. As the parameter is varied, one observes topological phase transitions, i.e., changes in the Chern integers of two bands due to the degeneracy of these bands at some parameter value. For small frequency, corresponding to a semiclassical regime, the degeneracies are shown to occur when the average energy of the two bands is approximately equal to the energy of the classical separatrix. Spectral and topological features of the Fibonacci crystal for small frequency leave a clear imprint on the corresponding Hofstadter butterfly for arbitrary frequency.

Scattering rate collapse driven by a van Hove singularity in the Dirac semimetal PdTe2

“…The very low value of the optical scattering rate together with the plasma frequency determined above allows us to estimate the resistivity to be ρ DC (T = 10K) ≈ 0.5± 0.2 µΩ · cm, very close to what is reported in recent transport experiments [9,14]. Combined with our observation of a frequency independent scattering rate up to the vHS energy scale E vHS suggests therefore that at low temperature the transport experiments are dominated by simple impurity and electron-electron scattering.…”

“…One such example is PdTe 2 , which features both bulk Dirac points [1][2][3] as well as topological surface states [4] in combination with a transition to a superconducting phase with T c = 1.4 -2 K [5][6][7][8]. The superconducting state is conventional with an isotropic superconducting gap [8][9][10][11]. One peculiarity observed in these experiments is that PdTe 2 supports a type-I superconducting state [8,12], but recently some surface effects have been observed that leave open the possibility for an interesting surface superconducting state [13,14].…”

Enhanced, homogeneously type-II superconductivity in Cu-intercalated PdTe2

“…The candidate type II Dirac semimetal PdTe 2 [1][2][3] superconducts below 1.7 K [4][5][6][7][8]. Though initial experimental papers suggested the possibility of an unconventional nature of the superconducting phase of PdTe 2 , a number of experiments confirmed that the superconductivity in PdTe 2 is conventional in nature [9,10]. However, some of these experiments found evidence of type I behaviour as far as the magnetic properties of the superconducting phase of PdTe 2 are concerned [4,11,12].…”

Floquet systems with Hall effect: Topological properties and phase transitions

“…Now, the quantum Hamiltonian (30) is the Harper one [29], whose energy bands have Chern numbers uniquely determined by the TKNN Eq. (25). Specifically, in the case of s = 1/p with p odd, one has ′ s = 2 s = q ′ /p ′ with q ′ = 2 and p ′ = p. Using Eq.…”

“…We start from the Diophantine equation (25) for the total Chern number σ(b) of the lowest b bands and divide this equation by p. We then take the limit of q, p → ∞ of irrational s , choosing the lowest b bands (b → ∞) to be those below some fixed gap. Denoting b/p in this limit by ζ, 0 < ζ < 1, we obtain…”