Experimentally observable signatures of odd-frequency pairing in multiband superconductors

We investigate how hybridization (single-quasiparticle scattering) between two superconducting bands induces odd-frequency superconductivity in a multiband superconductor. An explicit derivation of the odd-frequency pairing correlation and its full frequency dependence is given. We also find that the density of states is modified, at higher energies, from the sum of the two BCS spectra to also include additional hybridization gaps with strong coherence peaks when odd-frequency pairing is present. These gaps constitute clear experimentally measurable signatures of odd-frequency pairing in multiband superconductors.

Figure 1

(a) Odd- and (b) even-interband pairing amplitudes in meV per ${\mathrm{nm}}^3$ when ${\mathrm{\Delta }}_2=2.5$ meV, ${\mathrm{\Delta }}_1=$ 2.5, 2.8, 4.5 meV (blue, orange, green), and $\mathrm{\Gamma }=3$ meV, with the band structure specified in the main text. (Inset:) First-order hybridization contributions to the interband pairing: $F_1\mathrm{\Gamma }{G}_2$ (top) and $-{\overleftarrow{G}}_1\mathrm{\Gamma }{F}_2$ (bottom). Solid (dashed) line represents the propagator in band 1 (2) and $\times$ the hybridization.

Figure 2

Total ($N$) and partial densities of states ($N_1, N_2$) when ${\mathrm{\Delta }}_1=2.5$ meV and ${\mathrm{\Delta }}_2=1$ meV for different values of $\mathrm{\Gamma }=0,0.5,3,6$ meV [(a)–(d)], with the band structure specified in the main text.

Figure 3

Total ($N$) and partial densities of states ($N_1, N_2$) when ${\mathrm{\Delta }}_2=2.5$ meV and $\mathrm{\Gamma }=3$ meV for different values of ${\mathrm{\Delta }}_1=0.5,2,2.5,2.8,4.5,7.5,10,15$ meV [(a)–(h)], with the band structure specified in the main text.

Figure 4

Total ($N$) and partial densities of states ($N_1, N_2$) when ${\mathrm{\Delta }}_1=3$ meV and ${\mathrm{\Delta }}_2=0$, i.e., only one band with native superconductivity, for different values of $\mathrm{\Gamma }=1,2,3,5$ meV [(a)–(d)] with the band structure specified in the main text.

Figure 5

Hybridized bands in the normal state (a) (bands are doubled due to particle-hole symmetry in the Hamiltonian) and in the superconducting state (b). Green (light) color corresponds to hole character, blue (dark) to electron character. The band structure is specified in the main text and the density of states for (b) is shown in Fig. 3.