Pavlo SukhachovNORDITA

Odd-frequency pairing

2

• Pairing amplitude:

• Permutations:Spin

Coordinates

Orbit

Time

[J. Linder and A.V. Balatsky, arXiv:1709.03986]

Pairing channel

3

Even-frequency pairing:

Odd-frequency pairing:

𝑺𝑺 𝑷𝑷∗ 𝝌𝝌 𝑻𝑻∗ Total

- + + + -

𝑺𝑺 𝑷𝑷∗ 𝝌𝝌 𝑻𝑻∗ Total

- + - - -

Potentials and gaps

4

Two ansatzes:

[P.O.Sukhachov, V. Juricic, A.V. Balatsky, Phys. Rev. B 100, 180502 (2019); arXiv:1908.11385]

Density of states 𝜈𝜈

5

No states in the gap Cusp-like features

Optical response in usual metals

6

[P.O.Sukhachov, A.V. Balatsky, Phys. Rev. B 100, 134516 (2019); arXiv:1908.08228]

Trace of the spectral function

7

Critical slope:

Critical slope:

Real part of the conductivity

8

Imaginary part of the conductivity

9

10

Summary1. Repulsive frequency-dependent potentials can lead

to the Berezinskii or, equivalently, odd-frequency pairing in Dirac semimetals.

2. The realization of both even- and odd-frequency pairings requires the coupling constants that exceed a critical value at the charge neutrality point.

3. The optical response is characterized by sharp peaks for the Berezinskii pairing whose position depends on the frequency profile of the gap.

4. Transparency windows (𝐼𝐼𝐼𝐼 𝜎𝜎 < 0) occur at the onsets of the attenuation peaks for the odd-frequency pairing.