Emergent phenomena in dispersionless quantum states

Dispersionless fermionic states (“flat bands”) are counterintuitive: with the electron velocity vanishing, our conventional notions of quasiparticle transport are no longer valid. We will discuss the quantum transport in the generalized families of perfectly flat bands [1], and find that while the conventional contributions indeed vanish, the quantum-geometric contribution gives rise to the enhanced electronic transport [2]. This contribution is connected to the Wannier orbital quantization in the perfectly flat bands [1], and is present only for geometrically-nontrivial bands (for example, flat Chern bands). We find similar expressions for thermal conductance, thermoelectric response, and superfluid weight in the flat bands. In particular, we report the anomalous thermopower associated with flat topological bands reaching values as large as kBeln2≈60 μV/k, the quantum unit of thermopower, not expected in conventional dispersive bands [2]. Time permitting, we shall also discuss entanglement entropy in dispersionless quantum states and its relation to quantum noise [3]. 

[1]  A. Kruchkov, “Quantum geometry, flat Chern bands, and Wannier orbital quantization,” Physical Review B (Letter), vol. 105, p. L241102, Jun 2022. 
[2]  A. Kruchkov, “Quantum transport in dispersionless electronic bands,” arXiv:2210.00351 (2022). 
[3]  T. Neupert, C. Chamon, and C. Mudry, “Measuring the quantum geometry of Bloch bands with current noise,” Physical Review B, vol. 87, no. 24, p. 245103, 2013.