Fermi surface resonance and quantum criticality in strongly interacting Fermi gases

Fermions in a Fermi gas obey the Pauli exclusion principle restricting any two fermions from occupying the same quantum state. Strong interactions between fermions can completely change the properties of the Fermi gas. In our theoretical study we find an exotic quantum phase in strongly interacting Fermi gases subject to a certain condition imposed on the Fermi surfaces that we call the Fermi surface resonance. The phase is quantum critical in time and space and can be identified by the power-law dependence of the spectral density in frequency and momentum. The linear-response functions are singular in the static limit and at the Kohn anomalies. We analyze the quantum critical state at finite temperatures $T$ and finite size $L$ of the Fermi gas and provide a qualitative $L-T$ phase diagram. The quantum critical phase can be experimentally found in typical semiconductor heterostructures.

Figure 1

Examples of the FSR. Some of the elementary resonant processes (not all of them) are shown by the arrows. (a) The simplest example of FSR can be realized in semiconductor heterostructures with two filled subbands [see Eq. (4)]. The spin degeneracy of the subbands is lifted by the applied magnetic field. The resonant Fermi surfaces are indicated by color. The gray Fermi surface is off resonance. (b) Three-dimensional example of the FSR. Only the resonant Fermi surfaces are shown.

Figure 2

Electron self-energy. (a) Feynman diagram for the exact self-energy for the case $N=2$. Solid lines correspond to the exact Green functions [see Eq. (9)]. The Fermi surface index $a\in \{1,2,3,4\}$ is indicated by color and corresponds to the example given in Fig. 1. The black (white) square corresponds to the exact (bare) interaction vertex. There are two more contributions to the self-energy that differ by the arrow directions. The Feynman diagrams for general $N$ can be drawn similarly. (b) The SCBA. The interaction vertex correction is neglected which is shown by two bare vertices (white squares).

Figure 3

The $L-T$ phase diagram illustrating the crossover between the LFL (blue) and quantum critical (QC) state (red). The dashed lines correspond to upper and lower bounds in Eq. (47). The upper bound for the wire length $L^{*}$ corresponds to Eq. (48).