Non-linear conductance in mesoscopic weakly disordered wires -- Interaction and magnetic field asymmetry

We study the non-linear conductance $\mathcal{G}\sim\partial^2I/\partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim0.006\,E_\mathrm{Th}^{-1}$ (and $\langle\mathcal{G}\rangle=0$), where $E_\mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $\mathcal{G}_a\sim0.001\,(gE_\mathrm{Th})^{-1}$, where $g\gg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_\varphi\ll L$, where $L_\varphi$ is the phase coherence length, we get $\mathcal{G}\sim(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$, and $\mathcal{G}_a\sim(L_\varphi/L)^{11/2}(gE_\mathrm{Th})^{-1}\ll\mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_\varphi\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim(L_T/L)(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $\mathcal{G}_a\sim(L_T/L)^2(L_\varphi/L)^{7/2}(gE_\mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed.Comment: RevTeX, 39 pages, 38 pdf figures ; v2: Sections II, VII, VIII & IX reorganised, refs added ; v3: Table I updated, Appendices B & C extended, to appear in Phys. Rev.

Minimal model for double Weyl points, multiband quantum geometry, and singular flat band inspired by LK-99

Two common difficulties in the design of topological quantum materials are that the desired features lie too far from the Fermi level and are spread over a too large energy range. Doping-induced states at the Fermi level provide a solution, where non-trivial topological properties are enforced by the doping-reduced symmetry. To show this, we consider a regular placement of dopants in a lattice of space group (SG) 176 (P6$\text{}_3$/m), which reduces the symmetry to SG 143 (P3). Our two- and four-band models feature symmetry-enforced double Weyl points at $\Gamma$ and A with Chern bands for $k_z\neq 0,\pi$, Van Hove singularities, nontrivial multiband quantum geometry due to mixed orbital character, and a singular flat band. The excellent agreement with density-functional theory (DFT) calculations on copper-doped lead apatite ('LK-99') provides evidence that minimal topological bands at the Fermi level can be realized in doped materials.Comment: Shortened for peer-review, phase convention adjusted, recent literature adde

Nontrivial quantum geometry of degenerate flat bands

The importance of the quantum metric in flat-band systems has been noticed recently in many contexts such as the superfluid stiffness, the dc electrical conductivity, and ideal Chern insulators. Both the quantum metric of degenerate and nondegenerate bands can be naturally described via the geometry of different Grassmannian manifolds, specific to the band degeneracies. Contrary to the (Abelian) Berry curvature, the quantum metric of a degenerate band resulting from the collapse of a collection of bands is not simply the sum of the individual quantum metrics. We provide a physical interpretation of this phenomenon in terms of transition dipole matrix elements between two bands. By considering a toy model, we show that the quantum metric gets enhanced, reduced, or remains unaffected depending on which bands collapse. The dc longitudinal conductivity and the superfluid stiffness are known to be proportional to the quantum metric for flat-band systems, which makes them suitable candidates for the observation of this phenomenon.Comment: 6+15 pages (including Supplemental Material), 2+2 figures; closer to published versio

Nonlinear conductance in weakly disordered mesoscopic wires: Interaction and magnetic field asymmetry

RevTeX, 39 pages, 38 pdf figures ; v2: Sections II, VII, VIII & IX reorganised, refs added ; v3: Table I updated, Appendices B & C extended, to appear in Phys. Rev. BInternational audienceWe study the non-linear conductance $\mathcal{G}\sim\partial^2I/\partial V^2|_{V=0}$ in coherent quasi-1D weakly disordered metallic wires. The analysis is based on the calculation of two fundamental correlators (correlations of conductance's functional derivatives and correlations of injectivities), which are obtained explicitly by using diagrammatic techniques. In a coherent wire of length $L$, we obtain $\mathcal{G}\sim0.006\,E_\mathrm{Th}^{-1}$ (and $\langle\mathcal{G}\rangle=0$), where $E_\mathrm{Th}=D/L^2$ is the Thouless energy and $D$ the diffusion constant; the small dimensionless factor results from screening, i.e. cannot be obtained within a simple theory for non-interacting electrons. Electronic interactions are also responsible for an asymmetry under magnetic field reversal: the antisymmetric part of the non-linear conductance (at high magnetic field) being much smaller than the symmetric one, $\mathcal{G}_a\sim0.001\,(gE_\mathrm{Th})^{-1}$, where $g\gg1$ is the dimensionless (linear) conductance of the wire. Weakly coherent regimes are also studied: for $L_\varphi\ll L$, where $L_\varphi$ is the phase coherence length, we get $\mathcal{G}\sim(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$, and $\mathcal{G}_a\sim(L_\varphi/L)^{11/2}(gE_\mathrm{Th})^{-1}\ll\mathcal{G}$ (at high magnetic field). When thermal fluctuations are important, $L_T\ll L_\varphi\ll L$ where $L_T=\sqrt{D/T}$, we obtain $\mathcal{G}\sim(L_T/L)(L_\varphi/L)^{7/2}E_\mathrm{Th}^{-1}$ (the result is dominated by the effect of screening) and $\mathcal{G}_a\sim(L_T/L)^2(L_\varphi/L)^{7/2}(gE_\mathrm{Th})^{-1}$. All the precise dimensionless prefactors are obtained. Crossovers towards the zero magnetic field regime are also analysed