Dynamical magnetic breakdown and quantum oscillations from hot spot scattering

Abstract

Quantum oscillations (QO) are a well-established probe of Fermi-surface (FS) geometry and in the presence of long-range density wave order can display new QO frequencies from reconstructed FS pockets. We show that such reconstructed frequencies can arise even in the absence of long-range density order. Considering electrons coupled to a fluctuating bosonic mode that scatters quasiparticles between sharp hot spots on the FS, we develop a semiclassical theory in which the interaction generates time-dependent tunneling processes analogous to magnetic breakdown. This dynamical magnetic breakdown produces new semiclassical orbits corresponding to reconstructed FS areas despite the absence of static order. Because tunneling probabilities depend on the thermal population of bosonic excitations, the resulting oscillation amplitudes exhibit characteristic deviations from standard Lifshitz-Kosevich behavior. Our results provide a mechanism to probe bosonic fluctuations in quantum critical metals and provide a framework for dynamical magnetic breakdown.

Figures (6)

• Figure 1: Left: Reconstruction scenario, where the large (deep purple) hole FS is folded in the presence of long-range density wave order and $\langle \phi \rangle \neq 0$ opens gaps at the (pink) hot spots, with hole-like (light blue) and electron-like (orange) pockets. The two resulting FS areas proportional to QO frequencies are sketched below. Right: Dynamical scenario without long-range order, where a fluctuating boson $\phi$ (with $\langle \phi \rangle=0$) scatters holes between hot spot pairs, allowing new semiclassical trajectories (e.g. the dashed pink orbit). The effective areas enclosed by the breakdown paths are sketched below.
• Figure 2: Tunneling geometry at a hot spot. In a given $(\phi_0^*,\phi_0)$ sector and at fixed $t$, the local FS geometry is hyperbolic with parameters $(\delta k_x,\delta k_y)$. The local system of axes $(k_x,k_y)$ and tunneling coordinate $z$ are those of Eqs.\ref{['eq:99']}. The tunneling of a (deep purple) particle through the junction can be described by a relation like Eq.\ref{['eq:115']} between wavefunction amplitudes $a_{L/R}^\pm$.
• Figure 3: Summary of wavefunction amplitudes at several points of the FS, and of phase factors accumulated along semiclassical paths. The red and blue semicircles belong to a single large circular FS. The "$\approx$", "$\approx$" and "$\parallel$" indicate (wavefunction) periodicity along the physical FS. Dotted lines are in the hot spot regions. Factors $e^{i\vartheta},e^{i\varphi/2}$ are the phases acquired by electrons along the corresponding semiclassical paths.
• Figure 4: Left: the temperature dependence of the QO amplitudes $A_\ast(T)$ for $\ast= \text{\small (} \! \text{\small )} , \text{\Square, \Circle}$ does not obey the Lifshitz-Kosevich dependence, i.e. $R_{\rm LK}^{[m_\ast]}=A_\ast(T)/P_\ast(T)$ from \ref{['eq:69']}. Right: evolution of the curves $A_{\text{\Circle}}(T), A_{(\!)}(T)$ for decreasing $\Omega \in [0.02,0.2].$ The dashed curves are in the limits $\Omega \rightarrow \infty$ (for $A_{\text{\Circle}}$) and $\Omega \rightarrow 0$ (for $A_{(\!)}$), and equate the corresponding dashed curves in the left panel. Note that here $\Omega,m_\star$ are treated as independent from $B,T$.
• Figure 5: Diagrammatic summary of the vertex correction equation.