Magnetic oscillations in a holographic liquid

We present a holographic perspective on magnetic oscillations in strongly correlated electron systems via a fluid of charged spin $1/2$ particles outside a black brane in an asymptotically anti-de-Sitter spacetime. The resulting backreaction on the spacetime geometry and bulk gauge field gives rise to magnetic oscillations in the dual field theory, which can be directly studied without introducing probe fermions, and which differ from those predicted by Fermi liquid theory.

Figure 1

Profile of the fluid charge density $\widehat{\sigma }$, with parameters chosen so that $\max {\ell }_{\text{filled}}=5$.

Figure 2

Phase diagram of dyonic electron fluid solutions for $\widehat{m}=0.5$, with axes normalized such that the boundary chemical potential is $\widehat{\mu }=1$. The different color shadings mark parameter regions with different maximum numbers of occupied Landau levels, increasing from left to right. In the limit $\widehat{\mathcal{B}}\to 0$ the edges between the regions all asymptote to ${\widehat{\mathcal{T}}}_c$, the maximal temperature at which the electron fluid is supported at $\widehat{\mathcal{B}}=0$.

Figure 3

Magnetization vs magnetic field strength for various values of $\widehat{m}$. Solid lines correspond to the electron fluid geometry, dashed ones to a dyonic black brane at same temperature and chemical potential. The labels denote temperatures $\widehat{\mathcal{T}}/{\widehat{\mathcal{T}}}_c=0.9(a),0.3(b),3·10^{-3}(c)$. In the leftmost plot $(b)$ was omitted due to too much visual overlap with the other curves. In the rightmost plot the relative sign of $\widehat{\mathcal{M}}$ and $\widehat{B}$ changes as a function of magnetic field, indicating a crossover from a diamagnetic to a paramagnetic state.

Figure 4

Period of the de Haas–van Alphen oscillations as a function of temperature for $\widehat{m}=0.5$, the dotted vertical line marks the critical temperature where the solution makes the transition to a dyonic black brane.