We propose the possible detection of broken mirror symmetries in correlated two-dimensional materials by elastotransport measurements. Using linear response theory we calculate the shearconductivity $Gamma_{xx,xy}$, defined as the linear change of the longitudinal conductivity $sigma_{xx}$ due to a shear strain $epsilon_{xy}$. This quantity can only be non-vanishing when in-plane mirror symmetries are broken and we discuss how candidate states in the cuprate pseudogap regime (e.g. various loop current or charge orders) may exhibit a finite shearconductivity. We also provide a realistic experimental protocol for detecting such a response.
Harpers equation (aka the almost Mathieu equation) famously describes the quantum dynamics of an electron on a one dimensional lattice in the presence of an incommensurate potential with magnitude $V$ and wave number $Q$. It has been proven that all states are delocalized if $V$ is less than a critical value $V_c=2t$ and localized if $V> V_c$. Here, we show that this result (while correct) is highly misleading, at least in the small $Q$ limit. In particular, for $V<V_c$ there is an abrupt crossover akin to a mobility edge at an energy $E_c$; states with energy $|E|<E_c$ are robustly delocalized, but those in the tails of the density of states, with $|E|>E_c$, form a set of narrow bands with exponentially small bandwidths $ sim t exp[-(2pialpha/Q)]$ (where $alpha$ is an energy dependent number of order 1) separated by band-gaps $ sim t Q$. Thus, the states with $|E|> E_c$ are almost localized in that they have an exponentially large effective mass and are easily localized by small perturbations. We establish this both using exact numerical solution of the problem, and by exploiting the well known fact that the same eigenvalue problem arises in the Hofstadter problem of an electron moving on a 2D lattice in the presence of a magnetic field, $B=Q/2pi$. From the 2D perspective, the almost localized states are simply the Landau levels associated with semiclassical precession around closed contours of constant quasiparticle energy; that they are not truly localized reflects an extremely subtle form of magnetic breakdown.
Because a material with an incommensurate charge density wave (ICDW) is only quasi-periodic, Blochs theorem does not apply and there is no sharply defined Fermi surface. We will show that, as a consequence, there are no quantum oscillations which are truly periodic functions of $1/B$ (where $ B$ is the magnitude of an applied magnetic field). For a weak ICDW, there exist broad ranges of $1/B$ in which approximately periodic variations occur, but with frequencies that vary inexorably in an unending cascade with increasing $1/B$. For a strong ICDW, e.g. in a quasi-crystal, no quantum oscillations survive at all. Rational and irrational numbers really are different.
Motivated by recent observations of charge order in the pseudogap regime of hole-doped cuprates, we show that {it crisscrossed} stripe order can be stabilized by coherent, momentum-dependent interlayer tunneling, which is known to be present in several cuprate materials. We further describe how subtle variations in the couplings between layers can lead to a variety of stripe ordering arrangements, and discuss the implications of our results for recent experiments in underdoped cuprates.
Measurements of the differential elastoresistance of URu$_2$Si$_2$ reveal that the fluctuations associated with the 17 K Hidden Order phase transition have a nematic component. Approaching the Hidden Order phase transition from above, the nematic susceptibility abruptly changes sign, indicating that while the Hidden Order phase has a nematic component, it breaks additional symmetries.
