# Transport in Strongly Corelated Systems

Materials exhibiting strong electron-electron interactions pose some of the most outstanding puzzles in condensed matter physics. Notable examples are the cuprate high-temperature superconductors and heavy fermion metals. Transport measurements, and specifically the electronic conductivity tensor, are perhaps one of the most accessible probes for studying the properties of these materials. These measurements often reveal surprising results, which are challenging to explain theoretically. A striking example is the resistivity in the normal (high temperature) state of the cuprate superconductors, which in many materials increases linearly in temperature without showing any sign of saturation. A second important example is the Hall resistivity, which in some materials changes sign upon cooling the system into the superconducting state. Explaining these phenomena will shed considerable light on the nature of both the ground state and normal state of these materials.### Selected Work

#### Sign Reversal of the Hall Response in a Crystalline Superconductor

We consider the Hall conductivity due to the motion of a vortex in a lattice-model of a clean superconductor, using a combination of general arguments, unrestricted Hartree-Fock calculations, and exact diagonalization. In the weak coupling limit, kFξ≫1, the sign of the Hall response of the superconducting state is the same as that of the normal (non-superconducting) state. For intermediate and strong coupling, however, (kFξ∼1) we find that the sign of the Hall response in the superconducting state can be opposite to that of the normal state. In addition, we find that the sign reversal of the Hall response is correlated with a discontinuous change in the density profile at the vortex core. Implications for experiments in the cuprate superconductors are discussed.- Erez Berg, Sebastian D. Huber, N. H. Lindner, Sign Reversal of the Hall Response in a Crystalline Superconductor, arXiv:1403.2729

#### Topological Transitions for Lattice Bosons in a Magnetic Field

The Hall response provides an important characterization of strongly correlated phases of matter. We study the Hall conductivity of interacting bosons on a lattice sub-jected to a magnetic eld. We show that for any density or interaction strength, the Hallconductivity is characterized by a single integer. We nd that the phase diagram is intersected by topological transitions between dierent integer values. These transitions lead to surprising eects, including sign reversal of the Hall conductivity and extensive regions in the phase diagram where it acquires a negative sign. This implies that ux ow is reversed in these regions – vortices there ow upstream. Our nding have immediate applications to a wide range of phenomena in condensed matter physics, which are eectively described in terms of lattice bosons.- S. D. Huber and N. H. Lindner, Topological Transitions for Lattice Bosons in a Magnetic Field, Proceedings of the National Academy of Sciences (PNAS) 108, 19925 (2011) ; arXiv:1105.0904 [cond-mat.str-el]

#### Conductivity of hard core bosons: A paradigm of a bad metal

Two dimensional hard core bosons suer strong scattering in the high temperature resistive state at half filling. The dynamical conductivity σ(ω) is calculated using non perturbative tools such as continued fractions, series expansions and exact diagonalization. We nd a large temperature range with linearly increasing resistivity and broad dynamical conductivity, signaling a breakdown of Boltzmann-Drude quasiparticle transport theory. At zero temperature, a high frequency peak in σ(ω) appears above a “Higgs mass” gap, and corresponds to order parameter magnitude fluctuations. The similarity between conductivity of hard core bosons and some universal trends in unconventional superconductors such as cuprates is discussed.- N. H. Lindner and A. Auerbach, Conductivity of hard core bosons: A paradigm of a bad metal, Phys. Rev.B 81, 054512 (2010) (Editor’s suggestion) ; arXiv:0910.4158