Abstract
We present a study of Hall transport in semi-Dirac critical phases. The construction is based on a covariant formulation of relativistic systems with spatial anisotropy. Geometric data together with external electromagnetic fields is used to devise an expansion procedure that leads to a low-energy effective action consistent with the discrete $PT$ symmetry that we impose. We use the action to discuss terms contributing to the Hall transport and extract the coefficients. We also discuss the associated scaling symmetry.
Highlights
Low-energy effective actions have become an important tool to study topological responses of quantum phases of matter [1]
The resulting effective action will be a local functional of the background sources, that must be invariant under the local symmetry transformations (3.15) and discrete symmetries of the fermionic action, in particular PT
Recent interest in odd responses is stimulated by experiments with fluids that break parity
Summary
Low-energy effective actions have become an important tool to study topological responses of quantum phases of matter [1]. Initially applied to phases with large symmetry groups such as Galilean or Poincaré, in recent years effective theories have been used to shed light on states with more exotic or reduced symmetry groups These symmetries can be realized in various topological materials undergoing quantum phase transitions from a conductor to a band insulator. To shed light on the generic low-energy properties of such quantum Hall states, we construct an effective action for systems with a semi-Dirac phase. Thought of as an elusive transport property, Hall viscosity has been experimentally identified in both hard [47] and soft [48] condensed matter experiments In this Rapid Communication we present a step-by-step construction of the low-energy effective theory.
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