TY - JOUR

T1 - Hall viscosity and momentum transport in lattice and continuum models of the integer quantum Hall effect in strong magnetic fields

AU - Tuegel, Thomas I.

AU - Hughes, Taylor L.

PY - 2015/10/26

Y1 - 2015/10/26

N2 - The Hall viscosity describes a nondissipative response to strain in systems with broken time-reversal symmetry. We develop a method for computing the Hall viscosity of lattice systems in strong magnetic fields based on momentum transport, which we compare to the method of momentum polarization used by Tu et al. [Phys. Rev. B 88, 195412 (2013)10.1103/PhysRevB.88.195412] and Zaletel et al. [Phys. Rev. Lett. 110, 236801 (2013)10.1103/PhysRevLett.110.236801] for noninteracting systems. We compare the Hall viscosity of square-lattice tight-binding models in magnetic field to the continuum integer quantum Hall effect (IQHE) showing agreement when the magnetic length is much larger than the lattice constant, but deviation as the magnetic field strength increases. We also relate the Hall viscosity of relativistic electrons in magnetic field (the Dirac IQHE) to the conventional IQHE. The Hall viscosity of the lattice Dirac model in magnetic field agrees with the continuum Dirac Hall viscosity when the magnetic length is much larger than the lattice constant. We also show that the Hall viscosity of the lattice model deviates further from the continuum model if the C4 symmetry of the square lattice is broken to C2, but the deviation is again minimized as the magnetic length increases.

AB - The Hall viscosity describes a nondissipative response to strain in systems with broken time-reversal symmetry. We develop a method for computing the Hall viscosity of lattice systems in strong magnetic fields based on momentum transport, which we compare to the method of momentum polarization used by Tu et al. [Phys. Rev. B 88, 195412 (2013)10.1103/PhysRevB.88.195412] and Zaletel et al. [Phys. Rev. Lett. 110, 236801 (2013)10.1103/PhysRevLett.110.236801] for noninteracting systems. We compare the Hall viscosity of square-lattice tight-binding models in magnetic field to the continuum integer quantum Hall effect (IQHE) showing agreement when the magnetic length is much larger than the lattice constant, but deviation as the magnetic field strength increases. We also relate the Hall viscosity of relativistic electrons in magnetic field (the Dirac IQHE) to the conventional IQHE. The Hall viscosity of the lattice Dirac model in magnetic field agrees with the continuum Dirac Hall viscosity when the magnetic length is much larger than the lattice constant. We also show that the Hall viscosity of the lattice model deviates further from the continuum model if the C4 symmetry of the square lattice is broken to C2, but the deviation is again minimized as the magnetic length increases.

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U2 - 10.1103/PhysRevB.92.165127

DO - 10.1103/PhysRevB.92.165127

M3 - Article

AN - SCOPUS:84946811721

VL - 92

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 16

M1 - 165127

ER -