Abstract
The half filled Landau level is expected to be approximately particle-hole symmetric, which requires an extension of the Halperin-Lee-Read (HLR) theory of the compressible state observed at this filling. Recent work indicates that, when particle-hole symmetry is preserved, the composite Fermions experience a quantized $\pi$-Berry phase upon winding around the composite Fermi-surface, analogous to Dirac fermions at the surface of a 3D topological insulator. In contrast, the effective low energy theory of the composite fermion liquid originally proposed by HLR lacks particle-hole symmetry and has vanishing Berry phase. In this paper, we explain how thermoelectric transport measurements can be used to test the Dirac nature of the composite Fermions by quantitatively extracting this Berry phase. First we point out that longitudinal thermopower (Seebeck effect) is non-vanishing due to the unusual nature of particle hole symmetry in this context and is not sensitive to the Berry phase. In contrast, we find that off-diagonal thermopower (Nernst effect) is directly related to the topological structure of the composite Fermi surface, vanishing for zero Berry phase and taking its maximal value for $\pi$ Berry phase. In contrast, in purely electrical transport signatures the Berry phase contributions appear as small corrections to a large background signal, making the Nernst effect a promising diagnostic of the Dirac nature of composite fermions.
Highlights
In contrast to the incompressible fractional quantum Hall states at filling fractions ν 1⁄4 1⁄2p=ð2p þ 1Þ, the half-filled Landau level (LL) exhibits a compressible state with nonzero longitudinal conductance. The origin of this compressible state is naturally explained by the (CF) picture from Halperin, Lee, and Read (HLR) [1], in which electrons bind two flux quanta apiece, becoming composite fermions [2] that feel zero average orbital magnetic field and form a metallic state with a composite Fermi surface
The HLR description begins by formally attaching flux to electrons and naturally leads to a low-energy description in terms of spinless CFs coupled to a Chern-Simons gauge field that breaks particle-hole symmetry (PHS)—which we will refer to as the “HLR state.”
It was recently realized [6,7,8,9,10,11] that the HLR picture could be modified to produce a manifestly particle-hole symmetric candidate phase for the half-filled Landau level —the composite Dirac liquid (CDL)
Summary
In contrast to the incompressible fractional quantum Hall states at filling fractions ν 1⁄4 1⁄2p=ð2p þ 1Þ, the half-filled Landau level (LL) exhibits a compressible state with nonzero longitudinal conductance The origin of this compressible state is naturally explained by the (CF) picture from Halperin, Lee, and Read (HLR) [1], in which electrons bind two flux quanta apiece, becoming composite fermions [2] that feel zero average orbital magnetic field and form a metallic state with a composite Fermi surface. Principle, possible that the experimental system chooses to spontaneously break PHS and form the HLR state, this option does not appear to be energetically favored in numerical simulations [5] It was recently realized [6,7,8,9,10,11] that the HLR picture could be modified to produce a manifestly particle-hole symmetric candidate phase for the half-filled Landau level —the composite Dirac liquid (CDL). We show how the Nernst effect in combination with conductivity and thermopower measurements can be used to quantitatively extract the composite Fermi-surface Berry phase
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