Fermi Surface Geometry and Toplogy of Composite Fermions

The nature of the composite fermion Fermi liquid formed for filling fraction ν = 1/2 in the lowest Landau level in two-dimensional electron systems with circular symmetry subject to a high magnetic fields has been the subject of much discussion recently [1,2]. However, little attention had so far been paid to the geometry of the Fermi surface for non-parabolic electron dispersions, and dispersions without continuous rotational symmetry. 

This talk will describe our investigation [3-5] on the shape of the Fermi surface of the composite fermion Fermi fluid at filling fraction ν = 1/2 for non-parabolic electron dispersions,as well as dispersions with discrete, n-fold rotational symmetry. Using a combination of analytic results andnumerical many-body computations based on the infinite Density Matrix Renormalization Group (iDMRG) method [6], we obtain, for the first time, a comprehensive understanding of the elasticity of the composite fermion Fermi surface, and the relationship between the geometry and topology of the composite fermion Fermi surface and that of the Fermi surface at zero magnetic field. In particular, our numerical results for mass anisotropy, with no adjustable parameters, agree with experimental findings on strained GaAs layers [7].

* This work was supported by US Department of Energy, Division of Basic Energy Sciences Grant Number DE-SC0002140.

[1] 	D. T. Son, Physical Review X 5, 031027 (2015).
[2] 	Chong Wang, Nigel R. Cooper, Bertrand I. Halperin and Ady Stern, Physical Review X 7, 031029 (2017); B. I Halperin, P. A. Lee & N. Read, Physical Review B 47, 7312 (1993).
[3] 	Matteo Ippoliti, Scott D. Geraedts & R. N. Bhatt, Physical Review B 95, 201104 (2017) - Rapid Communications.
[4] 	Matteo Ippoliti, Scott D. Geraedts & R. N. Bhatt, Physical Review B 96, 045145 (2017).
[5] 	Matteo Ippoliti, Scott D. Geraedts & R. N. Bhatt, Physical Review B 96, 115151 (2017).
[6] 	Michael P. Zaletel, R. S. K. Mong, & Frank Pollman, Physical Review Letters 110, 236801 (2013).
[7] 	Insun Jo, K. A., Villegas Rosales, M. A. Mueed, L. N. Pfeiffer, K. W. West, K. W. Baldwin, R. Winkler, MediniPadmanabhan and M. Shayegan, Physical Review Letters 119, 016402 (2017).