Fluctuations and magnetoresistance oscillations near the half-filled Landau level

Abstract

We study theoretically the magnetoresistance oscillations near a half-filled lowest Landau level (ν = 1/2) that result from the presence of a periodic one-dimensional electrostatic potential. We use the Dirac composite fermion theory of Son [Phys. Rev. X 5 031027 (2015)], where the ν = 1/2 state is described by a (2+1)-dimensional theory of quantum electrodynamics. We extend previous work that studied these oscillations in the mean-field limit by considering the effects of gauge field fluctuations within a large flavor approximation. A self-consistent analysis of the resulting Schwinger-Dyson equations suggests that fluctuations dynamically generate a Chern-Simons term for the gauge field and a magnetic field-dependent mass for the Dirac composite fermions away from ν = 1/2. We show how this mass results in a shift of the locations of the oscillation minima that improves the comparison with experiment [Kamburov et. al., Phys. Rev. Lett. 113, 196801 (2014)]. The temperature-dependent amplitude of these oscillations may enable an alternative way to measure this mass. This amplitude may also help distinguish the Dirac and Halperin, Lee, and Read composite fermion theories of the half-filled Landau level.

Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System

“…These are puzzling at first sight, and might imply a breakdown of particle-hole symmetry. The question of whether or not the CFs obey the particle-hole symmetry has in fact sparked exciting new developments in the field of strongly interacting electron systems [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]40]. These theories mostly predict that the particle-hole symmetry should hold within the lowest LL, while Balram et al, [20] conclude that it could be broken when LLM is significant.…”

The Half-Full Landau Level

“…19 They found that (27) fit their data points better than the simple formula E g = C/|∆B|, though both formulas contain a single fitting parameter. However, it is impossible to draw firm conclusions from such small systems, and the data would also be compatible with an asymptotic dependence of the form (29).…”

“…Recent work by Mitra and Mulligan has suggested that the discrepancy may be an effect of gauge fluctuations. 29 Minima in the magneto-exciton spectrum and maxima in the static structure factor.…”

Geometric resonance of four-flux composite fermions

“…Figure 1(c) zooms in around ν = 1/4. From the period of the modulation, a = 240 nm, we determine the expected positions for the primary i = 1 GR resistance minima according to [3,10,15,16,21,22,26,27]. The difference between the expected B i=1 for the two assumptions is very small and cannot be resolved in our experiments.…”

“…For example, recent GR measurements of 2 CF Fermi sea revealed an unexpected asymmetry between the two sides of ν = 1/2 [9]. This asymmetry, and more generally the question of particle-hole symmetry, inspired renewed interest in the physics of a half-filled LL [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. Notable among the new studies is the theory involving a Dirac fermion description [10,[15][16][17][18][19][21][22][23][24][25][26][27].…”