Fractional quantum Hall valley ferromagnetism in the extreme quantum limit

Letter

Fractional quantum Hall valley ferromagnetism in the extreme quantum limit

Md. Shafayat Hossain, Meng K. Ma, Y. J. Chung, S. K. Singh, A. Gupta, K. W. West, K. W. Baldwin, L. N. Pfeiffer, R. Winkler, and M. Shayegan

Phys. Rev. B 106, L201303 – Published 17 November 2022

Abstract

Electrons' multiple quantum degrees of freedom can lead to rich physics, including a competition between various exotic ground states, as well as novel applications such as spintronics and valleytronics. Here we report magnetotransport experiments demonstrating how the valley degree of freedom impacts the fractional quantum states (FQHSs), and the related magnetic-flux-electron composite fermions (CFs), at very high magnetic fields in the extreme quantum limit when only the lowest Landau level is occupied. Unlike in other multivalley two-dimensional electron systems such as Si or monolayer graphene and transition-metal dichalcogenides, in our AlAs sample we can continuously tune the valley polarization via the application of in situ strain. We find that the FQHSs remain exceptionally strong even as they make valley polarization transitions, revealing a surprisingly robust ferromagnetism of the FQHSs and the underlying CFs. Our observation implies that the CFs are strongly interacting in our system. We are also able to obtain a phase diagram for the FQHS and CF valley polarization in the extreme quantum limit as we monitor transitions of the FHQSs with different valley polarizations.

Received 12 September 2022
Revised 31 October 2022
Accepted 8 November 2022

DOI:https://doi.org/10.1103/PhysRevB.106.L201303

Physics Subject Headings (PhySH)

Electrical conductivity Fractional quantum Hall effect Landau levels Magnetotransport Valleytronics

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Md. Shafayat Hossain ¹, Meng K. Ma¹, Y. J. Chung¹, S. K. Singh¹, A. Gupta ¹, K. W. West¹, K. W. Baldwin¹, L. N. Pfeiffer¹, R. Winkler ², and M. Shayegan ¹

¹Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA
²Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA

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Issue

Vol. 106, Iss. 20 — 15 November 2022

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Images

Figure 1
Sample description and characterization. (a) First Brillouin zone of bulk AlAs, showing anisotropic conduction-band valleys. (b) Sample geometry, showing the orientation of the two occupied valleys ( $X$ and $Y$ ) and the measured resistances ( $R_{[100]}$ and $R_{[010]}$ ). (c) Experimental setup for applying in-plane strain ( $ɛ$ ). (d) Piezoresistance of the sample at $B = 0$ and $T ≃ 0.03$ K, measured as a function of $ɛ$ . $α$ - $γ$ mark the valley occupancies. (e) Magnetotransport data at $T ≃ 0.03$ K, measured along [110], as a function of $ɛ$ showing numerous odd-denominator FQHSs in the lowest LL. Some of the LL fillings are marked in the top axis. (f) Magnetoresistance traces ( $R_{[110]}$ ) for different valley occupancies Traces are shown at three strain values as indicated (in units of $10^{- 4}$ ), which correspond to the cases when the 2D electrons occupy only the $X$ valley, only the $Y$ valley, and both $X$ and $Y$ valleys equally. Well-developed FQHSs, some of which are marked with dashed vertical lines, are seen in all traces.
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Figure 2
Valley transitions in the extreme quantum limit. (a)–(c) Piezoresistance along [110] at $p = 2$ –4, all taken at $T ≃ 0.3$ K, showing oscillations as a function of $ɛ$ until full valley polarization is reached. The $ɛ$ values for full valley polarization are marked with vertical dotted lines for different fillings. (d) Piezoresistances along [110] at $ν = 1 / 2$ . (e) Lambda level ( $Λ L$ ) diagram as a function of applied strain. $p$ denotes the $Λ L$ index. The $Λ Ls$ of the two valleys split as we apply $ɛ$ and instigate energy level coincidences and the consequent diamond-shaped regions as a function of $ɛ$ ; this in turn causes piezoresistance oscillations in (a)–(c). (f) Full valley polarization phase diagram in the extreme quantum limit extracted from the dotted vertical lines in (a)–(d). These energies are normalized to the Coulomb energy for various FQHSs and the CF Fermi sea at $ν = 1 / 2$ , and are plotted vs $1 / p$ . The data points are obtained from the average $| ɛ |$ values for full valley polarization for $ɛ > 0$ and $ɛ < 0$ , and the differences between the two sides are shown as the error bars. The data point at $ν = 1 / 2$ is based on $| ɛ |$ beyond which piezoresistance at $ν = 1 / 2$ saturates; see Fig. 2 and [29]. The black dotted lines connecting the data points represent the boundary between the partially and fully valley polarized phases. Theoretically calculated spin-polarization energy of CFs [31] is shown using red circles (at positive $p$ values) and are joined by a red line. A particle-hole symmetric red line is also drawn for negative $p$ . (g) Charge distribution and Fermi sea for our AlAs sample when the electrons occupy a single valley (top) and two valleys equally (bottom), obtained from self-consistent quantum mechanical calculations [30].
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