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High-mobility holes in gallium nitride and their quantum oscillations

Nature Electronics (2026)Cite this article

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Abstract

Gallium nitride (GaN) is used in solid-state lighting and in high-performance radio frequency and power electronics. However, due to inefficient hole doping and low hole mobility, quantum oscillations in p-type GaN have not been observed, which limits studies of valence bands and hole transport engineering. Here we report high hole mobilities in a polarization-induced two-dimensional hole gas at a gallium nitride/aluminium nitride interface. The holes degenerately occupy two valence bands of GaN—the light-hole and heavy-hole bands—and have mobilities of 2,000 cm2 V−1 s−1 and 400 cm2 V−1 s−1 at 2 K, respectively. We use Shubnikov–de Haas oscillations of holes from both valence bands to extract their respective sheet densities and quantum scattering times and the effective masses of light holes and heavy holes. The hole mobilities of our heterostructure highlight the possibility of developing cryogenic GaN complementary metal–oxide–semiconductor technology with potential applications in quantum computing control electronics.

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Fig. 1: Structural and transport properties of a GaN/AlN 2DHG.
Fig. 2: FFT analysis of SdH oscillations.
Fig. 3: Calculated band dispersions and effective masses.
Fig. 4: Field dependence of LH mass.

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Source data that support the findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank V. Protasenko for help with the operation of the molecular beam epitaxy system. We thank E. Mueller, N. Harrison, J. Palmstrom, J. Singleton, L. Winter, C. Yu and R. Chaudhuri for fruitful discussions on quantum transport and epitaxy. We thank D. Deen with Quantinuum for discussions on cryogenic CMOS. C.F.C.C., J.E.D., Z.Z., J.-C.C., S.J.B, J.E., F.G., D.J. and H.G.X are grateful for support by SUPREME, one of seven centres in JUMP 2.0, Semiconductor Research Corporation (SRC) programme sponsored by DARPA. C.F.C.C., J.E.D. and H.G.X. acknowledge support by the NSF FuSe programme, grant no. CMMI-2329063. J.E.D., D.J. and H.G.X. acknowledge support as part of ULTRA, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under grant no. DE-SC0021230. N.P., D.A.M., D.J. and H.G.X. acknowledge support by the Army Research Office grant no. W911NF2220177. Characterizations and measurements were performed in part at Cornell NanoScale Facility, a National Nanotechnology Coordinated Infrastructure (NNCI) member supported by NSF grant no. NNCI-2025233. We also made use of the Cornell Center for Materials Research Shared Facilities. The Thermo Fisher Spectra 300 X-CFEG was acquired with support from PARADIM, an NSF MIP (grant no. DMR-2039380) and Cornell University. O.E.A.V., S.A.C., F.F.B., R.D.M. and the National High Magnetic Field Laboratory are supported by the National Science Foundation through grant no. NSF/DMR-2128556, the State of Florida and the US DOE.

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Author notes

  1. Samuel J. Bader

    Present address: Foundry Technology Research, Intel Corporation, Hillsboro, OR, USA

Authors and Affiliations

  1. Department of Physics, Cornell University, Ithaca, NY, USA

    Chuan F. C. Chang

  2. School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA

    Joseph E. Dill, Samuel J. Bader & David A. Muller

  3. School of Electrical and Computer Engineering, Cornell University, Ithaca, NY, USA

    Zexuan Zhang, Jimy Encomendero, Debdeep Jena & Huili Grace Xing

  4. Department of Physics, The University of Texas Austin, Austin, TX, USA

    Jie-Cheng Chen & Feliciano Giustino

  5. Oden Institute for Computational Engineering and Sciences, The University of Texas Austin, Austin, TX, USA

    Jie-Cheng Chen & Feliciano Giustino

  6. Department of Materials Science and Engineering, Cornell University, Ithaca, NY, USA

    Naomi Pieczulewski, Debdeep Jena & Huili Grace Xing

  7. National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, NM, USA

    Oscar E. Ayala Valenzuela, Scott A. Crooker, Fedor F. Balakirev & Ross D. McDonald

  8. Kavli Institute at Cornell for Nanoscale Science, Ithaca, NY, USA

    David A. Muller, Debdeep Jena & Huili Grace Xing

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Contributions

H.G.X. and D.J. supervised the project. C.F.C.C. and Z.Z. grew the GaN/AlN epitaxial structures. J.E.D. and J.E. fabricated the Hall bar devices. C.F.C.C., J.E.D., O.E.A.V., F.F.B. and S.A.C. performed the pulsed-field magnetotransport experiments. C.F.C.C. performed the 9 T magnetotransport experiments. N.P. and D.A.M. provided STEM images. C.F.C.C. analysed the magnetotransport data. J.-C.C. and F.G. performed first-principle GW calculations. C.F.C.C performed other theoretical calculations. C.F.C.C. wrote the manuscript. C.F.C.C., S.A.C., R.D.M., S.J.B., D.J. and H.G.X. revised the manuscript.

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Correspondence to Chuan F. C. Chang, Debdeep Jena or Huili Grace Xing.

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Competing interests

H.G.X., D.J. and S.J.B. are inventors on US patent no. 11158709B2 held by Cornell University, which covers the polarization-induced 2DHG heterostructure used in this study. The remaining authors declare no competing interests.

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Extended data

Extended Data Fig. 1 Low-field magnetotransport measurement and two-channel Drude model fitting.

a-b, Longitudinal resistance (Rxx) and Hall resistance (RHall = Rxy = VHall/Ix) up to 9 T were measured in a PPMS system using DC current and static magnetic fields. Data for T = 2 K (a) and T = 17 K (b) are shown as examples. Solid circles are data, and the dashed lines are fits to a two-channel classical Drude model (see Supplementary Note I). As discussed in Supplementary Note I, table-top Hall effect measurements using a small B (for example, up to ±1 T) give an apparent Hall density (napparent) and an apparent mobility (μapparent) based on Rsh (Rxx at 0 T) and the slope of Rxy in the ±1 T range, as shown in (a) and (b); PPMS measurements of Rxx and Rxy up to 9 T allow for the separation of LH and HH mobilities (c) and densities (d) via two-channel fitting. Error bars indicate the range spanned by three independent fitting procedures (to Rxx(B), to Rxy(B), and simultaneously to both); the symbols denote the midpoint of this range. This systematic spread constitutes the primary source of uncertainty as discussed in ref. 40. SdH oscillations were subsequently observed for both LHs and HHs using pulsed magnetic field up to 72 T.

Extended Data Fig. 2 Fabricated sample with a Hall bar structure.

a, Optical micrograph of the fabricated sample mounted on the measurement puck with Cu wires attached as electrical leads for current injection (Ix) and voltage measurement (Vxx). b, Close-up view of the Hall bar showing its dimensions. The longitudinal resistance Rxx is calculated as Rxx = (Vxx/Ix) × (W/L).

Extended Data Fig. 3 Rxx measured up to 72 T with a 40 kHz AC injection current for lock-in measurement.

a, Rxx(B) recorded during the rising-field (0 → 72 T, dashed curves) and falling-field (72 → 0 T, solid curves) portions of the pulsed-field measurements (the field sweep profile is shown in the inset). Only four temperatures are shown as examples. b-e, Falling-field Rxx(B) measured at 1.8 K (b, c) and 4.0 K (d, e) using IRMS = 50 μA (colored) versus IRMS = 25 μA (grey).

Extended Data Fig. 4 Background subtraction of Rxx.

a, Solid lines show the measured Rxx, from which a fifth-order polynomial background (dashed lines) is fitted. b, Subtracting out the polynomial background yields the combined light hole and heavy hole oscillations (curves offset for clarity). The combined oscillations are then fitted to the single-channel LK equation (black dashed lines) to obtain the LH oscillations which, when subtracted, reveal the HH oscillations shown in Fig. 2c. See Methods and Supplementary Fig. 1 for more details on background subtraction.

Extended Data Fig. 5 FFT analysis using different window functions.

a-d, Prior to performing FFT, both LH and HH oscillation signals (see Fig. 2) are multiplied by Tukey windows (black solid lines) of different r-values—r = 1.0 (a), which is the Hanning window; r = 0.8; r = 0.6 (b); r = 0.4 (c); r = 0.2 (d)—to obtain the mean and standard deviation in extracted FFT peak frequencies and amplitudes.

Extended Data Fig. 6 Rxx measured with DC injection current.

DC-current measurement of Rxx was taken at T = 1.4 K (blue) and T = 17 K (red) to approximate the true, undistorted background resistance \({R}_{{xx}}^{{\rm{bg}}}\) (see Methods). A simple linear interpolation was used to approximate \({R}_{{xx}}^{{\rm{bg}}}(B,\,T)\) at intermediate temperatures between 1.4 K and 17 K (grey).

Extended Data Fig. 7 Extraction of the quantum mobility μq.

(Left) Dingle plot of the LH oscillation peaks at 1.8 K and 15 K. \(\widetilde{{\boldsymbol{\Delta }}{{\boldsymbol{R}}}_{{\bf{LH}}}}=\frac{{\boldsymbol{\Delta }}{{\boldsymbol{R}}}_{{\bf{LH}}}}{{{\boldsymbol{R}}}^{{\bf{bg}}}({\boldsymbol{T}},{\boldsymbol{B}})}\) is the background-normalized light hole oscillation amplitude. A linear fit (dashed line, with slope s) gives the quantum mobility as μq = −π/s. (Right) μq as a function of temperature, showing no discernable temperature dependence.

Extended Data Fig. 8 Summary of electrical transport results for a similar sample consisting of InGaN:Mg/UID-GaN/AlN measured in a van der Pauw geometry.

a, b, Analysis of two-channel fitting of Hall measurements up to 9 T. See the caption of Extended Data Fig. 1 for more description, including the definition of the plotted error bars. c-h, Data and analysis of 58 T pulsed-field measurements showing LH SdH oscillations. See the captions of Fig. 2 and Fig. 4 for more description, including the definition of the numerical uncertainties and plotted error bars.

Extended Data Fig. 9 Landau level calculations.

a-d, The quantized wave vectors k (vertical lines) were calculated for B = 32 T (a-b) and B = 72 T (c-d) as described in Methods. Their intersections with the HH (a,c) and LH (b,d) dispersions determine the LLs. Only the occupied LLs and the lowest unoccupied LL are shown. e, The Landau fan diagram showing the LLs for HH (solid blue lines) and LH (dashed red lines). Despite band nonparabolicity, both LH and HH LLs are approximately uniformly spaced near EF. Consistently, the cyclotron masses of the LLs near EF converge to 0.28–0.29 m0 for LH and 1.94 m0 for HH at both magnetic fields.

Extended Data Table 1 Material parameters used for k·p band structure and energy band diagram calculations shown in Fig. 1c, Fig. 3 and Extended Data Fig. 9
Full size table

Supplementary information

Supplementary Information (download PDF )

Supplementary Figs. 1–4, Notes I and II and Tables 1–3.

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Chang, C.F.C., Dill, J.E., Zhang, Z. et al. High-mobility holes in gallium nitride and their quantum oscillations. Nat Electron (2026). https://doi.org/10.1038/s41928-026-01590-8

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