Non-activated transport of strongly interacting two-dimensional holes in GaAs

D. C. Tsui; D. S. Novikov; Jian Huang; K. W. West; L. N. Pfeiffer

REVIEW

Non-activated transport of strongly interacting two-dimensional holes in GaAs

Jian Huang, D. S. Novikov, D. C. Tsui, L. N. Pfeiffer, K. W. West

Mesoscale and Nanoscale Physics · Submitted 2 Mar 2006 · 24 references

Pith's verdict: A careful low-density transport measurement whose qualitative claim holds up, but the quantitative power law is thinner than it looks until the companion paper appears.

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arXiv IDcond-mat/0603053 (version 3)

Pith IDZP4SDWOV, Pith's permanent record of this paper and its review

CitationD. C. Tsui, D. S. Novikov, Jian Huang, K. W. West, L. N. Pfeiffer. "Non-activated transport of strongly interacting two-dimensional holes in GaAs." arXiv:cond-mat/0603053 (2006). https://pith.science/paper/ZP4SDWOV

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Claim paper

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Editor's note

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You should know two things. First, the paper reports a genuinely new data point: clean GaAs 2D hole systems stay conducting, with sigma growing roughly like T^alpha (alpha between about 1.6 and 2.2), at densities down to 7e8 cm^-2. That is a record-low regime where everyone expected localized or pinned behavior. Second, the paper is honest about what it cannot explain: the transport mechanism and even the ground state are left open, and the detailed analysis of the power law is explicitly deferred to a companion paper (Ref 14). That deferral is the main soft spot, because the central quantitative claim lives in a narrow temperature window below 150 mK and no error bars are given for alpha.

What the paper does well: the qualitative contrast is convincing. The clean samples' conductivity at base temperature is three orders of magnitude above the disordered sample #6 at the same density, and the curvature clearly bends away from the VRH fits in Fig 3. That is real evidence that something non-activated is happening. The four-terminal measurement and the check that varying current drive does not change rho are appropriate cautions, and the authors do not oversell the theory - the l_phi ~ lambda_F argument is explicitly plausible rather than derived.

Where the soft spots are, in proportion: the stress-test worry about a static shunt (gate leakage or a parallel conduction path) is fair but not decisive. The current-drive check only rules out Joule heating, not a fixed conductance in parallel, and no depletion or gate-leakage trace is reported. If such a shunt existed at ~0.1 e^2/h, it would mimic the base-temperature conductivity. However, the disordered-sample contrast cuts against a common-artifact story: sample #6 would presumably have the same shunt, yet its low-T conductivity is orders of magnitude lower. That does not rule out a defect specific to the clean HIGFETs, but it moves the artifact hypothesis from "likely" to "possible." The thermalization assumption - hole temperature tracking the fridge down to 80 mK - is also untested, though the weak T-dependence at the lowest densities would require a mostly T-independent heating mechanism, which is not the usual symptom.

The citation pattern is fine. The self-citations to Refs 12-14 are to the group's own prior work and the companion paper; that is normal in an experimental sequence. The paper does not dress up speculation as result; the discussion of the Wigner crystal melting is clearly labeled as estimates.

Bottom line: this deserves referee review. The qualitative observation - if reproduced - is important for the 2D metal-insulator transition debate, and the authors have been appropriately careful in what they claim. The referee should ask for the companion paper's analysis, for gate-leakage and depletion checks, and for a discussion of thermometry. I would not desk-reject it.

Referee report

Significance

If the central claim holds, this is an important experimental result: it suggests that dilute two-dimensional holes can remain delocalized down to densities where the Fermi wavelength approaches 1 μm, contradicting the conventional expectation of Anderson or Coulomb-gap activated insulating behavior. The qualitative clean-versus-disordered sample comparison gives a falsifiable contrast and supports the main qualitative finding. The theoretical discussion is explicitly speculative and not used to derive σ(T), so there is no circularity burden on that account. However, the quantitative power-law exponent is extracted from a narrow temperature range without error bars, and the paper does not provide several standard control measurements that would be needed to fully underpin the 'not an insulator' conclusion.

Major objections (3)

[The measurements section, Fig. 4] The claim that the low-temperature conductivity is an intrinsic property of the 2D hole layer requires excluding a parallel conduction path. The reported check that the measured resistivity did not change with varied current drive rules out Joule-heating effects, but it does not rule out a static shunt whose magnitude is set by the gate voltage rather than by the source-drain excitation. At p = 7×10^8 cm^-2 the base-temperature conductivity is roughly 0.1 e^2/h, so a temperature-independent parallel conductance of that order would mimic the finite σ on which the 'not an insulator' conclusion rests. The paper does not report a p = 0 depletion conductance measurement, a direct gate-leakage measurement, or an independent check that the four-terminal conductance is entirely through the hole layer. This is load-bearing for the central claim and should be addressed experimentally or explicitly discussed as a residual uncertainty.
[Fig. 4 and the paragraph extracting α] The power-law exponent α is fitted over the temperature interval from 80 mK to 150 mK, which spans less than a factor of two in temperature. No fit residuals, confidence intervals, or sensitivity to the chosen fitting range are reported. The abstract states that σ ∝ T^α with 1 <~ α <~ 2, but the text reports α ≃ 2.2 for p = 7×10^8 cm^-2, which is outside that range. The qualitative non-activated behavior is still supported, but the quantitative power-law claim needs either a more careful extraction with error bars or a revised statement of the range.
[The measurements section, first paragraph] The analysis assumes that the hole temperature equals the refrigerator temperature down to 80 mK. No independent low-temperature thermometry of the hole gas or a quantitative estimate of the residual rf/current heating at the lowest temperatures is provided. If the holes are heated above the phonon bath at the lowest nominal temperatures, the apparent saturation or power-law flattening of σ(T) could be a heating artifact rather than an intrinsic property. The authors should either supply a power-dependence study over a wider range of drive amplitudes at the lowest densities or state explicitly why the 1 pA check is sufficient to exclude this possibility.

Minor objections (4)

[Fig. 3 caption] The dotted lines representing the Mott and Efros-Shklovskii VRH predictions are not parametrized, so the reader cannot judge how the comparison lines were chosen or how significant the deviation is. Giving the values of T* used for each density would improve the figure.
[Abstract and text, first paragraph] The abstract states that σ grows with temperature following a power law, while the main text says 'approximately as a power law at sufficiently low temperatures.' These statements should be made consistent, especially because the data show a crossover behavior at higher temperatures.
[References, Ref. 14] Reference 14 is a 'systematic analysis' by the same authors that is cited as the source of the detailed power-law study. Since it is an unpublished manuscript at the time of writing, its status should be given (e.g., submitted or in preparation) and the present paper should state clearly what new data are reported here.
[The measurements section, second paragraph] The text says ac four-terminal measurements were used at high density and both ac and dc setups were used at low density, but it is not stated which data are shown in Fig. 4. This is relevant for assessing possible phase-sensitive artifacts in the low-temperature, high-impedance regime.

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The paper

The paper claims

Record-low-density two-dimensional holes in clean GaAs devices conduct with a non-activated power-law conductivity, not as insulators.

The reading

This paper reports transport measurements of two-dimensional holes in undoped GaAs heterojunction field-effect transistors, at hole densities down to $p=7\times 10^8$ cm$^{-2}$, where the Fermi wavelength approaches one micrometer. At these record-low densities the conductivity does not freeze out exponentially; it decreases with cooling roughly as a power law, $\sigma(T)\propto T^{\alpha}$ with $1\lesssim\alpha\lesssim 2$. The authors contrast this with the activated variable-range-hopping behavior seen in more disordered samples and argue that in their clean devices the holes remain delocalized, forming a strongly correlated liquid rather than an Anderson insulator or a pinned Wigner crystal. If correct, the result means that $d\sigma/dT>0$ alone does not identify an insulator in this regime.

What carries the argument

The central object is the HIGFET (insulated-gate field-effect transistor), an undoped GaAs/AlGaAs device in which holes are induced by a metal gate rather than by dopants, so disorder is low and the density can be tuned down continuously. The mechanism that carries the argument is a comparison of temperature dependences: activated Anderson/VRH conductivity $\sigma\sim e^{-(T^*/T)^\nu}$ with $\nu=1/3$ or $1/2$ would bend sharply downward in a log-log plot, while the measured $\sigma(T)$ stays close to a straight line, i.e. a power law. The authors add a screening argument: the gate at distance $d$ turns the Coulomb $1/r$ interaction into a short-ranged $1/r^3$ dipole interaction for $r\gtrsim2d$, which makes a strongly correlated liquid energetically favored over a Wigner crystal, whose classical melting temperature is already low ($T_m\simeq56$ mK at $p=1\times10^9$ cm$^{-2}$).

Extended reading notes

Core claim

The central claim is that a clean two-dimensional hole system stays conducting down to densities where the Fermi wavelength is about a micron, with $\sigma(T)$ following a non-universal power law $\sigma \propto T^{\alpha}$, $1\lesssim\alpha\lesssim2$, at the lowest temperatures. Since the temperature dependence is weaker than any activated law and the low-temperature conductivity is orders of magnitude larger than in a more disordered sample at the same density, the paper concludes that the system is not an insulator even though $d\sigma/dT>0$. The authors interpret the absence of localization as a consequence of very strong carrier interactions, which destroy phase coherence on length scales of order the Fermi wavelength, and of gate screening, which weakens the long-range Coulomb tail and suppresses Wigner crystallization.

Load-bearing premise

The entire conclusion rests on the holes being in thermal equilibrium with the refrigerator down to 80 mK and on there being no hidden conduction path, such as gate leakage, contacts, or density inhomogeneities, at the lowest densities where the impedance is very high.

Editorial extensions

If this is right

If the central claim is right, dilute two-dimensional holes are delocalized at densities near one hole per square micron, so theories predicting a pinned Wigner crystal or universal insulating behavior in that regime need revision.
The exponent $\alpha$ grows with decreasing density (about 2.2 at $p=7\times10^8$ cm$^{-2}$ versus 1.6 at $p=8\times10^8$ cm$^{-2}$), so any transport theory must produce a density-dependent power law, not a fixed exponent.
Since the cleaner samples differ qualitatively from the disordered sample at the same density, sample disorder rather than density alone controls whether transport is activated; this sharpens the condition for observing non-activated behavior.
The result provides a concrete benchmark for theories of strongly correlated 2D liquids: they must account for a conductivity of order $0.1\,e^2/h$ at the lowest densities with a power-law temperature dependence.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper: the authors do not test how the power law behaves at even lower temperatures or densities; if the trend of growing $\alpha$ continues, the zero-temperature limit might be a quantum critical-like conductivity with a non-universal exponent, but that goes beyond what the paper establishes.
Beyond the paper: because the gate distance differs between samples (600 nm versus 250 nm) yet the authors do not compare exponents across samples, a natural test would be to vary $d$ while holding disorder fixed and see whether the apparent power-law exponent follows the screening length.
Beyond the paper: a direct experimental dial would be to add controlled disorder or a tilted magnetic field, which should eventually restore activated transport; locating the crossover density as a function of disorder would test the claim that the delocalized liquid is the intrinsic ground state.

Original abstract

We report on the transport measurements of two-dimensional holes in GaAs field effect transistors with record low densities down to 7*10^8 cm^{-2}. Remarkably, such a dilute system (with Fermi wavelength approaching 1 micrometer) exhibits a non-activated conductivity that grows with temperature following a power law. We contrast it with the activated transport obtained from measuring more disordered samples, and discuss possible transport mechanisms in this strongly-interacting regime.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,960 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.15 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.62 · randomized assignment 0.01 · states quantitative result 0.96 · compares with prior results 0.87 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We report on the transport measurements of two-dimensional holes in GaAs field effect transistors with record low densities down to 7*10^8 cm^{-2}. Remarkably, such a dilute system (with Fermi wavelength approaching 1 micrometer) exhibits a non-activated conductivity that grows with temperature following a power law. We contrast it with the activated transport obtained from measuring more disordered samples, and discuss possible transport mechanisms in this strongly-interacting regime.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We report on the transport measurements of two-dimensional holes in GaAs field effect transistors with record low densities down to 7*10^8 cm^{-2}.	contribution 0.97	0.96	0.08	asserted 1.00
s1	Remarkably, such a dilute system (with Fermi wavelength approaching 1 micrometer) exhibits a non-activated conductivity that grows with temperature following a power law.	result 1.00	0.89	0.72	asserted 1.00
s2	We contrast it with the activated transport obtained from measuring more disordered samples, and discuss possible transport mechanisms in this strongly-interacting regime.	interpretation 0.74	0.86	0.11	asserted 0.56

What kind of paper the classifier reports this is: empirical study 1.00 · evidence from observation or experiment 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: Temperature dependence of the resistivity of sample

Showing 2 of the paper's 4 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:cond-mat/0603053 by the authors.

References

Works cited (24)

[1]

T. Ando, A.B. Fowler, and F. Stern, Rev. Mod. Phys. 54 , 437 (1982)

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[2]

P.W. Anderson, Phys. Rev. 109 , 1492 (1958)

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[3]

E. Abrahams, P.W. Anderson, D.C. Licciardello, and T.V. Ramakrishnan, Phys. Rev. Lett. 42 , 673 (1979)

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[4]

N.F. Mott, J. Non-Cryst. Solids 1 , 1 (1968)

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[5]

B.I. Shklovskii and A.L. Efros, Electronic Properties of Doped Semiconductors , Springer-Verlag, Berlin (1984)

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[6]

B. Tanatar and D. M. Ceperley, Phys. Rev. B 39 , 5005 (1989)

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[7]

E. Abrahams, S.V. Kravchenko, and M.P. Sarachik, Rev. Mod. Phys. 73 , 251 (2001)

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[8]

Kravchenko, S. V., G. V. Kravchenko, J. E. Furneaux, V. M. Pudalov, and M. D'Iorio, Phys. Rev. B 50 , 8039 (1994)

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[9]

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[10]

B. E. Kane, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 67 , 1262 (1995)

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[11]

M. P. Lilly, J. L. Reno, J. A. Simmons, I. B. Spielman, J. P. Eisenstein, L. N. Pfeiffer, K. W. West, E. H. Hwang, and S. Das Sarma, Phys. Rev. Lett. 90 , 056806 (2003)

View on Pith 2003
[12]

Hwayong Noh, M. P. Lilly, D. C. Tsui, J. A. Simmons, E.H.Hwang, S.Das Sarma, L. N. Pfeiffer, and K. W. West, Phys. Rev. B 68 , 165308 (R) (2003)

View on Pith 2003
[13]

Hwayong Noh, M. P. Lilly, D. C. Tsui, J. A. Simmons, L. N. Pfeiffer, and K. W. West, Phys. Rev. B 68 , 241308 (R) (2003)

View on Pith 2003
[14]

Jian Huang et al. cond-mat/0610320 (2006)

View on Pith Pith review arXiv 2006
[15]

B.N. Narozhny, G. Zala, and I.L. Aleiner, Phys. Rev. B 65 , R180202 (2002)

View on Pith 2002
[16]

A. MacKinnon and B. Kramer, Phys. Rev. Lett. 47 , 1546 (1981); D. Vollhardt and P. W\"olfle, Phys. Rev. Lett. 48 , 699 (1982)

View on Pith 1981
[17]

S. Das Sarma and E. H. Hwang, Phys Rev. B 68 , 195315 (2003)

View on Pith 2003
[18]

B. Spivak, S. Kivelson, cond-mat/0510422 (2005)

View on Pith Pith review arXiv 2005
[19]

B. Spivak and S. A. Kivelson Phys. Rev. B 70 , 155114 (2004)

View on Pith 2004
[20]

B. Spivak, Phys. Rev. B 67 , 125205 (2003)

View on Pith 2003
[21]

Pan W, Lai K, Bayrakci SP, Ong NP, Tsui DC, Pfeiffer LN, West KW, Appl. Phys. Lett. 83 , 3519 (2003)

View on Pith 2003
[22]

R. Winkler, Spin-orbit coupling effects in two-dimensional electron and hole systems (Springer, New York, 2003)

View on Pith 2003
[23]

D.S. Fisher, B.I. Halperin, and R. Morf, Phys. Rev. B 20 , 4692 (1979)

View on Pith 1979
[24]

P. Hartmann, G.J. Kalman, Z. Donk\'o, and K. Kutasi, Phys. Rev. E 72 , 026409 (2005)

View on Pith 2005

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

T. Ando, A.B. Fowler, and F. Stern, Rev. Mod. Phys. 54 , 437 (1982)

View on Pith 1982

[2] [2]

P.W. Anderson, Phys. Rev. 109 , 1492 (1958)

View on Pith 1958

[3] [3]

E. Abrahams, P.W. Anderson, D.C. Licciardello, and T.V. Ramakrishnan, Phys. Rev. Lett. 42 , 673 (1979)

View on Pith 1979

[4] [4]

N.F. Mott, J. Non-Cryst. Solids 1 , 1 (1968)

View on Pith 1968

[5] [5]

B.I. Shklovskii and A.L. Efros, Electronic Properties of Doped Semiconductors , Springer-Verlag, Berlin (1984)

View on Pith 1984

[6] [6]

B. Tanatar and D. M. Ceperley, Phys. Rev. B 39 , 5005 (1989)

View on Pith 1989

[7] [7]

E. Abrahams, S.V. Kravchenko, and M.P. Sarachik, Rev. Mod. Phys. 73 , 251 (2001)

View on Pith 2001

[8] [8]

Kravchenko, S. V., G. V. Kravchenko, J. E. Furneaux, V. M. Pudalov, and M. D'Iorio, Phys. Rev. B 50 , 8039 (1994)

View on Pith 1994

[9] [9]

W. Mason, S. V. Kravchenko, G. E. Bowker, and J. E. Furneaux, 1995, Phys. Rev. B 52 , 7857

View on Pith 1995

[10] [10]

B. E. Kane, L. N. Pfeiffer, and K. W. West, Appl. Phys. Lett. 67 , 1262 (1995)

View on Pith 1995

[11] [11]

M. P. Lilly, J. L. Reno, J. A. Simmons, I. B. Spielman, J. P. Eisenstein, L. N. Pfeiffer, K. W. West, E. H. Hwang, and S. Das Sarma, Phys. Rev. Lett. 90 , 056806 (2003)

View on Pith 2003

[12] [12]

Hwayong Noh, M. P. Lilly, D. C. Tsui, J. A. Simmons, E.H.Hwang, S.Das Sarma, L. N. Pfeiffer, and K. W. West, Phys. Rev. B 68 , 165308 (R) (2003)

View on Pith 2003

[13] [13]

Hwayong Noh, M. P. Lilly, D. C. Tsui, J. A. Simmons, L. N. Pfeiffer, and K. W. West, Phys. Rev. B 68 , 241308 (R) (2003)

View on Pith 2003

[14] [14]

Jian Huang et al. cond-mat/0610320 (2006)

View on Pith Pith review arXiv 2006

[15] [15]

B.N. Narozhny, G. Zala, and I.L. Aleiner, Phys. Rev. B 65 , R180202 (2002)

View on Pith 2002

[16] [16]

A. MacKinnon and B. Kramer, Phys. Rev. Lett. 47 , 1546 (1981); D. Vollhardt and P. W\"olfle, Phys. Rev. Lett. 48 , 699 (1982)

View on Pith 1981

[17] [17]

S. Das Sarma and E. H. Hwang, Phys Rev. B 68 , 195315 (2003)

View on Pith 2003

[18] [18]

B. Spivak, S. Kivelson, cond-mat/0510422 (2005)

View on Pith Pith review arXiv 2005

[19] [19]

B. Spivak and S. A. Kivelson Phys. Rev. B 70 , 155114 (2004)

View on Pith 2004

[20] [20]

B. Spivak, Phys. Rev. B 67 , 125205 (2003)

View on Pith 2003

[21] [21]

Pan W, Lai K, Bayrakci SP, Ong NP, Tsui DC, Pfeiffer LN, West KW, Appl. Phys. Lett. 83 , 3519 (2003)

View on Pith 2003

[22] [22]

R. Winkler, Spin-orbit coupling effects in two-dimensional electron and hole systems (Springer, New York, 2003)

View on Pith 2003

[23] [23]

D.S. Fisher, B.I. Halperin, and R. Morf, Phys. Rev. B 20 , 4692 (1979)

View on Pith 1979

[24] [24]

P. Hartmann, G.J. Kalman, Z. Donk\'o, and K. Kutasi, Phys. Rev. E 72 , 026409 (2005)

View on Pith 2005