arXiv subjects

C. W. Liu

Publications and source records attributed to C. W. Liu.

At least 19 recordsLinked to original sources

arXiv2025

Inequivalence of the low-density insulating state and quantum Hall insulating states in a strongly correlated two-dimensional electron system

We find that the behaviors of the voltage-current characteristics as one enters the low-density insulating state and integer quantum Hall insulating states in the ultra-clean two-dimensional electron system in SiGe/Si/SiGe quantum wells are qualitatively different. The double-threshold voltage-current curves, representative of the electron solid formation at low densities, are not observed in the quantum Hall regime, which does not confirm the existence of a quasi-particle quantum Hall Wigner solid and indicates that quasi-particles near integer filling do not form an independent subsystem.

cond-mat.str-el↗

arXiv2025

Stabilization of a two-dimensional quantum electron solid in perpendicular magnetic fields

We find that the double-threshold voltage-current characteristics in the insulating regime in the ultra-clean two-valley two-dimensional electron system in SiGe/Si/SiGe quantum wells are promoted by perpendicular magnetic fields, persisting to an order of magnitude lower voltages and considerably higher electron densities compared to the zero-field case. This observation indicates the perpendicular-magnetic-field stabilization of the quantum electron solid.

cond-mat.str-el↗

arXiv2024

Triple-top-gate technique for studying the strongly interacting 2D electron systems in heterostructures

We have developed a technique that dramatically reduces the contact resistances and depletes a shunting channel between the contacts outside the Hall bar in ultra-high mobility SiGe/Si/SiGe heterostructures. It involves the creation of three overlapping independent gates deposited on top of the structure and allows transport measurements to be performed at millikelvin temperatures in the strongly interacting limit at low electron densities, where the energy of the electron-electron interactions dominates all other energy scales. This design allows one to observe the two-threshold voltage-current characteristics that are a signature for the collective depinning and sliding of the electron solid.

cond-mat.mes-hall↗

arXiv2024

Collective depinning and sliding of a quantum Wigner solid in a 2D electron system

We report the observation of two-threshold voltage-current characteristics accompanied by a peak of broadband current noise between the two threshold voltages in the insulating state at low densities in the 2D electron system in ultra-high mobility SiGe/Si/SiGe heterostructures. The observed results can be described by a phenomenological theory of the collective depinning of elastic structures, which naturally generates a peak of a broadband current noise between the dynamic and static thresholds and changes to sliding of the solid over a pinning barrier above the static threshold. This gives compelling evidence for the electron solid formation in this electron system and shows the generality of the effect for different classes of electron systems.

cond-mat.str-el↗

arXiv2023

Spin independence of the strongly enhanced effective mass in ultra-clean SiGe/Si/SiGe two-dimensional electron system

The effective mass at the Fermi level is measured in the strongly interacting two-dimensional (2D) electron system in ultra-clean SiGe/Si/SiGe quantum wells in the low-temperature limit in tilted magnetic fields. At low electron densities, the effective mass is found to be strongly enhanced and independent of the degree of spin polarization, which indicates that the mass enhancement is not related to the electrons' spins. The observed effect turns out to be universal for silicon-based 2D electron systems, regardless of random potential, and cannot be explained by existing theories.

cond-mat.mes-hall↗

arXiv2022

Spin effect on the low-temperature resistivity maximum in a strongly interacting 2D electron system

The increase in the resistivity with decreasing temperature followed by a drop by more than one order of magnitude is observed on the metallic side near the zero-magnetic-field metal-insulator transition in a strongly interacting two-dimensional electron system in ultra-clean SiGe/Si/SiGe quantum wells. We find that the temperature $T_{\text{max}}$, at which the resistivity exhibits a maximum, is close to the renormalized Fermi temperature. However, rather than increasing along with the Fermi temperature, the value $T_{\text{max}}$ decreases appreciably for spinless electrons in spin-polarizing (parallel) magnetic fields. The observed behaviour of $T_{\text{max}}$ cannot be described by existing theories. The results indicate the spin-related origin of the effect.

cond-mat.str-el↗

arXiv2021

Density dependence of the excitation gaps in an undoped Si/SiGe double-quantum-well heterostructure

We report low-temperature magneto-transport measurements of an undoped Si/SiGe asymmetric double quantum well heterostructure. The density in both layers is tuned independently utilizing a top and a bottom gate, allowing the investigation of quantum wells at both imbalanced and matched densities. Integer quantum Hall states at total filling factor $ν_{\text{T}} = 1$ and $ν_{\text{T}} = 2$ are observed in both density regimes, and the evolution of their excitation gaps is reported as a function of density. The $ν_{\text{T}} = 1$ gap evolution departs from the behavior generally observed for valley splitting in the single layer regime. Furthermore, by comparing the $ν_{\text{T}} = 2$ gap to the single particle tunneling energy, $Δ_{\text{SAS}}$, obtained from Schrödinger-Poisson (SP) simulations, evidence for the onset of spontaneous inter-layer coherence (SIC) is observed for a relative filling fraction imbalance smaller than ${\sim}50\%$

cond-mat.mes-hall↗

arXiv2021

Valley effects on the fractions in an ultrahigh mobility SiGe/Si/SiGe two-dimensional electron system

We observe minima of the longitudinal resistance corresponding to the quantum Hall effect of composite fermions at quantum numbers $p=1$, 2, 3, 4, and 6 in an ultraclean strongly interacting bivalley SiGe/Si/SiGe two-dimensional electron system. The minima at $p=3$ disappear below a certain electron density, although the surrounding minima at $p=2$ and $p=4$ survive at significantly lower densities. Furthermore, the onset for the resistance minimum at a filling factor $ν=3/5$ is found to be independent of the tilt angle of the magnetic field. These surprising results indicate the intersection or merging of the quantum levels of composite fermions with different valley indices, which reveals the valley effect on fractions.

cond-mat.mes-hall↗

arXiv2020

Manifestation of strong correlations in transport in ultra-clean SiGe/Si/SiGe quantum wells

We observe that in a strongly interacting two-dimensional electron system in ultra-clean SiGe/Si/SiGe quantum wells, the resistivity on the metallic side near the metal-insulator transition increases with decreasing temperature, reaches a maximum at some temperature, and then decreases by more than one order of magnitude. We scale the resistivity data in line with expectations for the transport of strongly correlated Fermi systems and find a nearly perfect agreement with theory over a wide range of electron densities.

cond-mat.str-el↗

arXiv2020

Metallic state in a strongly interacting spinless two-valley electron system in two dimensions

We have studied the strongly interacting, two-valley two-dimensional (2D) electron system in ultrahigh mobility SiGe/Si/SiGe quantum wells in parallel magnetic fields strong enough to completely polarize the electron spins thus making the electron system "spinless". It occurs that the metallic temperature dependence of the resistivity, although weaker than that in the absence of magnetic field, still remains strong even when the spin degree of freedom is removed. Several independent methods have been used to establish the existence of the genuine MIT in the spinless two-valley 2D system. This is in contrast to the previous results obtained on more disordered silicon samples, where the polarizing magnetic field causes a complete quench of the metallic temperature behavior.

cond-mat.str-el↗

arXiv2019

Quantum phase transition in ultrahigh mobility SiGe/Si/SiGe two-dimensional electron system

The metal-insulator transition (MIT) is an exceptional test bed for studying strong electron correlations in two dimensions in the presence of disorder. In the present study, it is found that in contrast to previous experiments on lower-mobility samples, in ultra-high mobility SiGe/Si/SiGe quantum wells the critical electron density, $n_{\text{c}}$, of the MIT becomes smaller than the density, $n_{\text{m}}$, where the effective mass at the Fermi level tends to diverge. Near the topological phase transition expected at $n_{\text{m}}$, the metallic temperature dependence of the resistance should be strengthened, which is consistent with the experimental observation of more than an order of magnitude resistance drop with decreasing temperature below $\sim1$ K.

cond-mat.str-el↗

arXiv2018

Fractional Quantum Hall Effect in SiGe/Si/SiGe Quantum Wells in Weak Quantizing Magnetic Fields

We have experimentally studied the fractional quantum Hall effect (FQHE) in SiGe/Si/SiGe quantum wells in relatively weak magnetic fields, where the Coulomb interaction between electrons exceeds the cyclotron splitting by a factor of a few XX. Minima of the longitudinal resistance have been observed corresponding to the quantum Hall effect of composite fermions with quantum numbers $p$ = 1, 2, 3, and 4. Minima with $p$ = 3 disappear in magnetic fields below 7 Tesla, which may be a consequence of the intersection or even merging of the quantum levels of the composite fermions with different orientations of the pseudo-spin, i.e., those belonging to different valleys. We have also observed minima of the longitudinal resistance at filling factors $ν$ = 4/5 and 4/11, which may be due to the formation of the second generation of the composite fermions.

cond-mat.str-el↗

arXiv2017

Unusual anisotropy of inplane field magnetoresistance in ultra-high mobility SiGe/Si/SiGe quantum wells

We find an unusual anisotropy of the inplane field magnetoresistance in ultra-high mobility SiGe/Si/SiGe quantum wells. The anisotropy depends on the orientation between the inplane field, $B_\parallel$, and current, $I$, relative to the crystallographic axes of the sample and is a consequence of the intrinsic ridges on the quantum well surface. For the simplest orientations between current and crystallographic axes, a method of recalculating the magnetoresistance measured at $I\perp B_\parallel$ into the one measured at $I\parallel B_\parallel$ is suggested and is shown to yield results that agree with the experiment.

cond-mat.mes-hall↗

arXiv2017

Indication of band flattening at the Fermi level in a strongly correlated electron system

Using ultra-high quality SiGe/Si/SiGe quantum wells at millikelvin temperatures, we experimentally compare the energy-averaged effective mass, $m$, with that at the Fermi level, $m_F$, and verify that the behaviours of these measured values are qualitatively different. With decreasing electron density (or increasing interaction strength), the mass at the Fermi level monotonically increases in the entire range of electron densities, while the energy-averaged mass saturates at low densities. The qualitatively different behaviour reveals a precursor to the interaction-induced single-particle spectrum flattening at the Fermi level in this electron system.

cond-mat.str-el↗

arXiv2017

Atomic-layer doping of SiGe heterostructures for atomic-precision donor devices

As a first step to porting scanning tunneling microscopy methods of atomic-precision fabrication to a strained-Si/SiGe platform, we demonstrate post-growth P atomic-layer doping of SiGe heterostructures. To preserve the substrate structure and elastic state, we use a T $\leq 800^\circ$C process to prepare clean Si$_{0.86}$Ge$_{0.14}$ surfaces suitable for atomic-precision fabrication. P-saturated atomic-layer doping is incorporated and capped with epitaxial Si under a thermal budget compatible with atomic-precision fabrication. Hall measurements at T$=0.3$ K show that the doped heterostructure has R$_{\square}=570\pm30$ $Ω$, yielding an electron density $n_{e}=2.1\pm0.1\times10^{14}$cm$^{-2}$ and mobility $μ_e=52\pm3$ cm$^{2}$ V$^{-1}$ s$^{-1}$, similar to saturated atomic-layer doping in pure Si and Ge. The magnitude of $μ_e$ and the complete absence of Shubnikov-de Haas oscillations in magnetotransport measurements indicate that electrons are overwhelmingly localized in the donor layer, and not within a nearby buried Si well. This conclusion is supported by self-consistent Schrödinger-Poisson calculations that predict electron occupation primarily in the donor layer.

cond-mat.mtrl-sci↗

arXiv2017

Effective g factor of low-density two-dimensional holes in a Ge quantum well

We report measurements of the effective $g$ factor of low-density two-dimensional holes in a Ge quantum well. Using the temperature dependence of the Shubnikov-de Haas oscillations, we extract the effective $g$ factor in a magnetic field perpendicular to the sample surface. Very large values of the effective $g$ factor, ranging from $\sim13$ to $\sim28$, are observed in the density range of $1.4\times10^{10}$ cm$^{-2}$ to $1.4\times10^{11}$ cm$^{-2}$. When the magnetic field is oriented parallel to the sample surface, the effective $g$ factor is obtained from a protrusion in the magneto-resistance data that signifies full spin polarization. In the latter orientation, a small effective $g$ factor, $\sim1.3-1.4$, is measured in the density range of $1.5\times10^{10}$ cm$^{-2}$ to $2\times10^{10}$ cm$^{-2}$. This very strong anisotropy is consistent with theoretical predictions and previous measurements in other 2D hole systems, such as InGaAs and GaSb.

cond-mat.mes-hall↗

arXiv2017

Density-controlled quantum Hall ferromagnetic transition in a two-dimensional hole system

Quantum Hall ferromagnetic transitions are typically achieved by increasing the Zeeman energy through in-situ sample rotation, while transitions in systems with pseudo-spin indices can be induced by gate control. We report here a gate-controlled quantum Hall ferromagnetic transition between two real spin states in a conventional two-dimensional system without any in-plane magnetic field. We show that the ratio of the Zeeman splitting to the cyclotron gap in a Ge two-dimensional hole system increases with decreasing density owing to inter-carrier interactions. Below a critical density of $\sim2.4\times 10^{10}$ cm$^{-2}$, this ratio grows greater than $1$, resulting in a ferromagnetic ground state at filling factor $ν=2$. At the critical density, a resistance peak due to the formation of microscopic domains of opposite spin orientations is observed. Such gate-controlled spin-polarizations in the quantum Hall regime opens the door to realizing Majorana modes using two-dimensional systems in conventional, low-spin-orbit-coupling semiconductors.

cond-mat.mes-hall↗

arXiv2017

Semiconductor, topological semimetal, indirect semimetal, and topological Dirac semimetal phases of Ge$_{1-x}$Sn$_{x}$ alloys

Electronic structures of Ge$_{1-x}$Sn$_{x}$ alloys (0 $\leq$ $x$ $\leq$ 1) are theoretically studied by nonlocal empirical pseudopotential method. For relaxed Ge$_{1-x}$Sn$_{x}$, a topological semimetal is found for $\textit x$ $>$ 41$\%$ with gapless and band inversion at $Γ$ point, while there is an indirect-direct bandgap transition at $x$ = 8.5$\%$. For strained Ge$_{1-x}$Sn$_{x}$ on a Ge substrate, semimetals with a negative indirect bandgap appear for $x$ $>$ 43$\%$, and the strained Ge$_{1-x}$Sn$_{x}$ on Ge is always an indirect bandgap semiconductor for $x$ $<$ 43$\%$. With appropriate biaxial compressive strains, a topological Dirac semimetal is found with band inversion at $Γ$ and one pair of Dirac cones along the [001] direction.

cond-mat.mes-hall↗