EuTe4: Layered CDW Semiconductor & Switchable States

• EuTe4 is a layered rare-earth tetratelluride exhibiting quasi-two-dimensional charge-density-wave orders in Te sheets, which induce a full semiconducting gap.
• Its CDW behavior arises from layer-dependent charge modulation in mono- and bilayer Te sheets, leading to unusual thermal hysteresis and metastable domain configurations.
• Non-equilibrium probes reveal reversible, non-volatile resistance switching with memristive behavior, highlighting potential for advanced thermoelectric and electronic applications.

EuTe$_4$ is a layered rare-earth telluride, rare-earth tetratelluride, and quasi-two-dimensional charge-density-wave compound whose defining feature is a CDW in square tellurium sheets that drives a semiconducting ground state rather than the partial gapping more typical of layered tellurides. Across the literature, it is described as a layered semiconductor, a magnetic semiconductor, a van der Waals material, and a polar CDW system, with the same material platform supporting Fermi-surface reconstruction, large thermal hysteresis, coexisting layer-dependent CDW orders, low-temperature antiferromagnetism, enhanced thermopower, and non-volatile optical and electrical switching between metastable states (Wu et al., 2019, Lv et al., 2024, Venturini et al., 2024).

1. Crystal chemistry and structural motifs

At room temperature, EuTe$_4$ was initially reported to crystallize in an orthorhombic structure with space group $Pmmn$ (No. 59), with refined lattice constants $a = 4.5119(2)\,\text{\AA}$, $b = 4.6347(2)\,\text{\AA}$, and $c = 15.6747(10)\,\text{\AA}$, and with consecutive near-square Te sheets separated by corrugated Eu–Te slabs (Wu et al., 2019). In this description, the crystal is built from layered “quintuple” stacks of corrugated Eu–Te slab, monolayer Te sheet, monolayer Te sheet, and corrugated Eu–Te slab, repeated along the $c$-axis. The shortest interlayer Te–Te contact between adjacent quintuple stacks is about $3.37$ $\text{\AA}$, substantially larger than a typical covalent Te–Te bond, and this weak inter-stack coupling is the structural basis for describing EuTe$_4$ as quasi-two-dimensional.

The Te-based electronic substructure is central. Four crystallographically distinct Te sites are reported in the high-temperature structure, with Te(3) and the Te(4)–Te(5) network forming two inequivalent near-square Te sheets, while Te(2) resides in the corrugated Eu–Te slabs. The intralayer Te–Te distance in the sheets is $_4$0, characteristic of hypervalent Te–Te bonding in square Te nets. Eu is reported as formally divalent, Eu$_4$1, and in the room-temperature structure it is 9-coordinate in a square-antiprismatic geometry. This Eu$_4$2 assignment is unusual within layered $_4$3Te$_4$4 systems and is important because the Te-sheet-derived states remain partially filled while Eu $_4$5 states are localized.

Subsequent ARPES, tr-ARPES, STM, and optical studies recast the same material in terms of Te monolayers and Te bilayers separated by Eu–Te spacer layers, with the coexistence of mono- and bilayer Te sheets treated as the structural origin of layer-dependent CDWs (Zhang et al., 2022, Lv et al., 2024, Liu et al., 2023). In the CDW supercell, one optical study further describes six inequivalent Te sheets per CDW supercell along $_4$6: two monolayers and two bilayers, with each bilayer contributing two Te sheets (Liu et al., 2023). This layered re-description is not a contradiction of the earlier crystallographic work so much as a shift of emphasis from crystallographic site labeling to electronically active Te sublayers.

The crystallographic description at elevated temperature has also evolved. A later thermoelectric and synchrotron X-ray study reports that in its high-temperature CDW phase, denoted CDW-I, EuTe$_4$7 crystallizes in the polar space group $_4$8 (No. 33), with lattice parameters $_4$9, $Pmmn$0, and $Pmmn$1 at $Pmmn$2 K, and that the polar lattice distortion persists even at $Pmmn$3 K (Takahashi et al., 22 Aug 2025). This suggests that the structural evolution above room temperature, including the relation between the originally reported $Pmmn$4 cell and the later high-temperature CDW-I structure, remains an active topic within the EuTe$Pmmn$5 literature.

2. Charge-density-wave order and lattice reconstruction

The original structural study established a phase transition near $Pmmn$6 K. Resistivity shows a sharp kink at about $Pmmn$7 K with pronounced hysteresis between cooling and warming curves, and differential scanning calorimetry shows a kink at the same temperature; together these observations indicate a first-order phase transition (Wu et al., 2019). Below this transition, single-crystal X-ray diffraction and TEM reveal a superstructure with periodic V-shaped Te trimers in the monolayer Te sheets, and the low-temperature structure is described as orthorhombic $Pmmn$8 or $Pmmn$9 with a $a = 4.5119(2)\,\text{\AA}$0 superstructure. In this distorted phase, Te–Te distances become strongly modulated, with shortened and lengthened bonds in the Te sheets and additional Te oligomerization involving Te tetramers and pentamers.

The CDW modulation is unidirectional and primarily in-plane. TEM selected-area electron diffraction at $a = 4.5119(2)\,\text{\AA}$1 K shows superlattice spots along $a = 4.5119(2)\,\text{\AA}$2, with a modulation vector reported as $a = 4.5119(2)\,\text{\AA}$3 in the original structural study (Wu et al., 2019). Later diffraction and ARPES studies describe the same CDW as incommensurate, with $a = 4.5119(2)\,\text{\AA}$4 from high-resolution X-ray diffraction and $a = 4.5119(2)\,\text{\AA}$5 from ARPES shadow-band analysis (Lv et al., 2021, Zhang et al., 2022). A further transport and ARPES study quotes $a = 4.5119(2)\,\text{\AA}$6 from its own XRD between $a = 4.5119(2)\,\text{\AA}$7 and $a = 4.5119(2)\,\text{\AA}$8 K while also citing the earlier $a = 4.5119(2)\,\text{\AA}$9 value (Zhang et al., 2023). These differing notations suggest a convention-dependent description of the same near-threefold modulation along $b = 4.6347(2)\,\text{\AA}$0.

A major later development is the recognition that EuTe$b = 4.6347(2)\,\text{\AA}$1 exhibits an unconventional hysteretic transition entirely within the incommensurate CDW phase. Transport, photoemission, diffraction, and X-ray absorption show that the hysteresis loop has a temperature width of more than $b = 4.6347(2)\,\text{\AA}$2 K, that the CDW wavevector does not change within experimental uncertainty between $b = 4.6347(2)\,\text{\AA}$3 and $b = 4.6347(2)\,\text{\AA}$4 K, and that the phenomenon occurs with no change in CDW modulation periodicity (Lv et al., 2021). In that interpretation, EuTe$b = 4.6347(2)\,\text{\AA}$5 does not undergo a conventional lock-in or commensurate–incommensurate transition within the hysteretic window. Instead, the hysteresis is attributed to switching of the relative CDW phases in different layers, a mechanism described phenomenologically by

$b = 4.6347(2)\,\text{\AA}$6

where $b = 4.6347(2)\,\text{\AA}$7 is the relative CDW phase between layers.

Later structural and transport work extends the CDW hierarchy. A thermoelectric study reports at least two distinct CDW states: a high-temperature CDW-I with $b = 4.6347(2)\,\text{\AA}$8 and a low-temperature CDW-II with $b = 4.6347(2)\,\text{\AA}$9, with strong hysteresis in diffraction, resistivity, and Seebeck coefficient around $c = 15.6747(10)\,\text{\AA}$0 K (Takahashi et al., 22 Aug 2025). This later framework emphasizes not only a single low-temperature CDW transition but a broader landscape of competing and nearly degenerate CDW orders.

3. Electronic structure and the semiconducting CDW state

Density-functional calculations on the high-temperature structure show that EuTe$c = 15.6747(10)\,\text{\AA}$1 is metallic before CDW reconstruction, with strongly anisotropic quasi-two-dimensional bands. The states near the Fermi level are dominated by Te $c = 15.6747(10)\,\text{\AA}$2 and $c = 15.6747(10)\,\text{\AA}$3 orbitals from the Te sheets, whereas Eu $c = 15.6747(10)\,\text{\AA}$4 states are localized around $c = 15.6747(10)\,\text{\AA}$5 eV below $c = 15.6747(10)\,\text{\AA}$6 and do not substantially control the Fermi-surface topology (Wu et al., 2019). The calculated Fermi surface contains concave-square hole pockets around $c = 15.6747(10)\,\text{\AA}$7, spindle-shaped electron pockets around $c = 15.6747(10)\,\text{\AA}$8 and $c = 15.6747(10)\,\text{\AA}$9, and convex-square hole pockets near $c$0, and the static Lindhard response exhibits its largest peak near $c$1, in agreement with the observed CDW modulation.

When the experimentally determined low-temperature $c$2 structure is used in DFT, the density of states at the Fermi level is strongly reduced, from $c$3 states/(eV·formula unit) in the room-temperature structure to $c$4 states/(eV·f.u.) in the low-temperature structure within GGA and $c$5 states/(eV·f.u.) with HSE06, and the low-temperature structure is lower in total energy by about $c$6 meV per formula unit (Wu et al., 2019). This supports a nesting-driven lattice instability that gaps most of the Fermi surface and produces a narrow-gap semiconducting state.

Transport experiments track the same reconstruction. At $c$7 K, the in-plane resistivity is about $c$8, and below the CDW transition it follows activated behavior with an activation energy $c$9 meV from an Arrhenius fit (Wu et al., 2019). Hall measurements indicate $3.37$0-type conduction with carrier concentration decreasing from about $3.37$1 at $3.37$2 K to $3.37$3 at $3.37$4 K and mobilities of about $3.37$5 at $3.37$6 K and $3.37$7 at $3.37$8 K.

ARPES established that the CDW gap is fully open across the Fermi surface. A 2022 study reported that a Fermi-surface nesting vector $3.37$9 drives the CDW, that no spectral weight appears at $\text{\AA}$0 anywhere on the Fermi surface, and that the low-energy CDW gap $\text{\AA}$1 is strongly anisotropic, ranging from about $\text{\AA}$2 to $\text{\AA}$3 meV at $\text{\AA}$4 K and reaching about $\text{\AA}$5 meV at intermediate temperature (Zhang et al., 2022). The same work identified an extra, larger gap $\text{\AA}$6 at higher binding energy, up to about $\text{\AA}$7 meV, associated with interactions between different orbits of the main bands rather than a simple nesting gap.

A later ARPES study sharpened the anisotropy. It reports a global Fermi-level gap with no spectral weight at $\text{\AA}$8 anywhere in the Brillouin zone, a minimal low-lying gap of about $\text{\AA}$9 eV along $_4$0, and a maximal gap of about $_4$1 meV along $_4$2, as well as a higher-binding-energy hybridization-induced gap near $_4$3 to $_4$4 eV (Elius et al., 8 Aug 2025). This is a momentum-dependent CDW gap in the literal sense that the energy at which spectral weight reappears below $_4$5 depends strongly on in-plane direction.

EuTe$_4$6 is therefore unusual even within layered tellurides: it is one of the rare cases in which a quasi-two-dimensional, Te-net-based, Fermi-surface-reconstructed CDW yields a true semiconducting state rather than a bad metal or partially gapped metal. Later work, however, qualifies the microscopic explanation. Time- and angle-resolved photoemission argues that the semiconducting equilibrium state is not explained by perfect nesting alone and instead reflects the coexistence of two layer-dependent CDWs plus interlayer interactions (Lv et al., 2024). This reframes EuTe$_4$7 from a simple nesting-driven Peierls semiconductor to a more complex correlated CDW semiconductor.

4. Layer-dependent orders, metastability, and polar order

The most significant revision of the early picture is the demonstration that EuTe$_4$8 hosts two interacting CDW orders located on different Te sublayers. tr-ARPES identifies two distinct single-particle gaps in the CDW state along $_4$9–X, $_4$00 eV and $_4$01 eV, and assigns the larger gap to a Te bilayer CDW and the smaller gap to a Te monolayer CDW (Lv et al., 2024). After photoexcitation, these gaps exhibit dichotomous dynamics: the larger bilayer gap shows less renormalization and faster recovery, while the monolayer gap is more strongly renormalized and recovers more slowly. The same study attributes the semiconducting equilibrium state to interlayer interactions between these coexisting CDW orders and identifies additional momentum-dependent gap renormalization in the monolayer that cannot be captured by density-functional theory alone.

This layer dependence helps explain the extraordinary hysteresis of EuTe$_4$02. The unconventional hysteretic transition reported in 2021 lies entirely within the incommensurate CDW phase, does not change the CDW periodicity, and is interpreted as switching of the relative CDW phases in different layers (Lv et al., 2021). Resistivity, ARPES leading-edge gap, and CDW peak intensity all show large hysteresis, whereas the basic band topology and CDW wavevector remain unchanged. A later STM and transport study connected this behavior to CDW domains with different Te trimerization directions at the surface, proposing that three-dimensional stacking of distinct yet energetically close CDW domain configurations is important for the thermal hysteretic behavior (Zhang et al., 2023).

EuTe$_4$03 also became a polar-order material once the CDW stacking problem was viewed layer by layer. In the polar-order framework, the dominant atomic displacement associated with the CDW lies along the $_4$04-axis, each Te sheet carries a local polarization $_4$05 tied to CDW-induced Te-trimer formation, and the global state depends on how these local polarizations stack along $_4$06 (Liu et al., 2023). Angle-dependent second-harmonic generation identifies the CDW phase as non-centrosymmetric polar with point group $_4$07, with two independent in-plane tensor components, $_4$08 and $_4$09. The polarization is explicitly described as improper: it emerges as a secondary order parameter tied to the CDW distortion rather than as an independent ferroelectric instability.

Taken together, these results define EuTe$_4$10 as a stacked, layer-resolved CDW system in which amplitude, phase, and stacking are all active variables. A plausible implication is that the unusual breadth of the hysteresis and the existence of hidden states stem from this enlarged order-parameter space rather than from a single scalar CDW amplitude alone.

5. Magnetism, transport anomalies, and thermoelectric response

Magnetically, EuTe$_4$11 is a localized-moment Eu$_4$12 system. Magnetic susceptibility shows an antiferromagnetic transition at $_4$13 K in one study and $_4$14 K in another, with effective moments $_4$15 and $_4$16, both close to the Eu$_4$17 expectation (Wu et al., 2019, Elius et al., 8 Aug 2025). Heat-capacity measurements in field yield a magnetic phase boundary

$_4$18

with $_4$19 for field along $_4$20 (Elius et al., 8 Aug 2025). A thermoelectric study further reports strong in-plane magnetic anisotropy, a spin-flop transition for $_4$21 at about $_4$22 T, and saturation around $_4$23 T for that field orientation (Takahashi et al., 22 Aug 2025).

The low-temperature magnetotransport is striking. EuTe$_4$24 exhibits large negative magnetoresistance, with $_4$25 at $_4$26 K and fields above $_4$27 T for field along the $_4$28-axis (Zhang et al., 2023). That effect is associated with the canting of magnetically ordered Eu spins. By contrast, the broad thermal hysteresis in resistivity does not change under magnetic field up to $_4$29 T, which excludes a thermal magnetic hysteresis mechanism for the room-temperature-scale CDW hysteresis.

Thermoelectrically, EuTe$_4$30 is notable for a large Seebeck coefficient and exceptionally low thermal conductivity near and above room temperature. Single-crystal XRD, magnetic, and thermoelectric measurements show that the CDW-induced polar lattice distortion persists even at $_4$31 K, that the Seebeck coefficient near room temperature reaches values exceeding $_4$32, and that thermal conductivity near room temperature is as low as $_4$33, potentially reflecting the competition of two types of CDW states (Takahashi et al., 22 Aug 2025). More specifically, the reported Seebeck coefficients are about $_4$34 on heating and $_4$35 on cooling near $_4$36 K, remaining above $_4$37 over a substantial $_4$38–$_4$39 K range, while $_4$40 is about $_4$41 at $_4$42 K and roughly $_4$43 near room temperature and above.

The corresponding thermoelectric figure of merit reaches $_4$44 at $_4$45 K (Takahashi et al., 22 Aug 2025). The same study stresses that simple band calculations do not reproduce either the experimentally observed semiconducting gap or the magnitude of the Seebeck coefficient, and it discusses electron correlation, multiple Fermi pockets, spin/lattice instabilities, and possible phason drag as plausible contributors. This places EuTe$_4$46 at the intersection of CDW physics and correlated thermoelectric transport rather than within a conventional one-electron semiconductor framework.

6. Non-equilibrium control and broader significance

EuTe$_4$47 is unusual among CDW materials in that its metastable states can be manipulated non-thermally at room temperature. Ultrafast optical work showed that femtosecond laser pulses can write, erase, and rewrite non-volatile polar states at room temperature in a fully reversible all-optical manner (Liu et al., 2023). In that study, weak and strong fluence regimes are distinguished, with a critical fluence $_4$48 mJ/cm$_4$49. Depending on excitation history, the material can be driven into a high-resistance SHG-off state or into a low-resistance polar state with strongly enhanced $_4$50. The proposed mechanism is layer-specific phase inversion dynamics: monolayer and bilayer Te sheets, which have different CDW gaps and different melting thresholds, undergo selective CDW phase inversion, thereby changing the stacking of local polarizations without changing the in-plane CDW period.

Electrical control extends this metastability into device form. Micron-scale EuTe$_4$51 flakes contacted in four-probe geometry support electrically driven non-volatile resistance switching between CDW states from $_4$52 to $_4$53 K, including room temperature (Venturini et al., 2024). The switching is driven primarily by electric field, is fully reversible via a thermal erase procedure, and is fast and non-thermal. Threshold voltage is nearly temperature-independent, threshold current decreases strongly with decreasing temperature, and the final resistance is essentially independent of pulse duration from $_4$54 ns to $_4$55 s. For $_4$56 ns pulses at room temperature, the deposited energy is about $_4$57 pJ, with an estimated temperature rise of only $_4$58 K, and the switching completes on a sub-microsecond timescale, likely faster than the $_4$59 ns rise time of the circuit (Venturini et al., 2024). Because the resistance of the new electronic state is tuneable by pulse voltage, the device acts as a memristor.

These non-equilibrium results feed back into the equilibrium understanding of EuTe$_4$60. They imply a corrugated free-energy landscape with multiple metastable minima associated with distinct CDW stackings, layer-resolved phase configurations, or both. That picture is consistent with the giant thermal hysteresis, the coexistence of mono- and bilayer CDWs, the polar SHG response, and the ability to access hidden states that are thermodynamically inaccessible by slow heating and cooling.

EuTe$_4$61 is therefore significant not merely as a layered telluride with a CDW, but as a compact platform in which a fully gapped CDW semiconductor, interacting layer-dependent charge order, Eu$_4$62 magnetism, polar order, metastability, thermoelectric enhancement, and room-temperature non-volatile control all coexist. The literature increasingly treats it as a model system for studying how multiple electronic instabilities in quasi-two-dimensional Te networks can restructure both equilibrium and non-equilibrium states (Wu et al., 2019, Lv et al., 2024, Takahashi et al., 22 Aug 2025).