CsV3Sb5: Kagome Metal & Superconductor

• CsV3Sb5 is a kagome metal defined by a V kagome lattice that exhibits a density-wave transition at approximately 94 K along with nontrivial topological electronic states.
• Studies reveal its superconducting state is multiband and anisotropic, featuring orbital-selective pairing with both isotropic and highly anisotropic gap components.
• External tuning via pressure or chemical substitution sharply modulates the CDW and superconducting phases, highlighting the material’s sensitivity to control parameters.

CsV$_3$Sb$_5$ is a kagome metal and superconductor in which a V kagome lattice, a density-wave-like transition near $94\,\mathrm{K}$, low-temperature superconductivity near $2.8$–$3.5\,\mathrm{K}$ at ambient pressure, multiband electronic structure, and nontrivial topology are realized in the same material platform. Across transport, thermodynamic, spectroscopic, scattering, STM/STS, and first-principles studies, it has emerged as a canonical AV$_3$Sb$_5$ system for examining the interplay among charge order, orbital order, superconductivity, topology, phonons, and time-reversal-symmetry-breaking phenomena (Ni et al., 2021, Wang et al., 2021, Bhandari et al., 2024).

1. Crystal structure, band topology, and lattice instability

CsV$_3$Sb$_5$ crystallizes in the hexagonal space group $P6/mmm$, with V atoms arranged on a kagome net and a layered structure containing two Sb sublattices. DFT studies describe the pristine material as metallic, quasi-2D, and multiorbital, with several Dirac points near the Fermi level, van Hove singularities from V-$_5$0 orbitals near the $_5$1 point, and a quasi-2D cylindrical Fermi surface centered at $_5$2 that is derived from Sb-$_5$3 states (Bhandari et al., 2024, Naher et al., 2023). Spin-orbit coupling opens a narrow gap at Dirac points near $_5$4, while its effect on other bands is minor; in the same calculations, the $_5$5 invariant in both pristine and CDW phases is $_5$6, indicating a strong topological character (Bhandari et al., 2024).

The lattice sector is comparably nontrivial. In the pristine phase, phonon dispersion calculations show two negative modes at the $_5$7 and $_5$8 points, indicating lattice instability, whereas the distorted $_5$9 CDW phase has all positive phonon modes and is dynamically stable (Bhandari et al., 2024). A related first-principles study described pressure-dependent mechanical stability up to moderate pressure and a tendency toward structural instability around $94\,\mathrm{K}$0, while a separate high-pressure Raman and phonon analysis found no structural phase transition up to $94\,\mathrm{K}$1, underscoring that “stability” depends on which instability channel is being probed and over what pressure range (Naher et al., 2023, Chen et al., 2021).

The interlayer electronic structure is unusually sensitive to computational fidelity. A first-principles analysis of the $94\,\mathrm{K}$2 dispersion found that structurally faithful PBE+D3+SOC calculations can yield a symmetry-allowed band crossing between $94\,\mathrm{K}$3 and $94\,\mathrm{K}$4, but GW renormalization shifts the interlayer-character bands and removes that crossing (Watkins et al., 2023). This suggests that c-axis electronic structure, topological band bookkeeping, and any $94\,\mathrm{K}$5-dependent interpretation of CDW or superconducting phenomena require explicit control of vdW corrections, many-body renormalization, and irrep tracking.

2. Density-wave hierarchy, orbital order, and surface polarity

At ambient pressure, CsV$94\,\mathrm{K}$6Sb$94\,\mathrm{K}$7 shows a prominent density-wave-like transition at $94\,\mathrm{K}$8 or $94\,\mathrm{K}$9, depending on probe (Li et al., 2024, Song et al., 2021). STM/STS identified two charge orders: a $2.8$0 checkerboard superlattice and a $2.8$1 stripe superlattice on the Sb-terminated surface (Wang et al., 2021). Resonant tender x-ray scattering later established that the material hosts conjoined CDWs, specifically a $2.8$2 order at $2.8$3 and a $2.8$4 order at $2.8$5 (Li et al., 2022).

The hierarchy between orbital and charge sectors is a central theme. $2.8$6V and $2.8$7Cs NMR measurements found that the transition at $2.8$8 is first order and associated with orbital ordering: the $2.8$9V Knight shift splits suddenly at $3.5\,\mathrm{K}$0, while quadrupole splitting associated with CDW order appears only gradually below $3.5\,\mathrm{K}$1, with second-order-like behavior (Song et al., 2021). The same study concluded that the ordered state carries a $3.5\,\mathrm{K}$2 modulation and that remarkable magnetic fluctuations from V $3.5\,\mathrm{K}$3 orbitals above $3.5\,\mathrm{K}$4 are suppressed below $3.5\,\mathrm{K}$5 by orbital ordering (Song et al., 2021). In this formulation, the CDW is a secondary electronic order, whereas orbital order is primary.

The out-of-plane component of the CDW has a distinct orbital basis. At the Sb $3.5\,\mathrm{K}$6-edge, resonant enhancement is present at the $3.5\,\mathrm{K}$7 CDW wavevector but absent at the $3.5\,\mathrm{K}$8 wavevector, directly linking Sb $3.5\,\mathrm{K}$9 states to the 3D CDW component (Li et al., 2022). Under hydrostatic pressure, the two CDW onset temperatures separate, and at $_3$0 the $_3$1 CDW emerges $_3$2 above the $_3$3 CDW (Li et al., 2022). This establishes that the two modulations are conjoined at ambient pressure but can be decoupled by pressure.

Surface polarity further complicates the CDW phenomenology. Micro-focused ARPES resolved polar cleaved surfaces with Cs- and Sb-terminated regions that have markedly different fermiology (Kato et al., 2022). On the Cs-terminated surface, low-temperature spectra show doubling of V-derived bands and a CDW-gap opening consistent with 3D CDW-induced band folding. On the Sb-terminated surface, there is no band doubling and no CDW-gap opening, indicating suppression of the bulk-originated CDW by polar charge (Kato et al., 2022). Surface-sensitive superconducting and density-wave measurements in CsV$_3$4Sb$_3$5 therefore cannot be interpreted without explicit attention to termination-dependent self-doping.

3. Superconducting state, anisotropy, and multigap structure

Ambient-pressure superconductivity in CsV$_3$6Sb$_3$7 is strongly anisotropic and multiband. A systematic mixed-state study reported $_3$8, $_3$9, $_5$0, and an anisotropy ratio $_5$1, with the temperature dependence of $_5$2 requiring a minimum two-band effective model rather than a single-band WHH description (Ni et al., 2021). The same work found $_5$3, a two-gap fit to $_5$4, a London penetration depth $_5$5, and a two-stage superconducting evolution in which $_5$6 and the diamagnetic signal change little below $_5$7 before increasing abruptly below $_5$8 (Ni et al., 2021). In-plane angular-dependent magnetoresistance in the mixed state is two-fold, and below the same $_5$9 its orientation twists by $_3$0, matching the kagome geometry (Ni et al., 2021).

Direct momentum-space gap measurements established a pronounced orbital selectivity. Laser ARPES at $_3$1 resolved three principal Fermi-surface sheets: $_3$2 (central circular pocket, Sb $_3$3-dominated), $_3$4 (hexagonal pocket, mainly V $_3$5), and $_3$6 (outer triangular pocket, mixed V $_3$7 and Sb $_3$8) (Mine et al., 2024). The $_3$9 sheet shows a highly anisotropic superconducting gap with anisotropy over $_5$0, a gap maximum along the V–V bond direction ($_5$1-$_5$2), and a nearly nodal minimum along $_5$3-$_5$4. By contrast, the $_5$5 and $_5$6 sheets are isotropic and nodeless (Mine et al., 2024). This is the clearest experimental basis for the now-common description of superconductivity in pristine CsV$_5$7Sb$_5$8 as orbital-selective and strongly anisotropic.

Specific heat gives a complementary thermodynamic decomposition. In pristine CsV$_5$9Sb$P6/mmm$0, the electronic specific heat is fitted by an isotropic $P6/mmm$1-wave gap $P6/mmm$2 and a highly anisotropic extended $P6/mmm$3-wave gap $P6/mmm$4 with anisotropy parameter $P6/mmm$5; the corresponding ratios $P6/mmm$6 are $P6/mmm$7 and $P6/mmm$8, both smaller than the BCS weak-coupling limit of $P6/mmm$9 (Li et al., 2024). This thermodynamic result is consistent with the ARPES observation that one gap component is isotropic while another is highly anisotropic (Mine et al., 2024).

Microscopic theories currently split into at least two classes. SCDFT calculations attribute the two-gap state to orbital-selective EPC: a large, highly anisotropic gap with average magnitude $_5$00 on V-$_5$01-dominated Fermi surfaces and a small, isotropic gap $_5$02 on the Sb(1)-$_5$03 cylinder, together with EPC-induced kinks at approximately $_5$04 and $_5$05 (Lv et al., 24 Aug 2025). A distinct DFT+FLEX/RPA study instead found two competing pairing solutions, $_5$06 and $_5$07, with an Eliashberg spectral function purely due to electronic correlations and strongly peaked near $_5$08, and superconducting coupling constants in the range $_5$09–$_5$10 depending on the nearest-neighbor Coulomb interaction $_5$11 (Tian et al., 2024). The literature therefore contains both EPC-based and charge-fluctuation-based microscopic descriptions of the same anisotropic multigap phenomenology.

4. Pressure and chemical substitution as control parameters

Pressure strongly enhances superconductivity while weakening charge order. STM/STS and transport under hydrostatic pressure showed that the CDW state declines gradually with increasing pressure and that the superconducting transition temperature reaches $_5$12 at around $_5$13 (Wang et al., 2021). In the range $_5$14–$_5$15, the superconducting transition becomes broad, which was related to strong competition among the two CDW states and superconductivity (Wang et al., 2021).

At higher pressure, the phase diagram acquires a second superconducting dome. One in-situ high-pressure study reported an SC-I phase in which $_5$16 rises from $_5$17 to $_5$18 and is suppressed near $_5$19, followed by a reentrant SC-II phase emerging above $_5$20, peaking at $_5$21 at $_5$22, and persisting to $_5$23 (Chen et al., 2021). Raman and phonon calculations in that work found weakening of the $_5$24 mode and strengthening of the $_5$25 mode without structural phase transition as the system enters SC-II; electronic-structure calculations found enlarged Fermi surface, increased carrier density, and closing of the gap associated with the $_5$26 invariant above about $_5$27 (Chen et al., 2021). This places pressure-tuned superconductivity in a regime where CDW, topology, and EPC can all change concurrently.

Chemical substitution within the kagome plane produces equally large effects. Specific heat on Cs(V$_5$28Ta$_5$29)$_5$30Sb$_5$31 showed complete suppression of the CDW signature in specific heat and resistivity, an increase of $_5$32 from $_5$33 to $_5$34, and a jump of the Sommerfeld constant $_5$35 from $_5$36 to $_5$37 (Li et al., 2024). The superconducting state evolves simultaneously: the pristine material requires an $_5$38-wave plus highly anisotropic extended $_5$39-wave fit, whereas the Ta-doped compound is fitted by two isotropic $_5$40-wave gaps, $_5$41 and $_5$42, with $_5$43 and $_5$44, both indicating strong-coupling superconductivity (Li et al., 2024). The same work attributes this to increased DOS near the Fermi level released through suppression of the CDW gap.

Ti substitution reveals an orbital-selective route through the same phase space. Orbital-resolved QPI and DFT on CsV$_5$45Ti$_5$46Sb$_5$47 found that pristine CsV$_5$48Sb$_5$49 hosts unidirectional coherent states involving both in-plane and out-of-plane V $_5$50 orbitals, while the out-of-plane component disappears when Ti doping suppresses the CDW and global electronic nematicity (Huang et al., 5 Feb 2025). In the same study, the Sb $_5$51 orbital remained important in both the pseudogap and superconducting states, and the superconducting gap evolved from V-shaped in pristine material to U-shaped in Ti-doped samples (Huang et al., 5 Feb 2025). This suggests that kagome-plane substitution does not merely tune carrier count; it reorganizes the active orbital content of the low-energy states.

5. Vortices, intrinsic Josephson physics, and nonreciprocal transport

Vortex spectroscopy in CsV$_5$52Sb$_5$53-derived superconductors has exposed doping-tunable core phenomenology. Low-temperature STM/STS on Ta- and Ti-doped compounds found full-gap pairing superconductivity and the absence of long-range charge orders, in contrast to pristine CsV$_5$54Sb$_5$55 (Huang et al., 2024). Both doped systems show field-driven vortex-lattice reorientation, a hallmark of multiband superconductivity. In Ta-doped material, the vortex core hosts conventional Caroli–de Gennes–Matricon behavior with a broad ZBCP localized at the core center that rapidly splits into finite-energy peaks, giving the conventional cross-shaped or “X-type” spatial evolution (Huang et al., 2024). In Ti-doped material, the ZBCP is sharp, non-split, and persists over a long distance across the vortex, producing a “Y-type” evolution; the same study judged Fu–Kane Majorana scenarios unlikely and instead emphasized doping-dependent changes in $_5$56, $_5$57, and orbital character (Huang et al., 2024).

Recent nanoplate and microbridge experiments push CsV$_5$58Sb$_5$59 into an intrinsic Josephson regime. In nanoplates thicker than $_5$60, Fraunhofer-like $_5$61 patterns and Shapiro steps demonstrate both intrinsic dc and ac Josephson effects, with an effective junction area of roughly $_5$62, much smaller than the physical electrode area (Le et al., 22 Aug 2025). Thermal cycling modulates both the Fraunhofer pattern and the Shapiro spectra, and this was interpreted as evidence that the Josephson weak links are dynamic superconducting domain boundaries rather than fabricated tunnel barriers (Le et al., 22 Aug 2025). A pronounced asymmetry between positive and negative current directions was further taken as support for time-reversal-symmetry breaking and chiral order (Le et al., 22 Aug 2025).

Transport nonreciprocity has made the same domain physics macroscopically accessible. Zero-field nonreciprocal superconducting critical currents were observed in both flakes and micro-bridges, with the sign of the asymmetry changing randomly after repeated heating to $_5$63 and cooling into the superconducting state (Ge et al., 5 Jun 2025). Applying a perpendicular magnetic field at $_5$64, above the CDW transition, and then removing it before entering the superconducting state deterministically trains the asymmetry direction (Ge et al., 5 Jun 2025). This was interpreted as direct evidence that the CDW state above $_5$65 may also break the $_5$66 time-reversal symmetry and that its macroscopic directionality is inherited by the superconducting state (Ge et al., 5 Jun 2025).

Under rf irradiation, the intrinsic Josephson diode response becomes a quantum rectifier. In CsV$_5$67Sb$_5$68, a dc voltage appears without applied bias and scales linearly with frequency as $_5$69; with increasing rf power, the rectified voltage develops quantized Shapiro-step structure (Lou et al., 21 Aug 2025). Combined with the intrinsic Fraunhofer and Shapiro phenomenology, this places CsV$_5$70Sb$_5$71 among the few correlated superconductors in which spontaneous symmetry breaking, domain physics, Josephson dynamics, and rf rectification are all observed in a single material platform.

6. Phonons, transport coefficients, and competing microscopic pictures

Phonons are implicated not only in CDW formation but also in magnetic and transport anomalies. First-principles calculations identified “anomalous phonons” in both pristine and CDW phases, meaning phonon modes with circular or elliptical atomic motion and nonzero atomic polarization $_5$72 (Wang et al., 2024). In the CDW phase, lattice distortion amplifies these motions, especially on V atoms; for the CDW-phase $_5$73 mode 77 at the $_5$74 point, the frequency is about $_5$75 and $_5$76 (Wang et al., 2024). The calculated local magnetic field is of order $_5$77, and the phonon magnetic moment per V atom is of order $_5$78, leading that study to propose a lattice-based explanation for the local magnetic fields detected by $_5$79SR and for anomalous Hall phenomena without invoking static electronic moments (Wang et al., 2024).

Low-temperature transport presents a comparatively conventional normal-state baseline. A 2026 study of electric and thermal transport identified CsV$_5$80Sb$_5$81 as a metallic Fermi liquid with moderate correlations and strong electron-phonon collision cross section (Menil et al., 23 Feb 2026). The in-plane resistivity below about $_5$82 follows

$_5$83

with $_5$84, $_5$85, and $_5$86 (Menil et al., 23 Feb 2026). The Wiedemann–Franz law is satisfied in the zero-temperature limit, while downward deviation at finite temperature arises from the mismatch between electrical and thermal quadratic resistivities; within a Bloch–Grüneisen description, the inferred electron-phonon coupling constant is $_5$87 (Menil et al., 23 Feb 2026). This transport phenomenology is fully compatible with a strong e-ph channel.

The central microscopic debate is therefore not whether CsV$_5$88Sb$_5$89 is multiband or whether EPC exists; both are well established. The unresolved issue is how EPC, charge fluctuations, orbital selectivity, and density-wave competition are weighted in the pairing kernel. SCDFT attributes the two-gap structure to orbital-selective EPC tied to V–V bond-stretching, V–Sb bond-bending, and Cs shearing phonons (Lv et al., 24 Aug 2025). DFT+FLEX/RPA attributes the same superconducting scale to charge fluctuations peaked near $_5$90, with $_5$91 and $_5$92 pairing channels remaining closely competitive (Tian et al., 2024). Taken together with the doping and pressure results, this suggests that CsV$_5$93Sb$_5$94 is best viewed not as a single-mechanism superconductor, but as a kagome system in which the leading instability is acutely sensitive to how CDW reconstruction, orbital texture, DOS at $_5$95, and EPC are tuned.