Geometry-Induced Anisotropic Magnetoconductance (GAMC)

• Geometry-induced anisotropic magnetoconductance is a magnetotransport phenomenon where the device’s shape and structure modulate conductance through orbital coupling, mode matching, and interference effects.
• It involves diverse mechanisms such as finite-thickness interference, curved or corrugated surfaces, and quantum metric variations that convert field orientation into effective magnetic texture changes.
• Applications in quantum wells, topological insulators, and nanostructures provide insights into anisotropic responses, ballistic transport, and nonlinear magnetochiral rectification.

Searching arXiv for recent and foundational papers on geometry-induced anisotropic magnetoconductance and closely related magnetotransport mechanisms. Geometry-induced anisotropic magnetoconductance (GAMC) denotes a class of magnetotransport phenomena in which the dependence of conductance or resistance on magnetic-field direction, current direction, or magnetization orientation is controlled by geometry rather than by conventional spin-dependent scattering alone. In the literature surveyed here, the relevant “geometry” may be a corrugated quantum-well surface, an open curved nanostructure, a finite-thickness topological surface state, a symmetry-lowered tunnel barrier, a finite scattering region that supports Fabry–Pérot-like interference, a momentum-space mode-overlap constraint, or the quantum metric of Bloch states. The common feature is that geometry converts field orientation into a change in effective magnetic texture, available channels, interference conditions, or nonlinear response coefficients, thereby producing anisotropic magnetoconductance or magnetoresistance (Melnikov et al., 2017, Chang et al., 2014).

1. Conceptual scope and relation to adjacent magnetotransport effects

The GAMC label is best understood as an umbrella for several transport responses that are reported under different names in different subfields. Closely related papers use the language of anisotropic magnetoresistance (AMR), ballistic anisotropic magnetoresistance (BAMR), tunneling anisotropic magnetoresistance (TAMR), planar Hall effect (PHE), magnetochiral anisotropy (MCA), and electric magnetochiral anisotropy (eMChA). In these works, the anisotropy is traced not to a single universal microscopic mechanism but to geometry-dependent orbital coupling, geometry-controlled mode matching, finite wavefunction extent, symmetry lowering at interfaces, or quantum geometry in momentum space (Ominato et al., 2016, Nestoklon et al., 2012, Soori, 2021, Legg et al., 2021, Fontana et al., 13 Feb 2025).

Mechanism in the literature	Representative systems	Transport signature
Surface corrugation or finite thickness	SiGe/Si/SiGe quantum wells; Bi$_2$Se$_3$ thin films	OOP/IP anisotropic magnetoconductance or magnetoresistance
Curved or open real-space geometry	Rolled-up nanotubes; carbon nanoscrolls; bent nanoribbons	Field-direction-dependent channel count, positive magnetoconductance, BAMR/GAMC
Symmetry-lowered transmission geometry	Dirac–Weyl junctions; single-Mn tunnel diode; Rashba weak link	AMR-like conductance, TAMR-like transmission, AC-phase-sensitive anisotropy
Ballistic trajectory selection	Sinai billiards; rough graphene nanoribbons	Geometry-dependent transmission/reflection and magnetoconductance dips
Quantum-confined topological or quantum-geometric transport	QAH films; TI nanowires; tellurene	Giant AMR, MCA, eMChA, second-harmonic nonlinear response

A recurrent distinction in the cited papers is between conventional AMR and geometry-induced anisotropy. Conventional AMR is associated with spin-dependent scattering and spin-orbit interaction in ferromagnets, whereas several GAMC examples are explicitly described as orbital, geometric, or mode-overlap effects, or as finite-thickness interference effects that would not exist in an idealized strictly two-dimensional or symmetry-restored limit (Ominato et al., 2016, Chang et al., 2014, Melnikov et al., 2017).

2. Real-space geometry as an effective magnetic-field transformer

A canonical GAMC realization is the ultra-high mobility SiGe/Si/SiGe quantum well, where orientation-dependent in-plane-field magnetoresistance was traced to intrinsic ridges on the quantum-well surface (Melnikov et al., 2017). Atomic-force microscopy revealed a cross-hatched ridge pattern aligned along [110] and [-110], with period $\sim 10~\mu\text{m}$ and depth $\sim 50~\text{nm}$. Because the surface is corrugated rather than flat, an in-plane magnetic field $B_\parallel$ acquires a spatially varying local perpendicular component $B_\perp$. The 2D electron gas therefore experiences a geometry-induced orbital field in addition to the usual spin-polarization response. The anisotropy depends on the orientation of $I$ and $B_\parallel$ relative to the ridges: for $I \perp B_\parallel$, neighboring $B_\perp$-stripes act like narrow Hall bars and opposite Hall currents largely cancel in the longitudinal measurement; for $_3$0, the stripes are perpendicular to the current and the sample behaves more like a Corbino-like geometry, enhancing the resistance. The effect is strongest when current is parallel or perpendicular to the ridges, and it becomes essentially the same for $_3$1 and $_3$2 when the current is along [100], about $_3$3 to the ridge directions. The paper proposed the mapping

$_3$4

with $_3$5, and reported agreement between the recalculated and measured $_3$6 curves (Melnikov et al., 2017).

Rolled-up semiconductor nanoarchitectures provide a second archetype. In compact rolled-up nanotubes, the open curved geometry and hard-wall boundaries generate a magnetic spectrum containing quasi-1D Landau-like states, snake states, and edge/skipping states, and rotating the field changes how many subbands cross the Fermi level (Chang et al., 2014). The anisotropy is quantified as

$_3$7

with $_3$8 measured relative to the edge axis. A major result is the approximate scaling $_3$9 with winding number $\sim 10~\mu\text{m}$0, reflecting the growing weight of bulk-like magnetic subbands relative to edge states as the number of windings increases. The paper emphasized that this anisotropy is orbital and geometric, not spin-orbit-scattering-based, and stated that it can persist up to room temperature for realistic GaAs rolled-up structures (Chang et al., 2014).

A closely related but more recent bent-ribbon construction makes the geometric field conversion explicit. For a bent 2DEG nanoribbon, the left and right halves see effective fields

$\sim 10~\mu\text{m}$1

where $\sim 10~\mu\text{m}$2 is the external field, $\sim 10~\mu\text{m}$3 its orientation, and $\sim 10~\mu\text{m}$4 the bending angle (Liu et al., 21 Aug 2025). For $\sim 10~\mu\text{m}$5, one field orientation produces a uniform effective field, while the orthogonal orientation produces an effective magnetic dipole with opposite signs on the two halves. This selectively creates bulk cyclotron/Landau states, interface snake states, and edge skipping states, and the ballistic conductance $\sim 10~\mu\text{m}$6 therefore becomes strongly orientation dependent. The reported GAMC ratio

$\sim 10~\mu\text{m}$7

reaches about $\sim 10~\mu\text{m}$8 in a single-bend geometry, about $\sim 10~\mu\text{m}$9 in a twice-bent geometry, and about $\sim 50~\text{nm}$0 for a once-bent ribbon with $\sim 50~\text{nm}$1. The effect is reported to remain large at $\sim 50~\text{nm}$2 K, with approximately $\sim 50~\text{nm}$3, $\sim 50~\text{nm}$4, and $\sim 50~\text{nm}$5 for three example geometries, and to be observable even at weak fields, particularly in graphene (Liu et al., 21 Aug 2025).

Carbon nanoscrolls realize an allied curved-geometry mechanism, but with positive rather than suppressive magnetoconductance (Zhong et al., 2024). In a two-winding nanoscroll subject to an axial field, the field changes tangential quantization and creates additional zero-energy doublet modes at a half-integer flux quantum in the actual open-ended geometry. Because the zero-temperature conductance is $\sim 50~\text{nm}$6, the extra zero modes increase the mode count near charge neutrality, yielding a positive magnetoconductance coefficient

$\sim 50~\text{nm}$7

For a two-winding nanoscroll at about $\sim 50~\text{nm}$8 T, the reported low-density conductance is tripled, corresponding to a PMC of about $\sim 50~\text{nm}$9, and the effect persists under disorder or mild inter-turn misalignment (Zhong et al., 2024).

3. Geometry-controlled mode matching, symmetry lowering, and transmission anisotropy

In Dirac–Weyl magnetic junctions, GAMC appears as a momentum-space overlap effect rather than a real-space orbital-field conversion (Ominato et al., 2016). The device consists of doped Dirac semimetal leads and a ferromagnetic Weyl semimetal barrier of thickness $B_\parallel$0, with magnetization confined to the $B_\parallel$1-$B_\parallel$2 plane. Exchange shifts the Weyl Fermi surface in momentum space by $B_\parallel$3 in the projected $B_\parallel$4-$B_\parallel$5 plane, so the overlap between lead modes and barrier modes depends on the angle $B_\parallel$6 between magnetization and current. The total conductance is computed from the Landauer formula,

$B_\parallel$7

and for small shifts the paper derived the AMR-like form

$B_\parallel$8

The conductance is independent of $B_\parallel$9 at $B_\perp$0, minimal at $B_\perp$1, and periodic as $B_\perp$2. The paper stressed that this mechanism is completely different from conventional AMR, because it arises from geometric mode matching in projected $B_\perp$3-space, not from spin-dependent scattering (Ominato et al., 2016).

A localized, wavefunction-shape version of the same principle appears in the GaMnAs single-impurity tunnel diode (Nestoklon et al., 2012). There, the tunnel current is controlled by the spatial shape of a spin-orbit-coupled Mn acceptor wavefunction near an AlGaAs barrier. The transmission proxy is

$B_\perp$4

Rotating the Mn $B_\perp$5 spin changes the orbital character and spatial extent of the acceptor through $B_\perp$6-$B_\perp$7 exchange and strong spin-orbit coupling, while the barrier and reduced $B_\perp$8 symmetry convert that change into anisotropic leakage. For a Mn atom $B_\perp$9 monolayer from the barrier, the bound-state eigenenergy changes by almost $I$0 meV under out-of-plane rotation, the transmission is more than $I$1 lower for spin along [001], and the in-plane tunnel anisotropy is about $I$2, with [110] and $I$3 inequivalent (Nestoklon et al., 2012).

Finite scattering regions with spin-orbit coupling provide another transmission-based GAMC mechanism. In a 2DEG with SOC and an in-plane magnetic field applied only in a finite central region of length $I$4, the conductance becomes angle dependent because the finite geometry creates a scattering problem with Fabry–Pérot-like interference between multiple reflections inside the SOC+field region (Soori, 2021). The paper found that the longitudinal conductance $I$5 is $I$6-periodic and the transverse conductance $I$7 is $I$8-periodic in the field angle $I$9. The transverse oscillation amplitude is enhanced in patches of the $B_\parallel$0-plane, and $B_\parallel$1 can show one-fold, three-fold, five-fold, or seven-fold oscillations for large $B_\parallel$2 and $B_\parallel$3. A central conclusion was that SOC in a material is sufficient to observe PHE and anisotropic magnetoconductance without anisotropic magnetic ordering or nontrivial band topology (Soori, 2021).

The weak-link proposal based on the Aharonov–Casher phase isolates the role of geometric phase in an especially compact form (Shekhter et al., 2022). For a one-dimensional Rashba weak link of length $B_\parallel$4, the AC phase is $B_\parallel$5. At zero field it is hidden in a diagonal propagator and does not affect conductance, but a Zeeman field component perpendicular to the SOI pseudo-field mixes the spin channels and turns the phase into a measurable conductance anisotropy. In the ballistic regime the paper derived

$B_\parallel$6

making the anisotropy maximal at $B_\parallel$7 and $B_\parallel$8, and zero when $B_\parallel$9 or $I \perp B_\parallel$0. This establishes GAMC as a route to calibrating Rashba coupling through an angular magnetoconductance measurement rather than a ring-interference experiment (Shekhter et al., 2022).

4. Finite thickness, weak antilocalization, and topological transport channels

In Bi$I \perp B_\parallel$1Se$I \perp B_\parallel$2 thin films, GAMC is defined by the contrast between out-of-plane and in-plane magnetoconductance and is attributed to the finite penetration depth of topological surface states rather than to a generic crystallographic anisotropy (Sasmal et al., 2021). For an ideal strictly 2D state of zero thickness, an in-plane field would not thread flux through interference loops, but real topological surface states occupy a slab-like region of thickness $I \perp B_\parallel$3. The in-plane weak-antilocalization correction is modeled as

$I \perp B_\parallel$4

and the paper extracted $I \perp B_\parallel$5. The total anisotropy was analyzed by combining out-of-plane HLN-type WAL/WL terms with the in-plane finite-thickness term, while also subtracting electron-electron interaction corrections. The anisotropy $I \perp B_\parallel$6 shows a strong peak near $I \perp B_\parallel$7, and the fitted surface-channel prefactors were $I \perp B_\parallel$8 for c-Al$I \perp B_\parallel$9O$B_\perp$0/Bi$B_\perp$1Se$B_\perp$2 and $B_\perp$3 for SiO$B_\perp$4/Bi$B_\perp$5Se$B_\perp$6, consistent with stronger top-bottom decoupling in the more disordered SiO$B_\perp$7-grown films (Sasmal et al., 2021).

In InSb quantum wells, in-plane magnetoconductance mapping was used to extract anisotropic disorder and $B_\perp$8-factor parameters from the suppression of weak antilocalization (Mlack et al., 2019). Hall bars along $B_\perp$9 and $_3$00 were measured in a dilution refrigerator with a 4-1-1 vector magnet, and the in-plane response was found to track crystal direction rather than Hall-bar orientation. The in-plane suppression is predominantly Zeeman-driven, with disorder-induced orbital coupling as a secondary contribution. The best fit for one orientation yielded $_3$01 and $_3$02, implying $_3$03 for $_3$04. Averaged over angles, $_3$05, corresponding to $_3$06, while $_3$07 varies about $_3$08. These measurements show GAMC as a diagnostic of anisotropic electronic structure in a 2DEG with strong Zeeman response (Mlack et al., 2019).

A topological-channel version of giant anisotropy appears in the quantum anomalous Hall insulator based on an 8-quintuple-layer Cr-doped (Bi,Sb)$_3$09Te$_3$10 film (Kandala et al., 2015). When magnetization is out of plane, conduction proceeds through a single massless one-dimensional chiral edge state and $_3$11 is small; tilting the magnetization toward the plane reduces the magnetic gap, increases the edge-state penetration depth

$_3$12

and promotes intermixing with dissipative channels. The resulting AMR is modeled with a four-terminal Landauer–Büttiker form in which the edge transmission coefficient is

$_3$13

The anisotropic magnetoresistance ratio,

$_3$14

reaches approximately $_3$15 for device A, $_3$16 for device B, and $_3$17 for device C, whereas the purely in-plane AMR is only about $_3$18 and follows a conventional $_3$19 form. The giant out-of-plane anisotropy is therefore interpreted as a QAH edge-state to diffusive crossover rather than as ordinary ferromagnetic AMR (Kandala et al., 2015).

5. Ballistic trajectories, edge roughness, and geometry-selected orbit families

Sinai billiards make the trajectory-selection aspect of GAMC explicit. In normal and Andreev two-dimensional open cavities with a central antidot, particles move along magnetic-field-induced circular arcs, and the cavity geometry determines whether these arcs hit the antidot, the walls, or the leads (Fytas, 2020). For the normal case the conductance is

$_3$20

whereas in the Andreev case it is

$_3$21

The paper compared four geometries—square centered antidot, square displaced antidot, rectangular centered antidot, and circular centered antidot—and emphasized that the critical field $_3$22, above which the outgoing hole current vanishes in the Andreev case, depends only on geometry. The rectangular cavity gives the smallest $_3$23 and $_3$24, because the reduced vertical size increases electron reflection and hole transmission in ways that suppress conductance, while the circular cavity is exceptional in that $_3$25 for $_3$26. The general conclusion is that geometry selects the dominant orbit families—wall-bouncing trajectories, rosette-like orbits, or skipping orbits—and thereby shapes the magnetoconductance curve (Fytas, 2020).

Graphene nanoribbons with rough edges exhibit a different trajectory-selected signature: an edge roughness induced dip (ERID) in magnetoconductance when the cyclotron radius approaches the ribbon width (Xu et al., 2011). The conductance is computed from Landauer–Büttiker transport, $_3$27, with

$_3$28

For armchair ribbons of width $_3$29 and length $_3$30, the dip occurs at $_3$31, corresponding to $_3$32, and $_3$33 is nearly inversely proportional to the ribbon width. The anisotropy arises because armchair and zigzag edges couple very differently to roughness: armchair ribbons show a clear ERID, whereas zigzag ribbons require roughness amplitudes of about $_3$34 before the dip becomes visible. The microscopic explanation is that zigzag ribbons have strongly reduced current density within about $_3$35 from each edge, so edge roughness initially perturbs a region that carries little current. The dip survives only when bulk disorder is sufficiently weak (Xu et al., 2011).

These ballistic and semiclassical examples sharpen a common point: geometry-induced anisotropy need not mean a simple angular modulation of a uniform medium. It can also mean that geometry changes which orbit families are even available, and therefore changes the transmission/reflection partition itself. This suggests that GAMC is often most transparent in systems where channel counting or classical trajectory families can be identified directly (Fytas, 2020, Xu et al., 2011).

6. Nonlinear and quantum-geometric extensions

A nonlinear descendant of GAMC appears as giant magnetochiral anisotropy in topological-insulator nanowires (Legg et al., 2021). In thin bulk-insulating $_3$36 nanowires, a top gate artificially breaks inversion symmetry and splits quantum-confined topological surface-state subbands. A magnetic field then shifts these spin-polarized, strongly non-parabolic subbands, producing non-reciprocal transport described by

$_3$37

The paper reported $_3$38 in one device and values approaching $_3$39 across devices, and described this as the largest ever reported MCA rectification coefficient in a normal conductor. The angular dependence follows approximately $_3$40 for rotation in the $_3$41-plane and is essentially zero for rotation in the $_3$42-plane, consistent with the vector form $_3$43 (Legg et al., 2021).

Tellurene extends the geometry concept from real-space structure to Bloch-state geometry itself. In noncentrosymmetric polar media, the resistance is written as

$_3$44

where the eMChA coefficient $_3$45 is determined by the quantum metric dipole and the polarization $_3$46 (Fontana et al., 13 Feb 2025). The underlying semiclassical picture adds a geodesic correction built from Christoffel symbols of the quantum metric to the carrier velocity, and the normalized nonlinear coefficient obeys the predicted universal scaling $_3$47, verified by phase-sensitive second harmonic transport measurements on 2D tellurium films (Fontana et al., 13 Feb 2025).

The valence-band study of $_3$48-type tellurene generalized this result by showing that the nonlinear response is not purely chiral (Iacovelli et al., 14 Feb 2026). The paper distinguishes the chiral form

$_3$49

from the polar form

$_3$50

and argues that the valence band supports both, with $_3$51 and $_3$52. The key mechanism is multiband: an isolated low-energy valence block has finite quantum metric but vanishing metric dipole, whereas Löwdin downfolding from remote Weyl-node-containing bands generates nonzero Christoffel-symbol components and thus a finite polar coefficient $_3$53. The measured second-harmonic response $_3$54 and the shifted angular dependence $_3$55 are reproduced quantitatively by this mixed chiral-plus-polar picture (Iacovelli et al., 14 Feb 2026).

Taken together, these nonlinear studies suggest a broader interpretation of GAMC: the “geometry” responsible for anisotropic magnetoconductance need not be confined to device shape or boundary conditions. It can also be the geometry of wave functions in Hilbert space, encoded by subband curvature asymmetry, quantum confinement, or the quantum metric dipole. Across linear and nonlinear regimes, the recurring principle is the same: geometry converts field orientation into a transport anisotropy by controlling which states exist, how they interfere, and how effectively they couple to current (Legg et al., 2021, Fontana et al., 13 Feb 2025, Iacovelli et al., 14 Feb 2026).